Optimization of one or more anisotropic material properties of composite component

Abstract

The present disclosure relates to a method for optimizing anisotropic material properties of a composite part. The method includes providing a CAD model representing a component and including a feature tree having one or more CAD parameters each having an initial value. The at least one CAD parameter affects anisotropic material properties of the component. The method also includes providing an optimization procedure specified by one or more usage and / or manufacturing performance metrics including one or more objective functions and / or one or more constraints. The method further includes modifying the initial value of the one or more CAD parameters by solving the optimization program using a gradient-based optimization method. The optimization method takes one or more CAD parameters as free variables. The optimization method uses sensitivity. Each sensitivity is an approximation of a respective performance indicator relative to a respective derivative of a respective CAD parameter.

Description

Technical Field

[0001] The present disclosure relates to the field of computer programs and systems, and more particularly to methods, systems, and programs for optimizing one or more anisotropic material properties of composite components. Background Art

[0002] There are many hardware and software solutions for the design, engineering, and manufacturing of objects. CAD is an acronym for Computer-Aided Design, for example, it relates to software solutions for designing objects. CAE is an acronym for Computer-Aided Engineering, for example, it relates to software solutions for analyzing and simulating the physical behavior of future products. CAM is an acronym for Computer-Aided Manufacturing, for example, it relates to software solutions for defining the manufacturing process and resources of products. In such computer-aided design solutions, the graphical user interface plays an important role in terms of technical efficiency. These technologies can be embedded in Product Lifecycle Management (PLM) solutions. PLM refers to an engineering strategy under the concept of an extended enterprise, which helps enterprises share product data, apply common processes, and utilize enterprise knowledge to develop products from the conception of a product to the end of its product life cycle. The PLM solution provided by Dassault Systèmes (trademarks are CATIA, SIMULIA, DELMIA, and ENOVIA) provides an engineering center for organizing product engineering knowledge, a manufacturing center for managing manufacturing engineering knowledge, and an enterprise center that allows enterprises to integrate and connect to both the engineering center and the manufacturing center. All the solutions together deliver a common model that links products, processes, and resources to enable dynamic, knowledge-based product creation and decision support, thereby optimizing product definition, manufacturing preparation, production, and service.

[0003] In this context, there are CAD solutions for designing composite components. Such components typically have anisotropic material properties and / or are formed of anisotropic materials.

[0004] Anisotropic materials can be found anywhere from the simplest wooden table or plywood wall to the most advanced ultra-lightweight carbon fiber composite aerospace fuselage. An anisotropic material is a material that has one or more physical properties (such as stiffness, thermal conductivity) that depend on direction. Among these materials are orthotropic materials. An orthotropic material is an anisotropic material in which there are two mutually perpendicular planes of symmetry in the material properties.

[0005] Figure 1 An example of a composite part is shown, which is a table formed by an anisotropic wooden beam with fibers arranged along the beam length direction and an isotropic plastic hub with an isotropic void space as shown in the figure.

[0006] Figure 2 Another example of a composite part is shown, which is an aircraft wind turbine blade formed by an anisotropic conformal composite laminate around an isotropic foam core ( Figure 2 cross-sectional view of the blade shown in).

[0007] Before manufacturing, these objects are usually designed in CAD software. This allows for the definition of a parametric representation of the 3D part, including various properties regarding the position, orientation, and nature of the anisotropic materials (see Webinar Composites in 3DEXPERIENCE CATIA: https: / / youtu.be / omaMz_bnTEE).

[0008] For example, in the case of a wind turbine blade or an aircraft fuselage, CAE software can then be used to test / simulate / optimize this digital representation to verify or optimize its structural performance. Typically, such structural optimization is performed as multiple sequential optimizations, each of the multiple sequential optimizations acting on a subset of like variables, and where each optimization step requires a different representation of the object. For example, an initial topology optimization can be run, as discussed in MP, Sigmund O (2003) Topology optimization theory, methods, and applications, Springer, Berlin, using a density field with isotropic material properties to obtain a rough design idea and estimate. Then, the topology optimization design can be post-processed, as discussed in Olhoff N, MP, Rasmussen J. On CAD-integrated structural topology and design optimization. Comput Methods Appl Mech Eng. 1991;89(1), and subsequently fine-tuned using surface-based shape optimization, as in Olhoff N, Discussed in MP, Rasmussen J. On CAD-integrated structural topology and design optimization. Comput Methods Appl Mech Eng. 1991;89(1), Fallahpour M, Harbrecht H. Shape optimization for composite materials in linear elasticity. Optimization and Engineering. 2022;24(7), and Olhoff N, Rasmussen J, Lund E. A Method of "Exact" Numerical Differentiation for Error Elimination in Finite-Element-Based Semi-Analytical Shape Sensitivity Analyses. Mech. Struct. & Mach. 1993;21(1). Then, the shape based on surface optimization can be fixed. Then, as discussed in Bruyneel M, Fleury C. Composite structures optimization using sequential convex programming. Advances in Engineering Software. 2002;33 and Johansen L, Lund, E. Optimization of laminated composite structures using delamination criteria and hierarchical models. Struct Multidisc Optim. 2009;38, composite laminate patches are laid on the surface of the object and the angles of each lamina or patch are optimized. Then, the thickness (discussed in Pedersen P. On thickness and orientational design with orthotropic materials. Struct Optim. 1991;3) and angles of each laminate or sandwich patch can be optimized simultaneously, or the thickness of each laminate or sandwich patch can be optimized in another optimization step for thickness only (as in JH, Lund E. Structural gradient-based optimization of wind turbine blades with fixed outer geometry. Composite structures. 2018; 203) discussed). It can be found in JH, Lund E. Structural gradient-based optimization of wind turbine blades with fixed outer geometry. Composite structures. 2018; 203, Ghiasi H, Pasini D, Lessard L. Optimum stacking sequence design of composite materials Part I: Constant stiffness design. Composite Structures. 2009; 90(1) and Ghiasi H, Fayazbakhsh K, Pasini D, Lessard L. Optimum stacking sequence design of composite materials Part II: Variable stiffness design. 2010; 93(1) for an overview of both gradient-based methods (also known as sensitivity-based methods) and gradient-free methods for various previous optimization steps.

[0009] These optimization steps can each be robust and accurate, but the global result may be far from optimal because the set of parameters controlling the object shape and material properties is optimized using separate sequential steps. In other words, once material anisotropy is considered, the truly optimal topology or shape may become suboptimal.

[0010] Another issue is the lack of CAD representation when directly optimizing many low-level variables of material density and anisotropy throughout the design domain in an extended topology optimization framework (e.g., as discussed in https: / / www.researchgate.net / publication / 353194654_Large-Scale_Three-Dimensional_Anisotropic_Topol ogy_Optimization_of_Variable-Axial_Lightweight_Composite_Structures). These methods offer the maximum design freedom in the description of design variables used for optimization. Thus, in theory, they enable high-performance structural design. The drawback is that the final optimized structure may be difficult to reinterpret as a CAD model or may be non-manufacturable due to the complex shapes and material orientations present in the final optimized structure. This is shown in Figure 3 as shown Figure 3 a screenshot of the results obtained by this method is shown, with these complex shapes magnified.

[0011] Reference Gandhi Y, Minak GA. Review on Topology Optimization Strategies for Additively Manufactured Continuous Fiber-Reinforced Composite Structures. Appl. Sci. 2022;12 gives an additional overview of topology optimization methods including composite design variables. The following methods are the most common:

[0012] - Topology optimization using the so-called density method, which includes composite design variables and sensitivity calculations, is given, for example, in the references Xu Y, Zhu J, Wu Z, Cao Y, Zhao Y, Zhang W. A review on the design of laminated composite structures: constant and variable stiffness design and topology optimization. Adv Compos Hybrid Mater 2018; 1(3): 460, Hvejsel CF, Lund E. Material interpolation schemes for unified topology and multimaterial optimization. Struct Multidisc Optim 2011; 43(6), and Hozic D, Thore C, Cameron C, Sahbi Loukil M. A new method for simultaneous material and topology optimization of composite laminate structures using Hyperbolic Function Parametrization. Composite structures 2021; 276. The so-called topology optimization density method does not contain any CAD information, and the composite design variables are not coupled to the CAD description.

[0013] - References: Allaire G, Delgado G. Stacking sequence and shape optimization of laminated composite plates via a level-set method. J Mech Phys Solids 2016;97 and Yanan X, Yunkai G, Chi W, Jianguang F, Guangyong S, Grant P S, Qing L. Concurrent optimization of topological configuration and continuous fiber path for composite structures - A unified level set approach. Computer Methods in Applied Mechanics and Engineering 2022;399 also combine topological optimization and composite design variables, but apply the so-called level-set topology optimization. Similarly, none of these level-set topology optimization methods contain any CAD information. Additionally, the examples in these references do not use 3D continuum modeling required for general 3D coupling.

[0014] - The work in the references Smith H, Norato J. Topology optimization with discrete geometric components made of composite materials. Computer Methods in Applied Mechanics and Engineering. 2021; 376, Smith H, Norato J. Topology optimization of structures made of fiber-reinforced plates. Struct Multidisc Optim 2022; 65, and Greifenstein J, Letournel E, Stingl M, Wein F. Efficient spline design via feature-mapping for continuous fiber-reinforced structures. 2023; 66 applied the moving morphable component (MMC) method to optimize, respectively, strict rod structures, strict plate structures, and strict piecewise linear spline structures for orthotropic fiber-reinforced materials. Thus, these MMC methods for orthotropic fiber-reinforced materials do not disclose CAD descriptions, but only parametric descriptions of simple rod and beam members for design.

[0015] In this context, there is a need for improved methods for optimizing one or more anisotropic material properties of composite components. Summary of the Invention

[0016] Accordingly, a computer-implemented method for optimizing one or more anisotropic material properties of a composite component is proposed. The method includes providing a CAD model. The CAD model represents the composite component. The CAD model includes a feature tree having one or more CAD parameters. Each CAD parameter has an initial value. At least one CAD parameter affects one or more anisotropic material properties of the composite component. The method further includes providing an optimization program. The optimization program is specified by one or more use and / or manufacturing performance metrics. The one or more metrics include one or more objective functions and / or one or more constraints. The method further includes modifying the initial values of the one or more CAD parameters by solving the optimization program using a gradient-based optimization method. The optimization method takes the one or more CAD parameters as free variables. The optimization method uses sensitivities. Each sensitivity is an approximation of the corresponding derivative of the corresponding performance metric with respect to the corresponding CAD parameter. The sensitivities consist of:

[0017] - a respective derivative of each respective performance indicator with respect to an approximation of one or more material property fields, each of the one or more material property fields representing a distribution of an anisotropic material property of the one or more anisotropic material properties, and

[0018] - An approximate respective derivative of each of the one or more material property fields with respect to a respective CAD parameter.

[0019] The method may include one or more of the following:

[0020] - the CAD model is formed by one or more CAD components, each CAD component corresponds to a spatial region, and the method comprises: calculating one or more signed distance fields, each signed distance field corresponds to a respective CAD component, and for each given material property field of the one or more material property fields and each element of a mesh of the CAD model, each local material property value of the given material property field at the element of the mesh is obtained by a weighted combination of material property values ​​of the one or more CAD components, each value in the weighted combination being obtained by a projection of a signed distance between the element of the mesh and the respective CAD component;

[0021] - each weight corresponds to a projection of the signed distance value of the component by a function that maps [-∞; +∞] onto [0; 1] and has a well-defined first-order derivative, wherein, optionally, the function is a smoothed Heaviside projection;

[0022] - A weighted combination is a weighted sum;

[0023]

[0024] Among them, M ik is the mesh Ω of the CAD model mesh Ω of one or more properties at element i type The local material property value of property k in , j is the component, Ω comp is the set of all components, H ij is the weight, and m ijk is the material property of the component;

[0025]

[0026] where α ≥ 0 is the steepness coefficient of the smoothed Heaviside projection, where l is the average size of the elements in the grid, and SDF ij is the signed distance value from element i to component j;

[0027] - Each respective approximate derivative of one or more material property fields with respect to the respective CAD parameters is of the following type:

[0028]

[0029] where CAD p is the respective CAD parameter, where h p > 0 is a small perturbation, and where Ω param is a set of CAD parameters;

[0030] - Each sensitivity is of the following type:

[0031]

[0032] where Ω perfo is a set of performance metrics;

[0033] - One or more components are composed of a number of components;

[0034] - One or more anisotropic material properties are composed of a number of anisotropic material properties; and / or

[0035] - At least one CAD parameter affecting one or more anisotropic material properties of a composite part satisfies the constraints of the manufacturing process for manufacturing the composite part.

[0036] There is also provided a CAD model obtainable according to the method. Such a CAD model represents a composite part and includes a feature tree having one or more CAD parameters, at least one CAD parameter affecting one or more anisotropic material properties of the composite part. The CAD parameters have optimized values equal to the values produced by applying the method to the model. For example, the CAD parameters may have optimal values directly resulting from the optimization performed by the method, and the CAD model is thus the output of the method.

[0037] There is also provided a computer program including instructions for performing the method.

[0038] There is also provided a computer-readable data storage medium having recorded thereon the computer program and / or the CAD model.

[0039] There is also provided a computer system including a processor coupled to a memory having recorded thereon the computer program and / or the CAD model. Description of the Drawings

[0040] Non-limiting examples will now be described with reference to the drawings, where:

[0041] - Figures 1 to 15 shows the method; and

[0042] - Figure 16 illustrates an example of a computer system. DETAILED DESCRIPTION

[0043] A computer-implemented method for optimizing one or more anisotropic material properties of a composite part is provided. The method includes providing a CAD model. The CAD model represents the composite part. The CAD model includes a feature tree having one or more CAD parameters. Each CAD parameter has an initial value. At least one CAD parameter affects one or more anisotropic material properties of the composite part. The method further includes providing an optimization program. The optimization program is specified by one or more use and / or manufacturing performance metrics. The one or more metrics include one or more objective functions and / or one or more constraints. The method further includes modifying the initial values of the one or more CAD parameters by solving the optimization program using a gradient-based optimization method. The optimization method takes the one or more CAD parameters as free variables. The optimization method uses sensitivities. Each sensitivity is an approximation of the corresponding derivative of the corresponding performance metric with respect to the corresponding CAD parameter. The sensitivity consists of:

[0044] - the approximate corresponding derivative of each corresponding performance metric with respect to one or more material property fields, where each material property field in the one or more material property fields represents the distribution of an anisotropic material property among the one or more anisotropic material properties, and

[0045] - the approximate corresponding derivative of each of the one or more material property fields with respect to the corresponding CAD parameter.

[0046] The method constitutes an improved solution for optimizing one or more anisotropic material properties of a composite part.

[0047] The method optimizes one or more CAD parameters of a CAD model with respect to one or more performance metrics, at least one of which affects one or more anisotropic material properties of a composite part. In other words, this means that the method optimizes these one or more anisotropic material properties of the composite part by optimizing the CAD parameters that affect one or more anisotropic material properties to achieve an optimal value of one or more performance metrics. Thus, the method results in (i.e., outputs, e.g., as a CAD file) CAD models of composite parts having one or more anisotropic material properties (e.g., stiffness, thermal conductivity), which CAD models are optimized for the composite part to optimize the performance metrics, i.e., exhibit optimized performance with respect to these metrics. In other words, the method not only optimizes the shape of the part (since CAD parameters affect the shape), but also its anisotropic physical properties (e.g., fiber orientation), since at least one optimized CAD parameter affects the anisotropic physical properties. Each performance metric relates to the use of the part (e.g., response to a particular load during use, mass or stiffness) or the manufacture of the part (e.g., the metric captures constraints and / or tolerances of the manufacturing process or machine, and the part is optimized to meet those requirements). The method can include performance metrics for use (e.g., mass, stiffness, response to load) and performance metrics for manufacture (e.g., constraints on manufacturability for implementing the output model via a particular manufacturing process).

[0048] In addition, the method optimizes the CAD model of the composite part (i.e., optimizes the CAD parameters of the CAD model of the composite part). This means that the output of the model is an optimized CAD model, i.e., the values of the CAD parameters of the optimized CAD model are optimized with respect to the optimization problem processed by the method. Such a model can be directly used for manufacturing the composite part, i.e., represents a manufacturable object, and its CAD parameters allow the specification of the manufacturing process to be fully defined. The output optimized CAD model can be (e.g., in the form of a CAD file, or e.g., after conversion to a corresponding CAM (Computer-Aided Manufacturing) file) used, for example, directly to control and / or set its manufacturing process and / or machine / tool, as further discussed below. Thus, contrary to existing optimization methods (existing optimization methods work on CAE models (e.g., finite element meshes) and may result in optimized parts that are actually too complex to manufacture due to the degrees of freedom they provide for searching for optimal values in the optimization (notably, the optimized orientation of the physical properties of the material may actually be non-manufacturable)), the output of the method as a CAD model can be directly used as a file for controlling and / or setting the manufacturing process for manufacturing the optimized part corresponding to the CAD model. In addition, as described above, manufacturability can be implemented by having one or more performance metrics that implement one or more manufacturing constraints. Optionally, manufacturability can be implemented without using dedicated performance metrics (which may be infeasible for some manufacturing environments), but can be implemented by using appropriate CAD parameters in the model (which may or may not be part of the parameters optimized by the method). This further demonstrates the technical advantage of directly optimizing the CAD model: manufacturability is ensured and can be implemented by CAD parameters. For example, at least one CAD parameter that affects one or more anisotropic material properties of the composite part can satisfy (or capture) the constraints of the manufacturing process for manufacturing the composite part.

[0049] Therefore, the method aims at the physical and / or geometric optimization of 2D or 3D objects of anisotropic / composite / microstructured / fibrous materials modeled in CAD software. The key feature of these CAD models is that they can be geometrically designed precisely and unambiguously by chaining a small number of high-level heterogeneous parametric design operations (sketch, extrude, chamfer, loft volumers, shell offset, fillet, pocket, trim, emboss, transformation, multi-instantiation, assemblies, Boolean operation), and edited by modifying their high-level geometric numerical parameters. Note that this is the main difference compared to simpler polyhedral representations such as triangular surface meshes, which can represent most shapes but do not provide the modification or parametric capabilities required in the context of industrial design and manufacturing.

[0050] The proposed method addresses the following issues:

[0051] Handling a large number of design variables (thus traditionally excluding gradient-free methods);

[0052] Handling heterogeneous parameters directly present in the representation of CAD constructs;

[0053] Modeling both shape and anisotropic material properties in a single common representation;

[0054] Mapping between the high-level CAD parameters and the low-level local material behavior that models mechanical and physical properties.

[0055] As discussed below, the method can address the previously mentioned challenges by projecting the CAD model of a component containing an anisotropic representation onto a continuous Eulerian representation. Local properties such as density, orientation, or fiber fraction can be captured by scalar fields on a volume mesh. Then, finite element analysis simulates the physical behavior of these scalar fields and evaluates key performance indicators (KPIs). The mathematical derivatives of the simulation and projection steps are evaluated separately and combined using the chain rule to obtain the gradient of the physical performance KPIs with respect to the CAD parameters applied to iteratively optimize the model.

[0056] The proposed method and its implementation provide the following benefits:

[0057] It directly modifies the heterogeneous parameters defined in the CAD representation. Thus, there is no need for a CAD reinterpretation step for the optimization results. Additionally, it can ensure the retention of manufacturability properties in the original CAD model.

[0058] It can use an efficient iterative gradient-based optimization scheme. Thus, it allows for the efficient calculation to optimize many CAD parameters. Additionally, it also allows setting many constraints on various performance indicators (KPIs), where these constraints can be active or inactive during the iterative optimization iterations.

[0059] It simultaneously optimizes both the shape and material properties as a unified coupled problem and thus achieves better optimization than solving a series of multiple decoupled optimization sub-problems.

[0060] This method is used to optimize one or more anisotropic material properties of a composite part. Thus, this method outputs a design of a composite part with such optimized anisotropic material properties. Specifically, this method takes as input the CAD model of such a part with CAD parameters (where at least one CAD parameter affects one or more anisotropic material properties of the composite part) and modifies their values (thus, in particular, the values of the parameters that affect the anisotropic material properties) to achieve (e.g., reach a convergence criterion) the optimal value of the performance indicator. Thus, the output of this method is an optimized CAD model, i.e., a CAD model with these optimized values of the CAD parameters, where the CAD parameters include those that affect the anisotropic material properties.

[0061] Thus, this method forms a design step (specifically, an optimization step of the design process where the existing CAD parameters are optimized) and is thus used for designing a mechanical product / component, i.e., a composite part. "Designing a mechanical component / mechanical product" refers to any action or series of actions that are at least part of the process of creating a model (3D or 2D) of the mechanical component / mechanical product. This method is the optimization step in this process.

[0062] A composite part is a part formed in a composite material. A composite material is a material made from two or more constituent materials. These constituent materials have significantly different chemical or physical properties and are combined to produce a material with properties different from those of the individual elements. Within the finished structure, the individual elements remain separate and distinct, thus distinguishing the composite material from mixtures and solid solutions. A composite part has anisotropic material properties, i.e., the properties of the composite material are direction-dependent. The composite material can be an orthotropic material, in which there are three mutually orthogonal planes of symmetry in the material properties. One or more anisotropic material properties can consist of several anisotropic material properties. Each anisotropic material property can also be referred to as a "type of material anisotropic property" such that each property in one or more material anisotropic properties is a corresponding type of material anisotropic property.

[0063] The method includes providing a CAD model representing the composite part and an optimization program. The provided CAD model and optimization program thus form the input to the method. The provided CAD model can be referred to as the "input CAD model". The provided CAD model is a feature-based CAD model including a feature tree. The concept of a feature-based CAD model itself is known from CAD and is further discussed below. Similarly, the concept of a feature tree is known from CAD. A feature tree is a tree organization of CAD operations (e.g., including Boolean and non-Boolean operations) on CAD features, where each CAD feature models a part of the composite part. More specifically, a feature tree is a directed acyclic graph (as discussed at https: / / en.wikipedia.org / wiki / Directed_acyclic_graph, which is incorporated herein by reference) that describes / captures the order and combination of CAD operations. As known from CAD itself, CAD features include shape / geometric information and parameter information for representing a part of the composite part modeled / captured by the CAD feature. As is known, CAD features can include a definition / specification of the geometry / shape corresponding to the part modeled by the CAD feature (e.g., defining / specifying geometric primitives) and one or more CAD parameters specifying the geometry and its topology. The feature tree thus includes one or more CAD parameters, each CAD parameter corresponding to a respective CAD feature of the feature tree. Non-limiting examples of such CAD parameters include the thickness of a plate, the depth of a pocket, the angle of a fiber ply, the control points of a subdivided surface. One or more of these CAD parameters affect the anisotropic material properties of the composite part.

[0064] CAD parameters that affect the anisotropic material properties of a component are CAD parameters whose values, when changed, modify at least one (e.g., all such) anisotropic material property of the component. Non-limiting examples of such parameters include the angle of a fiber ply, or a CAD variable that controls the profile of a wind turbine blade (which affects the shape of the cross-section in a composite laminate and also affects the material orientation in the composite laminate, as these material orientations conform to the shape and follow its curvature), or any CAD parameter that affects the material orientation of a composite component.

[0065] The model can include at least one CAD parameter that affects one or more anisotropic material properties of a composite component and captures the constraints of the manufacturing process for fabricating the composite component. This allows for the optimization of the design for a specific manufacturing process. Optionally or additionally, such constraints can be captured by the constraints of an optimization program that implements manufacturing performance metrics, which also allows for the optimization of the design for a specific manufacturing process.

[0066] The CAD model can be a 2D CAD model (i.e., forming a 2D CAD representation of the composite component) or a 3D CAD model (i.e., forming a 3D CAD representation of the composite component). In addition to the feature tree, the CAD model can also include a 2D geometric representation (if the model is 2D) or a 3D geometric representation (if the model is 3D), such as a B-rep obtained by executing the feature tree. The geometric representation can be or include a geometric representation of the outer surface of the composite component. Providing the method can include providing a mesh (i.e., 2D or 3D) that includes the geometric representation (e.g., geometric representation of the outer surface) of the model.

[0067] The input CAD model can be derived from a previous design process (e.g., a previous design process executed on another system or software during another design phase, for example). Providing the CAD model can include downloading the CAD model from a memory or server on which the CAD model has been stored for further design of the CAD model. Optionally, providing the CAD model can include designing the CAD model. Designing the CAD model can include, for example, designing the CAD model from scratch on a CAD system by iteratively building the feature tree. Optionally, designing the CAD model can include designing a first CAE model (i.e., a finite element model) representing the composite component on a CAE system using any CAE software solution, and converting the CAE model to a CAD model using any CAD-to-CAE conversion method, and optionally then storing the CAD model in a memory or server. Providing the CAD model can also include, for example, downloading a designed CAE model from a memory or server on which the CAE model has been stored for further design of the CAE model, and then converting the CAE model to the input CAD model.

[0068] Providing the optimization program can include downloading the optimization program from any memory or server available to the program. Optionally, providing the optimization program can include launching any software that implements the program. Alternatively, providing the optimization program can include encoding / programming the optimization program or downloading (and optionally modifying) an already encoded / programmed optimization program.

[0069] The optimization program includes an optimization algorithm to solve an optimization problem. The optimization problem refers to a mathematical optimization problem, which includes optionally minimizing or maximizing one or more objective functions under one or more constraints, or minimizing or maximizing any other quantity under constraints. Thus, the optimization program is specified by one or more usage and / or manufacturing metrics including the objective function and / or constraints. The optimization program includes an optimization algorithm that performs such minimization or maximization. The optimization program can be designed such that data related to the optimization can be input by the user before starting the optimization program, and the data includes the objective function, constraints, any convergence threshold, and / or any maximum value for the iterative steps of the algorithm. The method can include the step of the user providing at least a part of such data before the optimization step. The optimization program can also be designed such that the user can select an optimization method to perform the optimization. The method can include the step of the user selecting an optimization method. The selection of the optimization method can be constrained to a predefined list of optimization methods, that is, the user can only select the methods within the list. The list can consist only of gradient-based optimization methods because the optimization method used by the method is a gradient-based optimization method. The concept of gradient-based optimization methods (also known as "gradient methods") is well known (see, for example, https: / / en.wikipedia.org / wiki / Gradient_method, which is incorporated herein by reference). The gradient-based optimization method used by the method can be any one of the following methods (which can form the previously discussed list for user selection): gradient descent, stochastic gradient descent, coordinate descent, Frank-Wolfe algorithm, Landweber iteration, random coordinate descent, conjugate gradient method, derivation of the conjugate gradient method, nonlinear conjugate gradient method, biconjugate gradient method, biconjugate gradient stabilized method, and method of moving asymptotes.

[0070] One or more use and / or manufacturing performance metrics are data that define the underlying optimization problem, i.e., the optimization problem is to optimize the performance of a composite part represented by a CAD model according to the said performance metric(s). In other words, the performance metric(s) is / are data (e.g., a mathematical expression, such as a mathematical function or a constraint (e.g., captured by an equation or a system of equations)), which measure the performance that the composite part to be represented by the CAD model is to achieve and / or follow after being manufactured. The performance is related to use and / or manufacturing, i.e., the performance is the physical performance (e.g., behavior) of the composite part during use and / or during manufacturing, since the metric(s) is / are use and / or manufacturing performance metric(s). The performance of the product during use is the physical behavior of the part with respect to a given use of the product, such as the thermal behavior of the part, the aerodynamic behavior of the part, or the structural behavior of the part, e.g., when the part is subjected to one or more loads (e.g., thermal, structural loads, or fluid flow). The performance of the part during manufacturing is the physical behavior of the part with respect to a given manufacturing process of the part, such as the compatibility of the part with the constraints of the manufacturing process and / or the specifications of the manufacturing tools for performing the process.

[0071] One or more performance metrics include one or more objective functions. An objective function herein is a function to be optimized such that its value is optimized (i.e., minimized or maximized). The objective function measures the performance of the part with respect to the use and / or manufacturing of the product, and this function has the CAD model or one or more CAD parameters as variables. When the performance requirements are met, the function outputs a larger value, in which case the function will be maximized, or when the performance requirements are met, the function outputs a smaller value, in which case the function will be minimized.

[0072] One or more metric performances can additionally or alternatively include one or more constraints. A constraint herein is a mathematical expression (e.g., an equation or a system of equations, or a fixed value of a parameter) to be complied with during optimization. The constraint captures the performance that the composite part is to satisfy (i.e., enforce), such as a specified total volume of the material of the product, or aspects of the tolerances of the manufacturing process or manufacturing tools. Optimization can optimize the objective function under the constraints, i.e., the optimization aims to find the variable values that optimize the objective function while satisfying the constraints.

[0073] Examples of mechanical design performance metrics (also known as KPIs) that the method may involve are: maximizing stiffness, minimizing mass, minimizing stress, maximizing heat transfer coefficient, optimizing eigenmodes.

[0074] The method can include: for example, at the step of providing an optimization program, e.g., by a user, e.g., selecting performance metrics from a list for optimization, which selection results in an objective function and / or constraints for optimization.

[0075] CAD parameter values can be represented as is a CAD parameter set. Performance metrics can be referred to as "key performance indicators", and their values can be expressed as where Ω perfo is a set of performance metrics.

[0076] In addition to providing the input, the method also includes modifying the initial values of one or more CAD parameters. The modification of the initial values of one or more CAD parameters can be referred to as the optimization of one or more CAD parameters. In fact, this step seeks or tends to seek the values of one or more CAD parameters that are free variables for optimization, and the values of the one or more CAD parameters optimize one or more objective functions and / or satisfy one or more constraints. Therefore, modifying the initial values includes solving the optimization of the optimization program, that is, running the optimization algorithm of the optimization program to solve the optimization of the underlying optimization problem.

[0077] As discussed previously, the optimization uses a gradient-based optimization method. This optimization method takes one or more CAD parameters as free variables, performs optimization by modifying the values of these parameters, and uses the sensitivity of the performance metrics with respect to these variables (i.e., derivative approximation) to perform optimization, because this method is gradient-based, as is known in the optimization field itself. In other words, the CAD parameters are the optimization free variables that the optimization method can modify (i.e., the optimization can modify the values of the CAD parameters) to optimize the performance metrics, and the sensitivity corresponds to the partial derivative of the metric to be optimized with respect to the free variables. It should be understood that when it is said that the values of one or more CAD parameters are modified by optimization, the values may not be modified for all CAD parameters. For example, some CAD parameters can have their values fixed, and other CAD parameters that include or consist of those parameters that affect the anisotropic material properties have values that are free variables for optimization. In this case, the method can include, before optimization, (e.g., by the user) selecting the CAD parameters whose values are free variables, and then keeping the values of other CAD parameters unchanged during optimization. Optionally, all values of all parameters can be free variables for optimization. The method can include: the step of calculating the sensitivity and / or performance metrics before updating the CAD parameters using the optimization method.

[0078] The sensitivity consists of:

[0079] The approximate corresponding derivative of each corresponding performance metric with respect to one or more material property fields, where each material property field in the one or more material property fields represents the distribution of the anisotropic material property among the one or more anisotropic material properties, and

[0080] The approximate corresponding derivative of each of the one or more material property fields with respect to the corresponding CAD parameter.

[0081] Each material property field corresponds to one of the material properties, i.e., there is a corresponding material property field for each respective material property. Each material property field is a scalar value (also referred to as a material property value) or a distribution of local material property values, and represents the distribution of the anisotropic material property (e.g., material orientation, thermal conductivity) corresponding to the field. For example, for material orientation, the local property value can be the local XY (2D) or XYZ (3D) coordinates of the material orientation. The distribution of the material property values is on a grid (2D or 3D grid) of a space (2D or 3D) including a geometric (e.g., outer surface) representation of the composite component. The grid can be, for example, a grid of volume or surface elements (e.g., the elements are tetrahedra / triangles, hexahedra, or regular cubes / squares). For each material property field, each property value corresponds to a respective element of the grid and indicates the value of the property at that element. Each value of a given material property at each element of the grid can be referred to as a local material property value (i.e., the local material property value of the given material property) as it is related to the value of the material property at that element.

[0082] In an embodiment using a fibrous material (such as the use cases discussed below), the local property field M is encoded such that each element has 4 values (corresponding to 4 material anisotropic properties or property types): 1 value represents the material density, 2 values represent the rotation angles of the fiber orientation in 3D, and 1 value represents the ratio of the fibers (i.e., the ratio of anisotropic fibers to isotropic material, where the isotropic material often simulates the bonding "glue" or "matrix" of the manufactured fibers).

[0083] A CAD model can be formed by one or more CAD components. Each CAD component corresponds to a spatial region, i.e., forms a part of the CAD model. In this case, the method includes calculating one or more signed distance fields, each signed distance field corresponding to a CAD component. For each material property field, each local material property value of the field is derived from a weighted combination of the material properties of the components of the CAD model, where the material properties of the components of the CAD model are weighted by their signed distance to the local material property value. One or more components can consist of several components.

[0084] Each signed distance field corresponds to a CAD component. The concept of a signed distance field is known. A signed distance field is a distribution of signed distances with respect to a particular geometry. In this case, each signed distance field corresponds to a component and forms a distribution of signed distance values, each signed distance value corresponding to an element of the mesh and representing the signed distance between that element and the CAD component (or its geometric representation on the mesh, such as an outer surface representation). In other words, the signed distance field corresponding to a component is a distribution of signed distance values to the component on the mesh, the mesh including a geometric (e.g., outer surface) representation of the component (which may be part of the geometric representation of an entire composite part). Each signed distance value in the distribution corresponds to an element of the mesh and indicates the value of the distance (e.g., Euclidean distance, Manhattan distance, pixel distance) from that element to the (e.g., outer surface) representation of the component, the value having one sign when the element corresponds to an inner part of the component and having the opposite sign when the element corresponds to an outer part of the component.

[0085] Each local material property value of the field is derived from a weighted combination of the material properties of the components of the CAD model, the material properties of the components of the CAD model being weighted by their signed distance to the local material property value. For example, for each local material property and for each element of the mesh, the local material property value at that element is equal to a weighted combination of the material property values of the components, each material property value of a component being weighted by the signed distance between the element and that component, or being weighted by a projection of such a distance as described below. The weighted combination may be a weighted sum.

[0086] The method may include, for example, calculating the signed distance field and the material property field before updating the CAD parameters using an optimization method, as discussed further below. This projects the CAD model representation (i.e., on the mesh) into a set of scalar fields that encode the local material properties for each element of the mesh. As is known, the CAD model includes a geometric boundary representation on the mesh, which means that it defines a solid object, such as solid / void, steel, wood, plastic, concrete, carbon fiber laminate, air, void, by hierarchically separating space into regions or components with different material properties (see again Figure 1 and Figure 2 ). This projection defines the local material property of each volume element in the mesh as a measure of the material properties of nearby components weighted by a non-linear distance metric (signed distance). For example, referring to Figure 2In the use case shown, through this process, the elements in the foam core assembly will receive low stiffness isotropic material properties. Similarly, the elements at the interface between the composite laminate and the foam core assembly will receive a mixture of low stiffness isotropic material properties and high stiffness anisotropic material properties aligned with the local orientation of the composite laminate. Mathematically, as is known in the art, by calculating the projection of the tessellated representation of the CAD model onto the elements of the mesh Ω mesh of the component Ω comp to obtain this projection by the linear signed distance field (SDF) (see https: / / www2.imm.dtu.dk / pubdb / edoc / imm1289.pdf, which is incorporated herein by reference):

[0087]

[0088] where i represents the elements of the mesh Ω mesh of the CAD model, and j represents a component in the set of components Ω comp , and SDF ij (CAD) represents the signed distance field value between element i and component j.

[0089] Each weight can correspond to (e.g., be equal to) the projection of the signed distance value of the component by a function that maps [-∞; +∞] to [0; 1] and has a well-defined first derivative. This function can be a smooth non-linear Heaviside projection. The smooth non-linear Heaviside function controls the smearing of the material properties (see https: / / en.wikipedia.org / wiki / Heaviside_step_function, which is incorporated herein by reference). Any positive monotonic smooth approximation of the Heaviside function can replace the Heaviside function for this smearing step. The weight H ij can be given by the following formula (using the smooth non-linear Heaviside):

[0090]

[0091] where l is the size of the mesh element, and α is the desired smearing distance, which can be equal to 2 in implementation.

[0092] For each material property type k ∈ Ω type (e.g., material density, fiber azimuth angle, fiber elevation angle, fiber / adhesive ratio, fiber stiffness, adhesive hardness), the local material property value for each element i can be given by the following formula:

[0093]

[0094] where M ik is the local material property value at element i of property type k for the CAD model in mesh Ω mesh and j is a component, and Ω comp is the set of all components, H ij is the weight, and m ijk is the material property of the component.

[0095] Note that above, m ijk depends on i (the index of the element) because such a dependence can exist in physical reality. For example, if component j is a composite sheet glued to the surface of a part, the fiber angle in the composite varies in space within the component (which follows the tangent of the surface), so it actually depends on i. In other words, within component j, property k can vary from element i to another element.

[0096] A different function of the local property M ij can alternatively be used as the Heaviside function H ik Optionally, if the directly determined local properties exceed their feasible physical ranges, the above formula can be modified to impose bounds or additional scaling on the local properties.

[0097] In implementations using fibrous materials (such as the use cases discussed below), the local property field M is encoded such that each element has 4 values (i.e., k = 1...4): 1 value represents the material density, 2 values represent the rotation angles of the fiber orientation in 3D, and 1 value represents the ratio of the fibers (i.e., the ratio of anisotropic fibers to isotropic material, where the isotropic material often models the adhesive "glue" or "matrix" that makes the fibers). However, depending on the type and characteristics of the anisotropy employed, each element can use a single, several, or more values. Alternative implementations can use many values because there are multiple independent coefficients in the molding materials under consideration: (see https: / / pkel015.connect.amazon.auckland.ac.nz / SolidMechanicsBooks / Part_I / BookSM_Part_I / 06_LinearEl asticity / 06_Linear_Elasticity_03_Anisotropy.pdf, which is incorporated herein by reference).

[0098] As previously mentioned, the calculation of the signed distance field and the material property field, e.g., by calculating M i and Hij The above formula can constitute a step of the method, which is performed before modifying the value of the CAD parameter to iteratively modify the CAD model in an optimization loop until a certain convergence criterion, number of optimization iterations, running time, and / or KPI score is reached. The calculation steps of these fields can be referred to as "projection". Figure 4 The flowchart shows an implementation of the method, or more specifically, the flowchart of the steps after the step of providing the input. Figure 4 The flowchart shows the projection step, which is the first step in the flowchart.

[0099] In addition to the projection / calculation of the fields and still before the update of the value of the CAD parameter, the method may include the step of calculating a performance indicator (also referred to as the KPI as described above), which can be referred to as "simulation (or emulation)" (shown by Figure 4 the second step in the flowchart of). The method can calculate some KPIs, such as the mass of the component, by summing the values of these KPIs for each element of a given partition of the component (e.g., the mass of each element of a given partition or the entire structure). Other KPIs are more complex to calculate, and the method can calculate them by using finite element modeling known in the art to simulate the behavior of composite components. For example, calculating the deformation of a component under a load scenario may involve assembling the local stiffness matrix of each element into the global stiffness matrix K of the entire mesh and then solving the original solution of the equilibrium given by the state equation:

[0100] Ku = f

[0101] where f is the known nodal force vector and u is the unknown nodal displacement vector. The method can use an appropriate simulation method to perform this calculation. Therefore, calculating the KPI uses known methods, whether direct analytical calculation or simulation, and thus does not require further discussion.

[0102] The optimization of modifying the value of the CAD parameter uses sensitivity. Therefore, the method can calculate the sensitivity before updating the value of the CAD parameter, as described above, and the sensitivity is an approximation of the derivative.

[0103] The method can, for example, include the step of determining an approximation of the derivative of the KPI with respect to the value of the local property of each element after the simulation step but before the update of the CAD parameter:

[0104]

[0105] This can be done by using known methods.

[0106] For example, for the stiffness KPI, elements in an isotropic component will have orientation derivative values that are practically equal to zero. Thus, the fact that exposing the local angle of this element has no effect on the deformation of the structure, since this particular element is isotropic. Note that the derivative will not be exactly zero, because a strictly positive monotonic smoothed Heaviside function is specifically used in the projection step. In contrast, the local angle of an element in a composite laminated region of the structure may have a strong influence on the deformation of the structure for a given loading scenario, which will manifest as a large derivative value.

[0107] When using a continuous field representation of a component, these derivatives can be efficiently computed by using a method such as the adjoint method described in https: / / www.researchgate.net / publication / 342871596_Structural_topology_optimization_with_smoothly_varying_fiber_orientations (incorporated herein by reference). Using the adjoint method contributes to the computational performance of the methods disclosed in this disclosure. The reason is that, for the adjoint method, the number of calls to solve computationally expensive linear systems is proportional to the size of Ω perfo (which is typically less than 10), rather than being proportional to the size of Ω mesh (which is typically greater than 100000). The computation of the approximation of the derivative can be referred to as the step of computing the physical derivative, as shown in Figure 4 step 3 above.

[0108] The method may further include determining the derivative ik of the property field M p with respect to the CAD parameter CAD still after the simulation step but before updating the CAD parameters:

[0109]

[0110] These derivatives capture how each CAD parameter affects the local properties of each element in the mesh. This step enables the coupled optimization of CAD parameters that control both the shape and the local material properties of the composite component.

[0111] For example, a CAD variable that controls the profile of a wind turbine blade will affect the shape of the cross-section but also the material orientation in the composite laminate, since these material orientations are conformal to the shape and follow its curvature. Finite difference methods can be used to evaluate these derivatives. This is done by applying a small perturbation h pIt is achieved by sequentially applying to each CAD parameter and observing the effect on the material property value, as follows:

[0112]

[0113] where CAD p is the corresponding CAD parameter, where h p > 0 is a small perturbation, and where Ω param is the set of CAD parameters.

[0114] The above formula uses the central finite difference scheme, but the forward finite difference scheme or the backward finite difference scheme can also be used. The finite difference approximation is very stable and reliable for this purpose. This is explained by the fact that each CAD parameter usually affects the values of many grid elements, because for practical and industrial applications, Ω param << Ω mesh . Therefore, when aggregating the contributions of multiple elements to the CAD parameter, the numerical inaccuracies of the finite difference approximation will be canceled out. Note that the analytical derivatives of the CAD system are intractable for any significant CAD model, so it is beneficial to use approximations of the derivatives.

[0115] Derivative The calculation of the approximation can be referred to as the step of calculating the geometric derivative, as shown in step 4 of Figure 4 .

[0116] Once the geometric and physical derivatives are calculated, they can be combined using the chain rule. In other words, each sensitivity is of the following type:

[0117]

[0118] where Ω perfo is the set of performance metrics.

[0119] The method can then perform optimization using gradient-based optimization methods (e.g., first-order gradient-based optimization schemes such as gradient descent, moving asymptotes method, augmented Lagrangian, Adam, LBFGS) to modify (update) the values of the CAD parameters so as to tend to reach the optimal value of the KPI, as is known in the art. This can be referred to as "parameter update", as shown at step 5 of Figure 4 .

[0120] Steps 1 to 5 can be iterated (refer to Figure 4), i.e., the calculation of the field (projection step), the calculation of the KPIs (simulation step), the calculation of the approximation of the derivative (geometry and physics), and the update of the CAD parameters, where the CAD parameters resulting from the update (step 5) are used as the input for the projection step (step 1) of the next iteration. In other words, the method can include the step of providing an input and then the step of modifying the value of the CAD parameters by applying a gradient-based optimization method, and the step of modifying the value of the CAD parameters by applying a gradient-based optimization method can include the iteration of steps 1 to 5, where the optimization method is used in step 5 to update the parameters based on the sensitivities calculated as a result of the previous steps 1 - 4. This is shown in Figure 4 As a result of using gradient-based optimization, this iterative process can converge in 10 to 100 iterations.

[0121] The method outputs a CAD model and the values of its CAD parameters are optimized. The method can include further steps: storing the CAD model (e.g., as a CAD file) and / or inferring (by any known method) a CAM file from the CAD model / CAD file, and, for example, storing the CAM file, where the CAM file is used as control instructions for setting up and / or executing a manufacturing process to manufacture a composite part. The method can include sending such control instructions to a factory and / or executing the manufacturing process, in the latter case, the method being used to design and manufacture an optimized composite part. Alternatively, the method can be included in such a manufacturing process, but may not include the manufacturing step, although manufacturing is an implicit use of the output of the method.

[0122] Now, use cases of the method are discussed. These use cases illustrate the above advantages of the proposed method.

[0123] First use case: L-shaped bracket optimization

[0124] This use case significantly shows the importance of considering both shape and anisotropic material properties simultaneously in a coupled optimization formulation.

[0125] The CAD model provided in this use case represents Figure 5The L-shaped bracket shown. The bracket is fixed at the upper left and loaded downward on the right side of the middle. The CAD model includes 20 CAD parameters that control the shape of the bracket and consists of 10 sketch control points in 2D. The bracket is made of an isotropic core wrapped by a layer of surface-conformal anisotropic fibers. The anisotropic properties of one or more of the materials here include the density property of the foam core and the angular property of the orientation of the fibers, which depend on the shape of the bracket and are thus affected by the CAD parameters that control the shape. One or more of the CAD components here include one component for the foam core and one component for the conformal fiber layer of constant thickness around the foam core. One or more use and / or manufacturing performance metrics include stiffness and mass, where stiffness is a use performance indicator and will be maximized, and mass is a use performance indicator and will be minimized. The optimization program includes specifying the objective functions for these two metrics, as the objective functions formulate the weighting between maximizing stiffness and minimizing mass. The stiffness of the anisotropic material fibers in the fiber direction is 25 times that of the other directions of the anisotropic material or the isotropic core. Optimizing the material orientation by optimizing the control points thus allows for optimizing the stiffness. Note that the fiber orientation is constrained in the plane of this 2D example. Additionally, the fibers are conformal to the surface of the object, which means their orientation is completely determined by the shape of the outer contour of the object.

[0126] Figure 6 An optimization model is shown that uses an optimization method other than the method of the present disclosure, where this other method ignores the derivative of material anisotropy in the chain rule. Figure 7 An optimization model is shown that uses the proposed disclosed method, where the optimization thus includes the derivative of material anisotropy that produces consistent derivatives. Other than the difference in the use of derivatives, the two optimization setups are the same. In the figures, the short segments covering the object surface show the fiber orientation (the gray shading is set directly by the XYZ components of the orientation vector).

[0127] It is obvious from the figures that when the derivative of material anisotropy in the chain rule in the optimization is ignored, the optimization result produces sharp concave corners relative to the boundary of the design domain, which is a typical optimization result when optimizing stiffness using a strictly isotropic material. However, this design is far from optimal for anisotropic materials, because the sharp concave corners produced by the conformal fibers thus strongly reduce their load-bearing capacity (concavity concentrates stress, while convexity disperses stress, so convex corners are not a problem). The optimization results obtained by this method show that the consistent derivative of anisotropy captures the non-optimality of the sharp concave corners and thus guides the optimization to produce an optimized CAD model with a smoother and more continuous fiber orientation around the concave corners. In other words, a novel and improved bracket design with increased load-bearing capacity is obtained by using the claimed method, thus allowing for the manufacture of such a novel and improved component based on the CAD model output by this method.

[0128] The claimed method ensures that the optimized part consists of a foam core surrounded by a layer of fibrous material with a constant thickness and a globally conformal angle tangent to the surface of the part. Thus, in an industrial context, this type of design is typically manufactured by machining one or more foam blocks on a CNC (Computer Numerical Control) machine according to the shape of the foam core assembly. Fibrous material sheets (such as fiberglass or carbon fiber) are then glued around the foam core to obtain a lightweight, strong, and inexpensive production object. The method may include storing the optimized method as a file of control instructions (e.g., a CAM file) for performing such a manufacturing process and / or performing the machining process, which includes CNC machining and then gluing. Note that for explanatory purposes, this use case is discussed in 2D, but in reality, the bracket has a thickness and is a 3D object and is manufactured in 3D.

[0129] This comparative example highlights the advantages of the method, as it allows for mathematically and consistently including important material interactions of the physical model and tracing these interactions back to CAD parameters. In this case, the CAD parameters affect the shape of the outer contour, which affects the orientation and curvature of the conformal laminate sheet. These CAD parameters then affect the local fiber orientation, which ultimately affects the load-bearing capacity and overall mechanical properties of the object.

[0130] Second use case: 3D wind turbine blade optimization

[0131] The second use case relates to the optimization of 3D wind turbine blade optimization. Figure 8 A cross-section of a 3D wind turbine blade is shown. The CAD model of the 3D wind turbine is defined by an outer contour and an internal reinforcement structure. The outer contour has an externally predetermined shape obtained from hydrodynamic considerations, and the internal reinforcement structure will be the subject of optimization considering multiple load cases (torsion and bending). As Figure 8 shown, the material forming the blade consists of a composite sandwich structure having a soft lightweight foam core in the middle of the sandwich between two outer anisotropic fiberglass sheets. It is worth noting that the actual industrial model will have a stack of many different oriented laminates for each sheet. However, for visualization, each sheet in this optimization result has one fiber orientation. This is achieved without loss of generality because the method can capture the homogenized properties of one or more oriented laminates for the anisotropic constitutive law of each element. The initial design (i.e., the CAD model with the initial values of the CAD parameters) is in Figure 9As shown, and having anisotropic and isotropic regions. The fiber orientation is visualized as the short segments of the anisotropic regions (the gray shading is shown as the XYZ components of the orientation vectors).

[0132] The CAD parameters to be optimized are as follows. First, a set of CAD parameters sets the fiber orientation of the outer sheet, and this set of CAD parameters includes 4 angles to be optimized. In addition, the shapes of the 3 inner sheets are controlled by a set of 22 geometric CAD parameters. These 26 selected CAD parameters allow for the optimization of the foam core thickness, the shear web shape, and the fiber orientation throughout the model, which results in one or more anisotropic material properties. Note that this type of composite structure is manufactured by placing foam blocks of different thicknesses and then unfolding and gluing laminate sheets on the surfaces. Therefore, the sheet shapes must be developable surfaces (i.e., zero Gaussian curvature), and the fiber orientation must be globally conformal to the surface in order to be usable in this manufacturing method. This type of geometric manufacturing constraint is extremely challenging to implement in topology optimization, but is relatively easy when optimizing using the CAD representation enabled by the present method. One or more of the CAD components here include one component for the foam core, one component for the conformal composite sheet on the outer surface of the part, and three components for the three composite sheets on the inner surface of the part.

[0133] The performance metrics include two usage performance metrics, mass (to be minimized) and compliance (also to be minimized), where compliance is the reciprocal of stiffness. These usage performance metrics can be captured by the objective function in the optimization program, which aims to minimize both mass and compliance.

[0134] The CAD parameters of the model can also include CAD parameters that constrain the model to be manufacturable by implementing the following constraints: the developability of the surface formed by the sheet shape, and the fact that the fiber orientation must be globally conformal to the surface. These CAD parameters can include a series of known CAD operations (e.g., sketching, extrusion, rounding). As described above, these constraints on the CAD parameters of the CAD model allow for the manufacturability of the blade by the manufacturing method discussed above. This shows the above advantage that the CAD parameters can be optimized while being constrained to implement the manufacturability of the composite part. In other words, for example, while it is not feasible to formulate the conformality (or conformal) constraint according to the KPI in practice, it is easy through the parameterization of the CAD parameters and allows for the implementation of these constraints. This illustrates the important advantage of directly optimizing the CAD parameters as described above: manufacturability is guaranteed.

[0135] The optimized convergence history shows how the optimization smoothly modifies the internal structure of the wing turbine blade to reduce the mass and flexibility of the design compared to the mechanical properties of the design with the initial CAD parameter values. This is shown by Figure 10 and Figure 11 . As Figure 12 shows, compared to the initial design, the fiber orientation of the optimized model shows that the design changes from a parallel configuration of fibers to an orthogonal orientation with fiber angles of 90 degrees to each other in the composite sandwich structure. Additionally, it can also be seen in Figure 12 that the fiber orientation does remain globally consistent while being restricted to conform to the optimized surface.

[0136] Therefore, the output of the method is a CAD model of the blade with the 4 angles and 22 geometric CAD parameters discussed above, which is optimized to minimize the mass and flexibility of the blade while complying with the constraints of forcing the sheet shape to be a developable surface and the fiber orientation to be globally conformal to the surface. This optimized design is effectively achieved by this method and is manufacturable through a manufacturing process that includes placing foam blocks of varying thicknesses and then unfolding and gluing laminated sheets on the surface. Such a process can be directly set / controlled according to the optimized values of the CAD parameters. The manufactured component exhibits improved performance related to minimum mass and minimum flexibility.

[0137] Third use case: Wood frame optimization

[0138] The composite component here is a wood frame that supports the downward load of the top plate. The frame is modeled using a CAD model of 18 straight wooden beams that have fibers arranged along the length of the beams. These beams are connected at spherical hubs made of isotropic plastic. The CAD parameters include the positions of the hubs. Thus, the optimization controls the positions of these hubs, and thus this indirectly affects the total length of the beams and the fiber orientation throughout the design space. The total length of the beams and the fiber orientation form one or more anisotropic material properties. One or more CAD components here include one component for each wooden beam and one component for each isotropic plastic hub. The optimization program optimizes the performance metrics for the response to the load on the top plate. Specifically, the three KPIs include minimizing the mass, minimizing the global absolute displacement of the top plate (the top plate must remain in the same position), and minimizing the local displacement of the top plate relative to its rest shape (the top plate must maintain its original shape). Figure 13 shows the initial design, and Figure 14 shows the optimized frame structure.

[0139] Note that if used to perform this optimization, the previously mentioned moving morphable component (MMC) method has the drawback of having problems with optimizing the handling of "hubs". The components connected at the hub typically overlap, and the hub is not geometrically well - defined because the MMC cannot correctly capture the interactions between components. In contrast, CAD parameterization allows for the implementation of a globally consistent and coherent layout of geometric features.

[0140] Figure 15 The deformations of (a) the initial construction and optimization iterations (b) 5 and (c) 25 using the proposed method are shown respectively. As can be seen from the figure, the optimized structure is not only stiffer but also bears the top plate more evenly.

[0141] The optimized wooden frame structure can be manufactured by cutting several wooden beams to the length of each beam component and manufacturing plastic hubs (e.g., via plastic injection molding). The entire structure is then assembled by inserting the beams into their hubs and finally fastening the assembly with fasteners. The method can include such a manufacturing process, and / or storing the optimized model as a file of manufacturing instructions and / or sending the file to a factory that performs the manufacturing.

[0142] The method generally manipulates modeling objects, such as CAD models. A modeling object is any object defined by data, for example, stored in a database. By extension, the expression "modeling object" specifies the data itself. Depending on the type of system, modeling objects can be defined by different kinds of data. The system can actually be any combination of CAD systems, CAE systems, CAM systems, PDM systems, and / or PLM systems. In those different systems, modeling objects are defined by the corresponding data. Thus, one can speak of CAD objects, PLM objects, PDM objects, CAE objects, CAM objects, CAD data, PLM data, PDM data, CAM data, CAE data. However, these systems are not mutually exclusive because modeling objects can be defined by data corresponding to any combination of these systems. Thus, the system can be a CAD, CAE, PLM, and / or CAM system, as will be apparent from the definition of such systems provided below.

[0143] In the context of CAD solutions (e.g., CAD systems or CAD software), it further refers to any system, software, or hardware that is at least suitable for designing modeling objects based on a graphical representation of the modeling object and / or its structured representation (e.g., a feature tree), such as CATIA. In such a case, the data defining the modeling object includes data that permits the representation of the modeling object. A CAD system can, for example, provide a representation of a CAD modeling object using edges or lines (in some cases with faces or surfaces). The lines, edges, or surfaces can be represented in various ways, such as non-uniform rational B-splines (NURBS). Specifically, a CAD file contains specifications by which geometries can be generated, thereby permitting the representation to be generated. The specifications of the modeling object can be stored in a single CAD file or multiple CAD files. The typical size of a file representing a modeling object in a CAD system is in the range of one megabyte per part. And a modeling object can typically be an assembly of thousands of parts.

[0144] In a CAD environment, a modeling object can typically be a 2D or 3D modeling object, such as a product representing a part or an assembly of multiple parts, or perhaps an assembly of products. A 2D or 3D modeling object can be a manufactured product, i.e., a product to be manufactured. In the case of a "3D modeling object", it refers to any object modeled by data that permits its 3D representation. The 3D representation permits viewing the part from all angles. For example, a 3D modeling object can be manipulated and rotated about any of its axes or about any axis in the screen displaying the representation when in 3D representation. This significantly excludes 2D icons that are not 3D modeled. The display of the 3D representation facilitates design (i.e., increases the speed at which a designer statistically completes their task). This speeds up the manufacturing process in industry as the design of the product is part of the manufacturing process.

[0145] 2D or 3D modeling objects represent the geometry of products to be manufactured in the real world after their virtual design using, for example, CAD / CAE software solutions or CAD / CAE systems, such as components (e.g., mechanical components) or assemblies of multiple components (or equivalently, assemblies of multiple components, since assemblies of multiple components can be regarded as components themselves from a methodological perspective, or the method can be applied independently to each component of the assembly), or more generally, any rigid body assembly (e.g., a moving mechanism). CAD / CAE software solutions allow the design of products in a variety of unrestricted industrial fields, including: aerospace, architecture, construction, consumer goods, high-tech devices, industrial equipment, transportation, marine, and / or offshore oil / gas production or transportation. Thus, 3D modeling objects designed by this method can represent industrial products, which can be any mechanical component, such as components of land vehicles (including, for example, automotive and light truck equipment, racing cars, motorcycles, heavy vehicles and mobile equipment, trucks and buses, trains), components of aircraft (including, for example, airframe equipment, aerospace equipment, propulsion equipment, defense products, aviation equipment, space equipment), components of watercraft (including, for example, naval equipment, commercial ships, offshore equipment, yachts and workboats, marine equipment), general mechanical components (including, for example, industrial manufacturing machinery, heavy mobile machinery or equipment, installation equipment, industrial equipment products, fabricated metal products, tire manufacturing products), electromechanical or electronic components (including, for example, consumer electronics, safety and / or control and / or instrumentation products, computing and communication equipment, semiconductors, medical devices and equipment), consumer goods (including, for example, furniture, home and garden products, leisure goods, fashion products, products of hard goods retailers, products of soft goods retailers), packaging (including, for example, food and beverage and tobacco, beauty and personal care, household product packaging).

[0146] A CAD system can be history-based. In this case, the modeled object is further defined by data including the history of geometric features. The modeled object can actually be designed by a physical person (i.e., the designer / user) using standard modeling features (e.g., extrusion, revolution, cutting, and / or round) and / or standard surfacing features (e.g., sweep, blend, loft, fill, deform, and / or smoothing). Many CAD systems that support such modeling capabilities are history-based systems. This means that the creation history of the design features is typically preserved through an acyclic data flow that links the geometric features together through input and output links. Since the early 1980s, the history-based modeling paradigm has been well-known. The modeled object is described by two persistent data representations: the history and the B-rep (i.e., boundary representation). The B-rep is the result of calculations defined in the history. When representing the modeled object, the shape of the part displayed on the computer screen is the B-rep (e.g., tessellation). The history of the part is the design intent. Basically, the history collects information about the operations that the modeled object has undergone. The B-rep can be saved together with the history to make it easier to display complex parts. The history can be saved together with the B-rep to allow design changes to the part according to the design intent.

[0147] As for a PLM system, it additionally refers to any system suitable for managing modeled objects representing physical manufactured products (or products to be manufactured). In a PLM system, the modeled object is thus defined by data suitable for manufacturing a physical object. These can typically be dimension values and / or tolerance values. It is indeed better to have such values for the correct manufacturing of the object.

[0148] As for a CAE solution, it additionally refers to any solution, software for hardware, suitable for analyzing the physical behavior of modeled objects. A well-known and widely used CAE technique is finite element modeling (FEM), which is equivalently referred to as CAE modeling hereinafter. FEM typically involves dividing the modeled object into elements, i.e., a finite element mesh, and the physical behavior can be calculated and simulated through equations. Such a CAE solution is provided by Dassault Systèmes under the trademark of Another developed CAE technique involves the modeling and analysis of complex systems that consist of multiple components from different physical fields without CAD geometric data. The CAE solution allows the simulation of the product to be manufactured and thus its optimization, improvement, and verification. Such a CAE solution is provided by Dassault Systèmes under the trademark of CAE can be used to ensure that various structural requirements (such as but not limited to mass, stiffness, strength, durability) are met by the new CAD model. Some of these requirements may be referred to as key performance indicators (KPIs). For many industrial products (such as cars, airplanes, consumer packaged goods, high-tech), these KPIs are conflicting. For example, lower mass usually results in lower stiffness. Therefore, optimization methods are usually applied to find the best compromise among the KPIs.

[0149] In terms of CAM solutions, it refers to any solution, software for hardware, suitable for managing the manufacturing data of a product. Manufacturing data usually includes data related to the product to be manufactured, the manufacturing process, and the required resources. CAM solutions are used to plan and optimize the entire manufacturing process of a product. For example, it can provide CAM users with information about feasibility, the duration of the manufacturing process, or the quantity of resources (such as specific robots) that can be used at specific steps of the manufacturing process; and thus allows decisions on management or required investments. CAM is a subsequent process after the CAD process and potential CAE process. For example, a CAM solution can provide information about machining parameters or molding parameters consistent with the extrusion features provided in the CAD model. Such CAM solutions are provided by Dassault Systèmes, trademarked as CATIA, Solidworks, or

[0150] Therefore, CAD and CAM solutions are closely related. In fact, CAD solutions focus on the design of a product or component, and CAM solutions focus on how to manufacture it. Designing the CAD model is the first step in computer-aided manufacturing. In fact, CAD solutions provide key functions, such as feature-based modeling and boundary representation (B-Rep), to reduce the risk of errors and precision loss during the manufacturing process handled by CAM solutions. In fact, the aim is to manufacture the CAD model. Therefore, the virtual twin (also known as the digital twin) of the object to be manufactured has two goals:

[0151] - To check the correct behavior of the object to be manufactured in a specific environment; and

[0152] - To ensure the manufacturability of the object to be manufactured.

[0153] PDM stands for Product Data Management. In the context of PDM solutions, it refers to any solution, software for hardware, suitable for managing all types of data related to a specific product. PDM solutions can be used by all the participants involved in the product life cycle: mainly engineers, but also project managers, finance people, salesmen, and purchasers. PDM solutions are typically based on a product-oriented database. It allows the participants to share consistent data about their product and thus prevents the participants from using different data. Such PDM solutions are provided by Dassault Systèmes under the trademarks of

[0154] The modeling objects optimized by this method are CAD models, such as CAD models including or containing a feature tree and / or a B-rep. Such models can be derived from CAE models and can be generated by a CAE-to-CAD conversion process, and this method can include such a process, for example, in an initial stage.

[0155] The CAD model is feature-based (e.g., it includes a feature tree and optionally includes a corresponding B-rep obtained by executing the feature tree). The feature-based 3D model allows (e.g., during the determination of manufacturing files or CAM files as discussed below) the detection and automatic resolution of geometric errors (such as conflicts that will affect the manufacturing process) in the CAD model. A conflict is the mutual penetration between two parts of a 3D model, for example, due to their relative movement. In addition, such conflicts can sometimes be detected only via finite element analysis based on the CAD feature-based model. Therefore, the resolution of conflicts can be carried out by a CAD solution or automatically by the CAD solution by iteratively modifying the parameters of the features and performing finite element analysis.

[0156] As another example, the feature-based 3D model allows (e.g., during the determination of manufacturing files or CAM files as discussed below) the automatic creation of tool paths for a machine via computer numerical control (CNC). With CNC, each object to be manufactured gets a customized computer program stored in and executed by a microcomputer attached to the machine control unit of the machine. The program contains the instructions and parameters that the machine tool will follow. Mills, lathes, routers, grinders, and lasers are examples of general machine tools whose operations can be automatically controlled by CNC.

[0157] The key feature of a CAD model is that it can be designed precisely and unambiguously by chaining a small number of high-level parametric design operations, including but not limited to, for example, sketching, extrusion, chamfering, and edited by modifying its high-level parameters. This is the key difference from polyhedral representations, such as triangular surface meshes, which can represent any 3D shape but do not provide the modification or parametric capabilities required in the context of industrial design.

[0158] Since a CAD model is a parametric model of a part / product, it is lighter in terms of memory footprint compared to other models such as CAE models. In fact, instead of storing a collection of discrete geometric elements, such as finite elements, a CAD model allows storing a list of features and parameters, which is lighter in terms of memory and memory footprint. Thus, in addition to facilitating the editability of the model, working on a CAD model reduces the memory requirements of the underlying system compared to, for example, a CAE model. This means that the CAE-to-CAD conversion process effectively compresses the CAE model into a CAD model, which is lighter in terms of memory requirements (e.g., footprint) in addition to converting the CAE model into a more editable CAD model.

[0159] Generating a custom computer program from a CAD file can be automated. Thus, such generation can be error-proof and can ensure a perfect reproduction of the CAD model into a manufactured product. Compared to manual machining, CNC is considered to provide higher precision, complexity, and repeatability. Other benefits include higher accuracy, speed, and flexibility, as well as capabilities such as contour machining, which allows milling of contour shapes, including those generated in 3D designs.

[0160] A B-rep (i.e., boundary representation) is a 3D representation of a mechanical part. Specifically, a B-rep is a persistent data representation that describes a 3D modeling object representing a mechanical part. A B-rep can be the result of calculations and / or a series of operations performed during the design phase of a 3D modeling object representing a mechanical part. When representing a modeling object, the shape of the mechanical part displayed on the screen of a computer is a B-rep (e.g., tessellation). In an example, the B-rep represents a part of the model object.

[0161] B-Rep includes topological entities and geometric entities. Topological entities are: faces, edges, and vertices. Geometric entities are 3D objects: surfaces, planes, curves, lines, points. By definition, a face is a bounded part of a surface, called the support surface. An edge is a bounded part of a curve, called the support curve. A vertex is a point in 3D space. They are related to each other as follows. The bounded part of a curve is defined by two points (vertices) located on the curve. The bounded part of a surface is delimited by its boundary, which is a set of edges located on the surface. The boundaries of the edges of a face are connected by sharing vertices. Faces are connected by shared edges. If two faces share an edge, they are adjacent. Similarly, if two edges share a vertex, they are adjacent. In a CAD system, B-Rep collects in a suitable data structure the "bounded by" relationships, the relationships between topological entities and the supporting geometry, and the mathematical descriptions of the supporting geometry. An interior edge of B-Rep is an edge that is shared exactly by two faces. By definition, a boundary edge is not shared and it delimits only one face. By definition, a boundary face is delimited by at least one boundary edge. If all the edges of B-Rep are interior edges, B-Rep is considered closed. If B-Rep includes at least one boundary edge, B-Rep is considered open. A closed B-Rep is used to model a thick 3D volume because it delimits the internal part of the space that (virtually) encloses the material. An open B-Rep is used to model a 3D skin, which represents a 3D object whose thickness is small enough to be ignored.

[0162] The key advantage of B-Rep over any other representation type used in CAD modeling is its ability to represent arbitrary shapes accurately. All other representations in use (such as point clouds, distance fields, and meshes) perform approximations of the shape to represent it by discretization. On the other hand, B-Rep contains surface equations that represent the exact design and thus constitutes a true "master model" for further manufacturing, whether for the generation of tool paths for CNC or the discretization into the correct sample density for a given 3D printer technology. In other words, by using B-Rep, the 3D model can be an exact representation of the manufactured object. B-Rep is also advantageous for simulating the behavior of 3D models. In terms of stress, heat, electromagnetic, or other analyses, it supports local refinement of the simulation mesh to capture physical phenomena, and for kinematics, it supports realistic contact modeling between curved surfaces. Finally, B-Rep allows for small memory and / or file footprint. First, because the representation contains only parameter-based surfaces. In other representations such as meshes, equivalent surfaces consist of up to thousands of triangles. Second, because B-Rep does not contain any history-based information.

[0163] The method may include, during a production / manufacturing process, which may include, after the execution of the method, generating a physical product corresponding to a modeled object (CAD model) optimized by the method. The production process may include the following steps:

[0164] - Apply (e.g., automatically) the method so as to obtain an optimized CAD model output by the method;

[0165] - Use the obtained CAD model to manufacture a component / product.

[0166] Using a CAD model for manufacturing refers to any real-world action or series of actions involved in / participating in manufacturing a component represented by the CAD model. Using a CAD model for manufacturing may, for example, include one or more of the following steps:

[0167] - Edit the obtained optimized CAD model;

[0168] - Perform simulations, such as simulations for validating mechanical, usage, and / or manufacturing properties and / or constraints (e.g., structural simulations, thermodynamic simulations, aerodynamic simulations), based on the CAD model or a corresponding CAE model (e.g., the CAE model from which the CAD model originated after a CAE-to-CAD conversion process);

[0169] - Edit the CAD model based on the results of the simulations;

[0170] - Optionally (i.e., depending on the manufacturing process used, the production of the mechanical product may or may not include this step), (e.g., automatically) determine a manufacturing file / CAM file (e.g., including manufacturing instructions for manufacturing the product represented by the CAD model and / or control instructions for the manufacturing process and / or for commanding the manufacturing process or its manufacturing tools) based on the (e.g., edited) CAD model (e.g., control instructions from a CAD file storing the CAD model and / or the specifications of the CAD model), for the production / manufacturing of the product;

[0171] - Send the CAD file and / or the manufacturing file / CAM file to the factory, in view of manufacturing the product represented by the CAD model; and / or

[0172] - Produce / manufacture the mechanical product initially represented by the model output by the method (e.g., automatically) based on the determined manufacturing file / CAM file or the CAD model. This may include feeding the manufacturing file / CAM file and / or the CAD file (e.g., automatically) to a machine performing the manufacturing process.

[0173] The last step of production / manufacturing can be referred to as the manufacturing step or the production step. This step manufactures / makes components / products based on a CAD model and / or a CAM file, for example when the CAD model and / or CAD file is fed into the computer system of one or more manufacturing machines or controlling machines. The manufacturing step can include performing any known manufacturing process or a series of manufacturing processes, such as one or more additive manufacturing steps, one or more cutting steps (such as laser cutting or plasma cutting steps), one or more stamping steps, one or more forging steps, one or more bending steps, one or more deep drawing steps, one or more molding steps, one or more machining steps (such as milling steps) and / or one or more punching steps. Since the design method improves the design of the model (CAE or CAD) representing the component / product, manufacturing and its productivity are also improved.

[0174] Editing the CAD model can include the user (i.e., the designer) performing one or more versions of the CAD model, for example by using a CAD solution. Modifications to the CAD model can include one or more modifications to each of the geometry and / or parameters of the CAD model. The modifications can include any modification or series of modifications performed on the feature tree of the model (such as modifications to feature parameters and / or specifications) and / or modifications performed on the display representation (such as B-rep) of the CAD model. The modifications are modifications that maintain the technical function of the component / product, i.e., the user performs modifications that may affect the geometry and / or parameters of the model, but only for the purpose of making the CAD model technically more compliant with the downstream use and / or manufacturing of the component / product. Such modifications can include any modification or series of modifications that make the CAD model technically compliant with the specifications of the machines used in the downstream manufacturing process. Such modifications can additionally or optionally include any modification or series of modifications that make the CAD model technically compliant with the further use of the product / component after manufacturing, such modifications or series of modifications being, for example, based on the results of simulations.

[0175] The CAM file can include a manufacturing setup model obtained from the CAD model. The manufacturing setup can include all the data required to manufacture a mechanical product such that it has the geometry and / or distribution of the material corresponding to the data captured by the CAD model, possibly up to the manufacturing tolerance error. Determining the production file can include using any CAM (Computer-Aided Manufacturing) or CAD-to-CAM solution to determine the production file from the CAD model (e.g., any automatic CAD-to-CAM conversion algorithm) (e.g., automatically). Such a CAM or CAD-to-CAM solution can include one or more of the following software solutions, which enable the automatic generation of manufacturing instructions and tool paths for a given manufacturing process based on the CAD model of the product to be manufactured:

[0176] - Fusion 360,

[0177] - FreeCAD,

[0178] - CATIA,

[0179] - SOLIDWORKS,

[0180] - The NC Shop Floor Programmer of Dassault Systèmes shown at https: / / my.3dexperience.3ds.com / welcome / fr / compass-world / rootroles / nc-shop-floor-programmer,

[0181] - The NC Mill-Turn Machine Programmer of Dassault Systèmes shown at https: / / my.3dexperience.3ds.com / welcome / fr / compass-world / rootroles / nc-mill-turn-machine-programmer, and / or

[0182] - The Powder Bed Machine Programmer of Diassault Systèmes shown at https: / / my.3dexperience.3ds.com / welcome / fr / compass-world / rootroles / powder-bed-machine-programmer.

[0183] The product / component can be an additively manufacturable component, i.e., a component to be manufactured by additive manufacturing (i.e., 3D printing). In this case, the production process does not include the step of determining a CAM file, but proceeds directly to the production / manufacturing step by directly (e.g., automatically) feeding the CAD model to the 3D printer. The 3D printer is configured to directly and automatically 3D print the mechanical product when fed a CAD model representing the mechanical product (e.g., when 3D printing is initiated by a 3D printer operator). In other words, the 3D printer receives (e.g., automatically) the CAD model fed to it, reads (e.g., automatically reads) the CAD model, and prints (e.g., automatically prints) the component by adding materials, for example layer by layer, to reproduce the geometry and / or distribution of the materials captured by the CAD model. The 3D printer adds materials to thereby accurately reproduce in reality the geometry and / or distribution of the materials captured by the CAD model, up to the resolution of the 3D printer, and optionally with or without tolerance errors and / or manufacturing corrections. The manufacturing can include, for example, determining such manufacturing corrections and / or tolerance errors via a user (e.g., the operator of the 3D printer) or automatically (by the 3D printer or the computer system controlling it), for example by modifying the CAD file to match the specifications of the 3D printer. The production process can additionally or optionally include (e.g., automatically by the 3D printer or the computer system controlling it) determining the printing direction from the CAD model, for example to minimize the overhang volume (as described in European Patent No. 3327593, which is incorporated herein by reference), layer-slicing (i.e., determining the thickness of each layer and the layer-by-layer path / trajectory of the 3D printer head and other characteristics (e.g., for a laser beam, such as the path, speed, intensity / temperature, and other parameters)).

[0184] The product component can optionally be a machined component (i.e., a component manufactured by machining), such as a milled component (i.e., a component manufactured by milling). In this case, the production process can include the step of determining a CAM file. This step can be automatically performed by any suitable CAM solution to automatically obtain the CAM file from the CAD model of the machined component. The determination of the CAM file can include (e.g., automatically) checking whether the CAD model has any geometric features (e.g., errors or artifacts) that can affect the production process, and (e.g., automatically) correcting such peculiarities. For example, if the CAD model still includes sharp edges (since machining or milling tools cannot produce sharp edges), then machining or milling based on the CAD model may not be performed, and in this case, the determination of the CAM file can include (e.g., automatically) rounding or filleting such sharp edges (e.g., having a circular or fillet radius corresponding to, for example, substantially equal to the tolerance error, the radius of the cutting head of the machining tool), so that machining or milling based on the CAD model can be completed. More generally, the determination of the CAM file can automatically include rounding or filleting geometries within the CAD model that are incompatible with the radius of the machining or milling tool to enable machining / milling. This checking and possible correction (e.g., rounding or filleting of geometries) can be performed automatically as previously discussed, but can also be performed by a user (e.g., a machining engineer) who manually performs corrections on the CAD and / or CAM solution, such as constraining the solution for which the user performs the correction, and this correction makes the CAD model compliant with the specifications of the tool used in the machining process.

[0185] In addition to inspection, the determination of the CAM file can include (e.g., automatically) determining a machining or milling path, i.e., the path that a machining tool is to take to machine a product. The path can include a set of coordinates and / or a parametric trajectory for machining to be followed by the machining tool, and determining the path can include (e.g., automatically) calculating these coordinates and / or trajectories based on the CAD model. The calculation can be based on the calculation of the boundary of the Minkowski subtraction of the CAD model by the CAD model representation of the machining tool, as discussed, for example, in European Patent Application EP21306754.9 filed by Dassault Systèmes on December 13, 2021, and which is incorporated herein by reference. It is to be understood that the path can be a single path, e.g., continuously followed by the tool without breaking contact with the material to be cut. Optionally, the path can be a concatenation of a series of sub-paths to be followed by the tool in a certain order, e.g., each sub-path being continuously followed by the tool without breaking contact with the material to be cut. Optionally, the determination of the CAM file can then include (e.g., automatically) setting machine parameters, including cutting speed, cut / pierce height, and / or mold opening stroke, e.g., based on the determined path and the specifications of the machine. Optionally, the determination of the CAM file can then include (e.g., automatically) configuring nesting, where the CAM solution decides on the optimal orientation of the parts to maximize machining efficiency.

[0186] In the case of machining or milling a part, the determination of the CAM file thus results in and outputs a CAM file that includes the machining path and optionally the set machine parameters and / or specifications of the configured nesting. Then, the output CAM file can be (e.g., directly and automatically) fed to the machining tool and / or the machining tool can then be (e.g., directly and automatically) programmed by reading the file, on the basis of which the production process includes a production / manufacturing step in which the machine performs the machining of the product according to the production file, e.g., by directly and automatically executing the production file. The machining process includes the machining tool cutting a real-world block of material to reproduce the geometry and / or distribution of the material captured by the CAD model, e.g., up to a tolerance error (e.g., a few tens of micrometers for milling).

[0187] The product / component can optionally be a molded component, i.e., a component manufactured by molding (e.g., injection molding). In this case, the production process can include the step of determining a CAM file. This step can be automatically performed by any suitable CAM solution to automatically obtain the CAM file from the CAD model of the molded component. The determination of the CAM file can include (e.g., automatically) performing a series of molding checks based on the CAD model to check that the geometry and / or distribution of the material captured by the CAD model is suitable for molding, and (e.g., automatically) performing appropriate corrections if the CAD model is not suitable for molding. Performing the checks and appropriate corrections (if any) can be performed automatically or, optionally, by the user (e.g., a molding engineer) using, for example, CAD and / or CAM solutions that allow the user to perform appropriate corrections to the CAD model, but constrain his / her corrections such that the CAD model complies with the specifications of the molding tool. The checks can include: verifying that the virtual product represented by the CAD model is dimensionally consistent with the mold and / or verifying that the CAD model includes all draft angles required for demolding the product, as known through molding itself. Then, the determination of the CAM file can further include determining the amount of liquid material to be used for molding and / or the time for hardening / setting the liquid material within the mold based on the CAD model, and outputting a CAM file including these parameters. Then, the production process includes (e.g., automatically) performing molding based on the output file, where, for the determined hardening time, the mold forms the liquid material into a shape corresponding to the geometry and / or distribution of the material captured by the CAD model, e.g., up to a tolerance error (e.g., up to incorporating or modifying the draft angle for demolding).

[0188] The product / component can optionally be a stamped part, also possibly referred to as a "stamped part", i.e., a component to be manufactured during a stamping process. In this case, the production process can include (e.g., automatically) determining a CAM file based on the CAD model. The CAD model represents the stamped component, e.g., if the component will include some it may have one or more flanges and may, in the latter case, have additional material to be removed in order to form the developed state of one or more flanges of the component, as known through stamping itself. Thus, the CAD model includes a portion representing the component without flanges (in some cases the entire component), and may include an external additional patch portion representing the flanges (if any), which external additional patch portion may include additional material (if any). This additional patch portion can exhibit g2 continuity over a certain length and then g1 continuity over a certain length.

[0189] In this stamping scenario, the determination of the CAM file can include (e.g., automatically) determining the parameters of the stamping machine, such as the size of the stamping die or stamping punch and / or the stamping force, based on the geometry and / or distribution of the material of the virtual product captured by the CAD model. If the CAD model also includes a representation of the additional material to be removed to form the unfolded state of one or more flanges of the component, the additional material to be removed can be cut, for example, by machining, and the determination of the CAM file can also include determining the corresponding machining CAM file, e.g., as previously discussed. If there are one or more flanges, the determination of the CAM file can include determining the geometric specifications of the g2 continuity and g1 continuity portions, which allow the flanges to be folded towards the inner surface of the stamped component and along the g2 continuity length during the folding process after the stamping itself and the removal of the additional material. The CAM file thus determined can therefore include: the parameters of the stamping tool, the said specifications for folding the flanges (if any), and optionally the machining production file for removing the additional material (if any).

[0190] Then, the stamping production process can, for example, directly and automatically output the CAM file and perform the stamping process based on the file (e.g., automatically). The stamping process can include stamping (e.g., punching) a portion of the material to form the product represented by the CAD file, which may have unfolded flanges and additional material (if any). In appropriate cases, the stamping process can then include cutting the additional material based on the machining production file and folding the flanges based on the said specifications for folding the flanges, thereby folding the flanges along their g2 continuity length and giving the outer boundary of the component a smooth appearance. In the latter case, the shape of the component after manufacturing differs from its virtual counterpart as represented by the CAD model in that the excess material is removed and the flanges are folded, while the CAD model represents the component with the additional material and the flanges in the unfolded state.

[0191] The method is computer-implemented. This means that the steps (or substantially all steps) of the method are performed by at least one computer or any similar system. Thus, the steps of the method are performed by a computer, possibly fully automatically or semi-automatically. In an example, the triggering of at least some steps of the method can be performed through user-computer interaction. The level of user-computer interaction required can depend on the level of automation foreseen and be balanced with the need to fulfill the user's wishes. In an example, the level can be user-defined and / or pre-defined.

[0192] A typical example of the computer implementation of the method is to execute the method using a system suitable for this purpose. The system may include a processor coupled to a memory and a graphical user interface (GUI), and a computer program including instructions for executing the method is recorded on the memory. The memory may also store a database. The memory is any hardware suitable for such storage and may include several physically different parts (for example, one for the program and one for the database, possibly).

[0193] Figure 16 An example of the system is shown, where the system is a client computer system, such as the user's workstation.

[0194] The client computer of this example includes a central processing unit (CPU) 1010 connected to an internal communication BUS1000, and a random access memory (RAM) 1070 also connected to the BUS. The client computer may also be provided with a graphics processing unit (GPU) 1110 associated with a video random access memory 1100 connected to the BUS. The video RAM 1100 is also known as a frame buffer in the art. The mass storage device controller 1020 manages access to a mass storage device (such as a hard disk drive 1030). Mass storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including, for example, semiconductor memory devices such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks. Any of the foregoing may be supplemented or incorporated by a specially designed ASIC (application specific integrated circuit). The network adapter 1050 manages access to the network 1060. The client computer may also include a haptic device 1090, such as a cursor control device or a keyboard, etc. A cursor control device is used in the client computer to allow the user to selectively position the cursor at any desired position on the display 1080. In addition, the cursor control device allows the user to select various commands and input control signals. The cursor control device includes a plurality of signal generation devices for input control signals to the system. Generally, the cursor control device may be a mouse, and the buttons of the mouse are used to generate signals. Optionally or additionally, the client computer system may include a touchpad and / or a touch screen.

[0195] A computer program may include instructions executable by a computer, the instructions including means for causing the above system to perform the method. The program may be recorded on any data storage medium, including the memory of the system. The program may be implemented, for example, in digital electronic circuitry or in computer hardware, firmware, software, or combinations thereof. The program may be implemented as a device, such as a product tangibly embodied in a machine-readable storage device for execution by a programmable processor. The steps of the method may be performed by a programmable processor executing an instruction program to perform the functions of the method by operating on input data and generating output. Accordingly, the processor may be programmable and coupled to receive data and instructions from, and to send data and instructions to, a data storage system, at least one input device, and at least one output device. If desired, the application program may be implemented in a high-level procedural or object-oriented programming language, or in assembly or machine language. In any case, the language may be a compiled or interpreted language. The program may be a full installation program or an update program. The application of the program on the system in any case results in instructions for performing the method. The computer program may optionally be stored and executed on a server in a cloud computing environment that communicates with one or more clients via a network. In such a case, the processing unit executes the instructions included in the program, thereby causing the method to be executed on the cloud computing environment.

Claims

1. A computer-implemented method for optimizing one or more anisotropic material properties of a composite part, the method comprising: - Providing: A CAD model representing the composite part, the CAD model including a feature tree having one or more CAD parameters, each of the CAD parameters having an initial value, at least one CAD parameter affecting the one or more anisotropic material properties of the composite part; And An optimization program specified by one or more usage and / or manufacturing performance metrics, the one or more metrics including one or more objective functions and / or one or more constraints; And - Modifying the initial values of the one or more CAD parameters by solving the optimization program using a gradient-based optimization method, the optimization method taking the one or more CAD parameters as free variables, the optimization method using sensitivities, each sensitivity being an approximation of the corresponding derivative of a corresponding performance metric with respect to a corresponding CAD parameter, the sensitivity being composed of: An approximate corresponding derivative of each corresponding performance metric with respect to one or more material property fields, each material property field in the one or more material property fields representing the distribution of an anisotropic material property among the one or more anisotropic material properties, and An approximate corresponding derivative of each of the one or more material property fields with respect to a corresponding CAD parameter.

2. The method according to claim 1, wherein The CAD model is formed by one or more CAD components, each CAD component corresponding to a spatial region, and the method includes: calculating one or more signed distance fields, each signed distance field corresponding to a corresponding CAD component, and for each given material property field among the one or more material property fields and each element in the mesh of the CAD model, each local material property value of the given material property field at the element of the mesh is obtained by a weighted combination of the material property values of the one or more CAD components, each value in the weighted combination being derived from the projection of the signed distance between the element of the mesh and the corresponding CAD component.

3. The method according to claim 2, wherein Each weight corresponds to the projection of the signed distance value of the component by a function that maps [-∞; +∞] to [0; 1] and has a well-defined first derivative, where the function is a smooth Heaviside projection.

4. The method according to any one of claims 2 to 3, wherein, The weighted combination is a weighted sum.

5. The method according to claim 4, wherein, Where Mik is the local material property value of property k in Ωtype of one or more properties at element i of the mesh Ωmesh of the CAD model, j is a component, Ωcomp is the set of all components, Hij is the weight, and mijk is the material property of the component.

6. The method according to claim 5, wherein, Where α ≥ 0 is the steepness coefficient of the smooth Heaviside projection, where l is the average size of the element in the mesh, and SDFij is the signed distance value from element i to component j.

7. The method according to claim 5 or 6, wherein each respective approximate derivative of the one or more material property fields with respect to the respective CAD parameters is of the following type: where CADp is the corresponding CAD parameter, where hp > 0 is a small perturbation, and where Ωparam is the set of CAD parameters.

8. The method according to claim 7, wherein Each sensitivity is of the following type: where Ωperfo is the set of performance metrics.

9. The method according to any one of claims 2 to 8, wherein The one or more components are composed of a number of components.

10. The method according to any one of claims 1 to 9, wherein The one or more anisotropic material properties are composed of a number of anisotropic material properties.

11. The method according to any one of claims 1 to 10, wherein, At least one CAD parameter that affects the one or more anisotropic material properties of the composite part satisfies the constraints of the manufacturing process for manufacturing the composite part.

12. A CAD model obtainable by a method according to any one of claims 1 to 11.

13. A computer program comprising instructions which, when executed by a computer system, cause the computer system to perform a method according to any one of claims 1 to 11.

14. A computer-readable data storage medium having recorded thereon the computer program according to claim 13 and / or the CAD model according to claim 12.

15. A computer system comprising a processor coupled to a memory having recorded thereon the computer program according to claim 13 and / or the CAD model according to claim 12.

Images