Optimization of one or more anisotropic material characteristics of composite component

Abstract

To provide a method for optimizing topology or a shape, a CAD model to be obtained, a computer program, a data storage medium and a computer system in consideration of anisotropy of materials.SOLUTION: A method by a computer system comprises the steps of: providing a CAD model representing a composite component including a feature tree having a CAD parameter affecting anisotropic material characteristics, and an optimization program specified by a use or manufacturing performance index including an objective function or restriction; changing an initial value of the CAD parameter by solving the optimization program by using an inclination-based optimization method; and changing sensitivity as an approximate value of a derived function of a performance index regarding the CAD parameter to the one obtained by synthesizing an approximate derived function of which the material characteristic field represents distribution of the anisotropic material characteristics with an approximate derived function of a material characteristic field regarding the CAD parameter.SELECTED DRAWING: Figure 16

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 a composite part. [Background technology]

[0002] Numerous solutions, hardware, and software are available on the market for designing, engineering, and manufacturing objects. CAD stands for Computer-Aided Design, which refers to software solutions for designing objects. CAE stands for Computer-Aided Engineering, which refers to software solutions for analyzing and simulating the physical behavior of future products. CAM stands for Computer-Aided Manufacturing, which refers to software solutions for defining product manufacturing processes and resources. In such computer-aided design solutions, graphical user interfaces play a key role in the efficiency of the technology. These technologies may be incorporated into Product Lifecycle Management (PLM) systems. PLM refers to an engineering strategy that helps companies share product data, apply common processes, and leverage corporate knowledge for product development from conception to the end of the product's lifespan across the extended enterprise. Dassault Systèmes' PLM solutions (product names: CATIA, SIMULIA, DELMIA, and ENOVIA) provide an Engineering Hub to organize product engineering knowledge, a Manufacturing Hub to manage manufacturing engineering knowledge, and an Enterprise Hub to enable enterprise integration and connectivity to both the Engineering and Manufacturing Hubs. All solutions provide a common model linking products, processes, and resources, enabling dynamic, knowledge-based product creation and decision support that drives optimized product definition, manufacturing preparation, production, and service.

[0003] In this context, CAD solutions exist for designing composite parts, which often feature and / or are made of anisotropic material properties.

[0004] Anisotropic materials are found everywhere, from the simplest wooden table or plywood wall to the most advanced, ultra-lightweight carbon fiber composite aerospace bodies. An anisotropic material is one that has one or more physical properties (e.g., stiffness or thermal conductivity) that vary with direction. Among these materials are orthotropic materials, which are anisotropic materials that have two mutually perpendicular planes of symmetry for the material properties.

[0005] Figure 1 shows an example of a composite part that is a table formed from an anisotropic wood beam with fibers aligned along the length of the beam and an isotropic plastic hub with an isotropic void as shown in the figure.

[0006] FIG. 2 shows another example of a composite part, an aircraft wind turbine blade formed by anisotropic conformal composite laminates around an isotropic foam core (a cross section of the blade is shown in FIG. 2).

[0007] Before manufacturing, these objects are typically designed in CAD software, which allows defining a parameterized representation of the 3D part, including various properties related to the position, orientation, and properties of anisotropic materials (see the 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, this digital representation can be tested, simulated, and optimized using CAE software to verify or optimize structural performance. Often, the optimization of such structures is performed as multiple successive optimizations, each operating on a homogeneous subset of variables, with each optimization step requiring a different representation of the object. For example, an initial topology optimization can be performed using a density field with isotropic material properties to obtain rough design ideas and estimates, as described in Bendsoe MP, Sigmund O (2003), Topology Optimization theory, methods, and applications. Springer, Berlin.The topology-optimized design is then post-processed as described in Olhoff N, Bendsoe 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 EA Method of “Exact” Numerical Differentiation for Error Elimination in Finite-Element-Based Semi-Analytical Shape Sensitivity Fine tuning can be achieved using surface-based shape optimization as described in Analyses. Mech. Struct. & Mach. 1993;21(1). The surface-based optimized shape can then be fixed.Composite laminate patches are then placed on the surface of the object and the angles of each layer or patch are optimized, as described 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.The thickness of each laminate or sandwich patch can then be optimized simultaneously along with the angle, as described in Pedersen P. On thick and orientational design with orthotropical materials. Struct Optim. 1991;3., or in a separate optimization step for thickness alone, as described in Sjolund JH, Lund E. Structural gradient-based optimization of wind turning blades with fixed outer geometry. Composite structures. 2018;203. For an overview of both gradient-based (also known as sensitivity-based) and gradient-free methods in various previous optimization procedures, see Sjolund 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). Summary of the Invention [Problem to be solved by the invention]

[0009] While these optimization steps can be individually robust and accurate, the overall result may be far from optimal because the set of parameters controlling the object's shape and material properties are optimized using separate successive steps. In other words, the truly optimal topology or shape may be suboptimal when considering material anisotropy.

[0010] Another issue is the lack of a CAD representation when directly optimizing the many low-level variables related to material density and anisotropy across the entire design space in extended topology optimization frameworks (e.g., as described in https: / / www.researchgate.net / publication / 353194654_Large-Scale_Three-Dimensional_Anisotropic_Topology_Optimization_of_Variable-Axial_Lightweight_Composite_Structures). These methods offer the greatest design freedom in describing the design variables for optimization. Therefore, theoretically, high-performance structural designs are achieved. The drawback is that the final optimized structure may be difficult to reinterpret into a CAD model, or may be unmanufacturable due to the complex geometry and material orientation present in the final optimized structure. This is illustrated in Figure 3, which shows a screenshot of the results obtained by such methods, with the complex geometry zoomed in.

[0011] The reference Gandhi Y, Minak GA. Review on Topology Optimization Strategies for Additively Manufactured Continuous Fiber-Reinforced Composite Structures. Appl. Sci. 2022;12. provides a further overview of topology optimization methods that include composite design variables. The following methods are the most common:

[0012] Topology optimization using so-called density methods, including composite design variables and sensitivity calculations, is described, for example, in references Xu Y, Zhu J, Wu Z, Cao Y, Zhao Y, Zhang WA, "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 MA, "A new method for simultaneous material and topology optimization of composite laminate structures using Hyperbolic Function Parametrization." Composite Structures 2021;276. So-called topology optimization density methods do not include 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 PS, 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 topology optimization with composite design variables, but apply so-called level set topology optimization. Again, these level set topology optimization methods do not include CAD information. Additionally, the examples in these references do not use 3D continuum modeling, which is required for general 3D coupling.

[0014] The studies described in 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 apply moving morphable components (MMC) techniques to optimize strictly bar, strictly plate, and strictly piecewise linear spline structures, respectively, for orthotropic fiber-reinforced materials. Therefore, these MMC techniques for orthotropic fiber-reinforced materials do not disclose CAD descriptions, but only parametric descriptions of simple bar 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 parts. [Means for solving the problem]

[0016] Accordingly, a computer-implemented method for optimizing one or more anisotropic material properties of a composite part is proposed. 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 the one or more anisotropic material properties of the composite part. The method further includes providing an optimization program. The optimization program is identified by one or more usage 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 varying the initial values of the one or more CAD parameters by solving the optimization program using a gradient-based optimization method. The optimization method has the one or more CAD parameters as free variables. The optimization method uses sensitivities. Each sensitivity is an approximation of a derivative of a performance metric with respect to a respective CAD parameter. The sensitivities are: approximate derivatives of the performance index with respect to one or more material property fields, each material property field 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 and the approximate derivatives of each of the one or more material property fields with respect to each CAD parameter.

[0017] The method may include one or more of the following.

[0018] the CAD model is formed by one or more CAD components, each corresponding to a region of space, and the method includes calculating one or more signed distance fields for each CAD component, and for each material property field, each local material property value of that field is obtained from a weighted combination of material properties of the components of the CAD model, weighted by the signed distance to that local material property value; Each weight corresponds to a projection of the signed distance value of a component by a function that maps ]-∞;+∞[ to [0;1] and has a well-defined first derivative, optionally the function is a smooth Heaviside projection; The above weighted combination is a weighted sum;

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[0019] Also provided is a CAD model obtained by the method. Such a CAD model represents a composite part and includes a feature tree having one or more CAD parameters, at least one of which affects the one or more anisotropic material properties of the composite part. The CAD parameters have optimized values equal to values obtained by applying the method to the model. For example, the CAD parameters may have optimal values obtained directly by optimization performed by the method, and the CAD model is therefore an output of the method.

[0020] Additionally, a computer program comprising instructions for carrying out the method is also provided.

[0021] Furthermore, there is provided a computer-readable data storage medium having the computer program and / or the CAD model recorded thereon.

[0022] Furthermore, there is provided a computer system including a processor connected to a memory in which the computer program and / or the CAD model is stored. Non-limiting examples will now be described with reference to the accompanying drawings. [Brief explanation of the drawings]

[0023] [Figure 1] 1A and 1B are diagrams illustrating the present method. [Figure 2] 1A and 1B are diagrams illustrating the present method. [Figure 3] 1A and 1B are diagrams illustrating the present method. [Figure 4] 1A and 1B are diagrams illustrating the present method. [Figure 5] 1A and 1B are diagrams illustrating the present method. [Figure 6] 1A and 1B are diagrams illustrating the present method. [Figure 7] 1A and 1B are diagrams illustrating the present method. [Figure 8] 1A and 1B are diagrams illustrating the present method. [Figure 9] 1A and 1B are diagrams illustrating the present method. [Figure 10] 1A and 1B are diagrams illustrating the present method. [Figure 11] 1A and 1B are diagrams illustrating the present method. [Figure 12] 1A and 1B are diagrams illustrating the present method. [Figure 13] 1A and 1B are diagrams illustrating the present method. [Figure 14] 1A and 1B are diagrams illustrating the present method. [Figure 15] 1A and 1B are diagrams illustrating the present method. [Figure 16] FIG. 1 illustrates an example of a computer system. DETAILED DESCRIPTION OF THE INVENTION

[0024] 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 the 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 usage 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 varying the initial values of the one or more CAD parameters by solving the optimization program using a gradient-based optimization method. The optimization method has the one or more CAD parameters as free variables. The optimization method uses sensitivities. Each sensitivity is an approximation of a derivative of a performance metric with respect to a respective CAD parameter. The sensitivities are: - approximate derivatives of the performance index with respect to one or more material property fields, each material property field of said one or more material property fields representing a distribution of an anisotropic material property of said one or more anisotropic material properties; - approximate derivatives of each of the one or more material property fields with respect to each CAD parameter.

[0025] The method constitutes an improved solution for optimizing one or more anisotropic material properties of a composite part.

[0026] The method actually optimizes one or more CAD parameters of the CAD model with respect to one or more performance indicators, at least one of which affects one or more anisotropic material properties of the composite part. In other words, the method optimizes one or more anisotropic material properties of the composite part through the optimization of the CAD parameters that affect them, thereby achieving optimal values for one or more performance indicators. Thus, the method generates (i.e., outputs, for example, as a CAD file) a CAD model of the composite part having one or more anisotropic material properties (e.g., stiffness or thermal conductivity) optimally designed for the composite part, and optimizes the performance indicators of the composite part, i.e., achieving optimized performance with respect to these indicators. In other words, the method not only optimizes the part's shape (because CAD parameters affect the shape), but also its anisotropic physical properties (e.g., fiber orientation) because 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, stiffness, etc.) or to the manufacture of the part (e.g., the metric captures constraints and / or tolerances for the manufacturing process or machine that the part is optimized to meet). The method may include both use-related performance metrics (e.g., mass, stiffness, response to load, etc.) and manufacture-related performance metrics (e.g., constraints by a particular manufacturing process, e.g., to enhance the manufacturability of the output model).

[0027] Furthermore, the present method optimizes a CAD model of the composite part (i.e., optimizes its CAD parameters). This means that the output of the model is an optimized CAD model, i.e., a model in which the values of the CAD parameters are optimized with respect to the optimization problem addressed by the present method. Such a model can be directly used to manufacture the composite part; i.e., it represents a manufacturable object whose CAD parameters can fully define the specifications of the manufacturing process. The output optimized CAD model (e.g., in the form of a CAD file or after being converted into a corresponding CAM (computer-aided manufacturing) file) may be directly used to control and / or configure the manufacturing process and / or machines / tools, as described further below. Thus, in contrast to existing optimization methods that operate on CAE models (e.g., finite element meshes) and may result in optimized parts that are too complex to manufacture in practice (in particular, optimized orientations of material physical properties may not be manufacturable in practice) due to the degrees of freedom provided in the search for optimal values in the optimization, the output of the present method is a CAD model that can be directly used as a file to control and / or configure the manufacturing process to manufacture the optimized part corresponding to the CAD model. Furthermore, as discussed above, manufacturability can be enhanced by having one or more performance metrics that implement one or more manufacturing constraints. Alternatively, manufacturability can be enhanced without a dedicated performance metric (which may be impractical in some manufacturing contexts), but by using appropriate CAD parameters in the model (which may or may not be part of the parameters optimized by the method). This further illustrates the technical advantage of directly optimizing a CAD model: manufacturability is guaranteed and can be enhanced by CAD parameters. For example, the at least one CAD parameter that affects the one or more anisotropic material properties of the composite part may satisfy (or capture) the constraints of the manufacturing process for producing the composite part.

[0028] Therefore, this method targets the physical and / or geometric optimization of 2D or 3D objects with anisotropic, composite, microstructured, or fibrous materials modeled in CAD software. A key feature of these CAD models is that they can be designed geometrically accurately and unambiguously by chaining a small number of high-level, heterogeneous parametric design operations (sketch, extrusion, chamfer, loft volume, shell offset, fillet, pocket, trim, emboss, transform, multi-instancing, assembly, and Boolean operations) and can be edited to modify high-level geometric and numerical parameters. This is a key difference compared to simpler polyhedral representations, such as triangular surface meshes, which can represent most shapes but do not offer the necessary modification and parameterization capabilities in the context of industrial design and manufacturing.

[0029] The proposed method solves the following problems: -dealing with a large number of design variables (thus excluding traditional gradient-free methods); -Handling heterogeneous parameters present directly within the representation of the CAD construction; -Model both geometry and anisotropic material properties in a single common representation; -Mapping between high-level CAD parameters and low-level local material behavior that models mechanical properties and physical performance.

[0030] As described below, the present method may solve the aforementioned problem by projecting a CAD model containing anisotropic components into a continuous Eulerian representation. Local properties such as density, orientation, and fiber fraction can be captured by scalar fields on a volume mesh. The physical behavior of these scalar fields is then simulated by finite element analysis, and key performance indicators (KPIs) are evaluated. 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.

[0031] The proposed method and its implementation have the following advantages: - Directly modify heterogeneous parameters defined in the CAD representation, thus eliminating the need for a CAD reinterpretation step of the optimization results and ensuring the preservation of the manufacturability properties of the original CAD model.

[0032] This allows for an efficient iterative gradient-based optimization scheme, thus enabling computationally efficient optimization of many CAD parameters, and allows for many constraints against different performance indicators (KPIs), with constraints being active and inactive during the iterative optimization iterations.

[0033] - Both geometry and material properties are optimized simultaneously as an integrated, coupled problem, resulting in better optimization than solving a sequence of multiple, separate optimization sub-problems.

[0034] The method is for optimizing one or more anisotropic material properties of a composite part. The method thus outputs a design of the composite part having optimized anisotropic material properties. Specifically, the method receives as input a CAD model of such a part along with CAD parameters, at least one of which affects one or more anisotropic material properties of the composite part, and varies their values (and thus, in particular, the values of parameters affecting the anisotropic material properties) to reach an optimal value of a performance metric (e.g., up to a convergence criterion). The output of the method is thus an optimized CAD model, i.e., a CAD model having optimized values for CAD parameters, including parameters affecting the anisotropic material properties.

[0035] The method thus forms a design step (specifically, an optimization step in a design process where existing CAD parameters are optimized) for designing a mechanical product / component, i.e., a composite part. "Designing a mechanical part / product" refers to an action or series of actions that are at least part of the process of creating a modeled object (3D or 2D) of the mechanical part / product. The method is an optimization step within this process.

[0036] A composite part is a part made from composite materials. 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 fused together to create a material with properties different from those of the individual components. Within the finished structure, the individual components remain separate and distinct, which distinguishes a composite from a mixture or solid solution. A composite part has anisotropic material properties, meaning that the properties of the composite material vary with direction. A composite material may be orthotropic, meaning that the material properties have three mutually orthogonal planes of symmetry. The one or more anisotropic material properties may consist of several anisotropic material properties. Each anisotropic material property is also called a "material anisotropy property type," and each property in the one or more material anisotropy property types is a material anisotropy property type of each type.

[0037] 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 of the method. The provided CAD model is also referred to as the "input CAD model." The provided CAD model is a feature-based CAD model that includes a feature tree. The concept of a feature-based CAD model is known in CAD and will be described in more detail below. Similarly, the concept of a feature tree is well known in CAD. A feature tree is a tree structure of CAD operations (e.g., Boolean and non-Boolean operations) on CAD features, each of which models a portion of the composite part. More specifically, a feature tree is a directed acyclic graph that describes / captures the sequence and combination order of CAD operations (as described at https: / / en.wikipedia.org / wiki / Directed_acyclic_graph, which is incorporated herein by reference). As known in CAD, a CAD feature includes shape / geometry information and parametric information to represent the portion of the composite part modeled / captured by the CAD feature. As is known, a CAD feature includes a definition / specification of the geometry / shape (e.g., the geometric primitives of the definition / specification) corresponding to the part modeled by the CAD feature, and one or more CAD parameters that identify the geometry and its topology. Accordingly, a feature tree includes one or more CAD parameters corresponding to the CAD feature of the feature tree. Non-limiting examples of such CAD parameters include plate thickness, pocket depth, fiber ply angle, subdivision surface control points, etc. One or more of these CAD parameters influence the anisotropic material properties of the composite part.

[0038] A CAD parameter that affects the anisotropic material properties of a part is a CAD parameter whose value, when changed, changes at least one anisotropic material property (e.g., all anisotropic properties) of the part. Non-limiting examples of such parameters include the angle of the fiber plies, CAD variables that control the profile of a wind turbine blade (which follows its curvature along the shape and therefore affects not only the cross-sectional shape of the composite laminate but also the material orientation within the composite laminate), or any CAD parameter that affects the material orientation of a composite part.

[0039] The model may include at least one CAD parameter that affects one or more anisotropic material properties of the composite part and captures the constraints of a manufacturing process for producing the composite part, thereby enabling the design to be optimized for a particular manufacturing process. Alternatively, or additionally, such constraints may be captured by constraints of an optimization program that implements manufacturing performance metrics, thereby also enabling the design to be optimized for a particular manufacturing process.

[0040] The CAD model may be a 2D CAD model (i.e., forming a 2D CAD representation of the composite part) or a 3D CAD model (i.e., forming a 3D CAD representation of the composite part). The CAD model may include a feature tree as well as 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 execution of the feature tree. The geometric representation may be or include a geometric representation of an exterior surface of the composite part. Providing the method may include providing a mesh (i.e., 2D or 3D) including a geometric representation of the model, for example, a geometric representation of the exterior surface.

[0041] The input CAD model may be derived from a previous design process (e.g., performed during another design session, e.g., in another system or software). Providing the CAD model may include downloading the CAD model from a memory or server where the CAD model is stored with the design. Alternatively, providing the CAD model may include designing the CAD model. Designing the CAD model may include designing the CAD model from scratch on a CAD system, e.g., by iteratively building a feature tree. Alternatively, designing the CAD model may include first designing a CAE model (i.e., a finite element model) representing the composite part on a CAE system using any CAE software solution, converting the CAE model to a CAD model using any CAD-to-CAE conversion method, and optionally storing the CAD model in a memory or server. Providing the CAD model may also include downloading the designed CAE model, e.g., from a memory or server where the CAE model is stored with the design, and then converting the CAE model to the input CAE model.

[0042] Providing the optimization program may involve downloading the optimization program from any memory or server on which the program is available, or may involve launching any software in which the program is implemented, or may further alternatively involve coding / programming the optimization program or downloading (and optionally modifying) an already coded / programmed optimization program.

[0043] The optimization program includes an optimization algorithm for solving an optimization problem. An optimization problem refers to a mathematical optimization problem consisting of minimizing or maximizing one or more objective functions, optionally under one or more constraints, or minimizing or maximizing some other quantity under the constraints. Accordingly, an optimization program is identified by one or more use and / or manufacturing indicators, including the objective function and / or constraints. The optimization program includes an optimization algorithm that performs such minimization or maximization. The optimization program may be designed to allow a user to input data related to the optimization before launching the optimization program, including the objective function, constraints, convergence threshold, and / or maximum value of the algorithm's iteration steps. The method may include a step in which the user provides at least some of such data before the optimization step. The optimization program may be designed to allow a user to select an optimization method for performing the optimization. The method may include a step in which the user selects the optimization method. The selection of the optimization method may be limited to a predefined list of optimization methods; i.e., the user may only select methods from this list. Since the optimization method used by the method is a gradient-based optimization method, the list may consist exclusively of gradient-based optimization methods. Gradient-based optimization methods are also known as "gradient methods," and the concept 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 in the present method may be any of the following methods (which may form the aforementioned list for user selection): gradient descent, stochastic gradient descent, coordinate descent, Frank-Wolf algorithm, Landweber iteration, random coordinate descent, conjugate gradient method, methods derived from conjugate gradient method, nonlinear conjugate gradient method, double conjugate gradient method, double conjugate gradient stabilized method, and moving asymptote method.

[0044] The one or more use and / or manufacturing performance indicators are data that define the underlying optimization problem, i.e., the optimization problem corresponds to optimizing the performance of the composite part represented by the CAD model with respect to the performance indicators. In other words, the performance indicators are data (e.g., mathematical expressions, such as mathematical functions and constraints (e.g., captured by an equation or system of equations)) that measure the performance to be achieved and / or adhered to after the composite part represented by the CAD model is manufactured. The performance is with respect to use and / or manufacturing, i.e., because the indicators are use and / or manufacturing performance indicators, the performance is the physical performance (e.g., behavior) of the composite part during use and / or manufacturing. The performance of a product during use refers to the physical behavior of a part with respect to a particular 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, for example, when the part is subjected to one or more loads (e.g., thermal forces, structural loads, or fluid flow). The performance of a part during manufacturing refers to the physical behavior of a part with respect to a particular manufacturing process for the part, such as whether the part conforms to the manufacturing process constraints and / or the specifications of the manufacturing tools that perform the process.

[0045] The one or more performance indicators include one or more objective functions. An objective function is a function whose value is to be optimized (i.e., minimized or maximized) by the optimization. The objective function measures the performance of the part with respect to product use and / or manufacturing, and has the CAD model or one or more CAD parameters as variables. The function outputs a large value when performance is achieved, in which case the function is maximized, or a small value when performance is achieved, in which case the function is minimized.

[0046] The performance of the one or more metrics may additionally or alternatively include one or more constraints. A constraint here is a mathematical expression (e.g., an equation or set of equations, or fixed values of parameters) that must be adhered to during optimization. A constraint captures the performance that a composite part must meet (i.e., required), such as a specified total amount of material in a product or adherence to tolerances of a manufacturing process or manufacturing tools. Optimization may optimize an objective function under the constraints, i.e., the optimization aims to find variable values that optimize the objective function while satisfying the constraints.

[0047] Examples of performance indicators (also called KPIs) in mechanical design that may be included in the method include maximizing stiffness, minimizing mass, minimizing stress, maximizing heat transfer coefficient, and optimizing eigenmodes.

[0048] The method may include, for example, when providing an optimization program, selecting, for example by a user, the performance indicators to optimize, for example from a list, which selection generates an objective function and / or constraints for the optimization.

[0049] The CAD parameter values are

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[0050] In addition to providing the input, the method includes modifying the initial values of one or more CAD parameters. Modifying the initial values of the one or more CAD parameters is also referred to as optimizing the one or more CAD parameters. In fact, this step finds or tends to find values of one or more CAD parameters that are free variables of the optimization and that optimize one or more objective functions and / or satisfy one or more constraints. Modifying the initial values therefore consists of optimizing the optimization program, i.e., running the optimization program's optimization algorithm to solve the underlying optimization problem.

[0051] As described above, the optimization uses a gradient-based optimization method. The optimization method has as free variables one or more CAD parameters whose values are changed to perform the optimization. Because the method is gradient-based, as is known in the optimization field, the optimization is performed using the sensitivity (i.e., approximation of the derivative) of the performance metric with respect to these variables. In other words, the CAD parameters are free variables of the optimization that the optimization method can change to optimize the performance metric (i.e., the optimization can change the values of the CAD parameters), and the sensitivity corresponds to the partial derivative of the metric being optimized with respect to the free variables. Note that when it is said that the values of one or more CAD parameters are changed by the optimization, not all of the CAD parameters may be changed. For example, the values of some CAD parameters may be fixed, while the values of other parameters, including or consisting of parameters that affect anisotropic material properties, have values that are free variables of the optimization. In this case, the method may include selecting (e.g., by a user) the CAD parameters whose values are free variables prior to the optimization, while the values of the other CAD parameters remain fixed during the optimization. Alternatively, all values of all parameters may be free variables of the optimization. The method may include calculating sensitivity and / or performance metrics before updating the CAD parameters in an optimization method.

[0052] The sensitivity is: - approximate derivatives of the performance index with respect to one or more material property fields, each material property field of said one or more material property fields representing a distribution of an anisotropic material property of said one or more anisotropic material properties; - approximate derivatives of each of the one or more material property fields with respect to each CAD parameter.

[0053] Each material property field corresponds to one of the material properties. That is, for each material property, there is one corresponding material property field. Each material property field is a distribution of scalar values, also called material property values or local material property values, that represent the distribution of the anisotropic material property (e.g., material orientation or thermal conductivity) to which the field corresponds. For example, for material orientation, the local property values may be the local XY (2D) or XYZ (3D) coordinates of the material orientation. The distribution of material property values is located on a mesh (2D or 3D mesh) in space (2D or 3D) that contains the geometric (e.g., outer surface) representation of the composite part. The mesh may be, for example, a mesh of volumetric or surface elements (e.g., tetrahedral / triangular, hexahedral, or regular cubic / square elements). In each material property field, each property value corresponds to each element of the mesh and indicates the value of the property for this element. Each value of a specific material property in each element of the mesh is also called a local material property value (i.e., the value of a specific material property) because it relates to the material property value in that element.

[0054] In an embodiment using a fiber material, such as the use case described below, the local property field M is encoded to have four values per element (corresponding to the four material anisotropy properties or property types): one value for the material density, two values for the rotation angle of the fiber orientation in 3D, and one value for the fiber ratio (i.e., the ratio of anisotropic fibers to isotropic material, which often models the bonding "glue" or "matrix" in which the fibers are made).

[0055] The CAD model may be formed by one or more CAD components, each CAD component corresponding to a region of space, i.e. forming part of the CAD model. In this case, the method comprises calculating one or more signed distance fields for each CAD component. For each material property field, each local material property value of that field is obtained from a weighted combination of material properties of the components of the CAD model, weighted by the signed distance to that local material property value. The one or more components may consist of several components.

[0056] Each signed distance field corresponds to a CAD component. The concept of a signed distance field is well known. A signed distance field is a distribution of signed distances for a particular geometry. In this case, each signed distance field corresponds to a component and forms a distribution of signed distance values, where each signed distance value corresponds to an element of a mesh and represents the signed distance between this element and the CAD component (or its geometric representation, e.g., an exterior surface representation on the mesh). In other words, a signed distance field for a component is a distribution of signed distance values on a mesh to the component, where the mesh contains the geometric (e.g., exterior) representation of the component (which may be part of the geometric representation of the entire composite part). Each signed distance value in this distribution corresponds to an element of the mesh and indicates the distance value (e.g., Euclidean distance, Manhattan distance, pixel distance) from this element to the (e.g., exterior) representation of the component. This value has one sign if the element corresponds to an interior part of the component and the opposite sign if the element corresponds to an exterior part of the component.

[0057] Each local material property value of a field is obtained from a weighted combination of the material properties of the components of the CAD model, weighted by the signed distance to that local material property value. For example, for each local material property and each element of the mesh, the local material property value of this element is equal to a weighted combination of the material property values of the components, weighted by the signed distance between the element and the component, or by a projection of the distance as described below. The weighted combination may be a weighted sum.

[0058] The method may include, for example, calculating signed distance fields and material property fields, as further described below, before updating the CAD parameters with the optimization method. This involves projecting the CAD model representation (i.e., on the mesh) into a set of scalar fields that encode the local material properties of each element of the mesh. As is known, the CAD model includes a geometric boundary representation on the mesh, which defines solid objects by hierarchically dividing space into regions or components with different material properties (see again Figures 1 and 2) (e.g., solid / empty, steel, wood, plastic, concrete, carbon fiber laminate, air, void). This projection defines the local material properties of each volume element in the mesh as the amount of material properties of neighboring components weighted by a nonlinear distance metric (signed distance). For example, referring to the use case shown in Figure 2, this process results in elements within a foam core component receiving low-stiffness isotropic material properties. Similarly, elements at the interface between the composite laminate and the foam core component receive a mix of low stiffness isotropic and high stiffness anisotropic material properties along the local orientation of the composite laminate. Mathematically, this projection is expressed as a mesh Ω, as known in the art. mesh component Ω of the tessellated representation of the CAD model on the elements of compis obtained by computing a linear signed distance field (SDF) to (see https: / / www2.imm.dtu.dk / pubdb / edoc / imm1289.pdf, which is incorporated herein by reference):

number

[0059] Each weight may 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 may be a smooth nonlinear Heaviside projection. The smooth nonlinear Heaviside function controls the smearing of material properties (see https: / / en.wikipedia.org / wiki / Heaviside_step_function, which is incorporated herein by reference). For this smearing step, any monotonically increasing, smooth approximation of the Heaviside function can be used instead of the Heaviside function. The weight H ij is given by (using smooth nonlinear Heaviside):

number

[0060] Each material property type

number

number

[0061] In the above, m ijk varies with i (index of the element), because in physical reality such dependencies may exist. For example, if component j is a sheet of composite material glued to the surface of a part, the composite fiber angle varies in space within the component (following the tangent to the surface), and therefore indeed depends on i. In other words, within component j, property k may be different for each element i.

[0062] Heaviside function H ij The local property M is a function of ik A different function for σ may be used instead. Optionally, the above formula may be modified to enforce bounds or additional scaling on the local properties if the directly determined local properties are outside the realizable physical range.

[0063] In embodiments using fiber materials, such as the use case described below, the local property field M is encoded to have four values per element (i.e., k=1...4): one value for material density, two values for the rotation angle of the fiber orientation in 3D, and one value for the fiber ratio (i.e., the ratio of anisotropic fibers to isotropic material, which often models the bonding "glue" or "matrix" from which the fibers are fabricated). However, depending on the type and characteristics of anisotropy employed, it is possible to use one value per element, a few values, or even more values. In alternative embodiments, many values may be used, as the constituent materials under consideration have independent coefficients (see https: / / pkel015.connect.amazon.auckland.ac.nz / SolidMechanicsBooks / Part_I / BookSM_Part_I / 06_LinearElasticity / 06_Linear_Elasticity_03_Anisotropy.pdf, which is incorporated herein by reference).

[0064] As mentioned above, for example, the above M i and H ij Calculating the signed distance field and material property fields by calculating the expressions for , may form a method step that occurs before changing the values of the CAD parameters, and may iteratively modify the CAD model in an optimization loop until some convergence criterion, number of optimization iterations, run time, and / or KPI score is reached. This step of calculating the fields is also referred to as "projection." Figure 4 shows a flowchart of an embodiment of the method, and more specifically, a flowchart of the steps following the step of providing inputs. The flowchart in Figure 4 shows the first step of the flowchart, the projection step.

[0065] In addition to projecting / calculating fields, and prior to updating the CAD parameter values, the method may include a step known as "simulation" (shown as the second step in the flowchart in FIG. 4), which calculates performance indicators, also known as KPIs, as previously described. The method may calculate some KPIs, such as the mass of a part, by summing the values of the KPIs for each element of a particular partition of the part. This may be the mass of each element of a particular partition or the entire structure. Other KPIs are more complex to calculate, and the method may calculate them by simulating the behavior of the composite part using finite element modeling, as known in the art. For example, calculating the deformation of a part under a load scenario may involve incorporating the local stiffness matrices of each element into a global stiffness matrix K for the entire mesh, and then solving a fundamental solution of equilibrium given by the following state equation:

number

[0066] The optimization of changing the values of the CAD parameters uses sensitivities, so the method may calculate sensitivities, which are approximations of the derivatives as described above, before updating the CAD parameter values.

[0067] The method may, for example, comprise a step of determining, after the simulation step and before updating the CAD parameters, an approximation of the derivative of the KPI with respect to the local property value of each element:

number

[0068] For example, in the case of a stiffness KPI, the orientation derivative value of elements within an isotropic component is practically equal to zero. This therefore reveals the fact that the local angle of the current element does not affect the deformation of the structure because this particular element is isotropic. Note that the projection step intentionally uses a strictly monotonically increasing and smooth Heaviside function, so the derivative is not exactly zero. In contrast, the local angle of elements within the composite laminate region of the structure can have a strong influence on the structural deformation in certain loading scenarios, which can be characterized by a large derivative value.

[0069] Since a continuous field representation of the components is used, these derivatives

number

number

[0070] The method may further include, for example, after the simulation step, before updating the CAD parameters. p About the characteristic field Mik Derivative of

number

number

[0071] For example, the CAD variables that control the profile of a wind turbine blade affect the shape of the cross section, but also the material orientation within the composite laminate, since they follow the shape and its curvature. These derivatives may be evaluated using finite difference methods, which allow for small perturbations h to each CAD parameter. p This is achieved by applying the following in sequence and observing the effect on the material property values:

number

[0072] The above formulation uses a central finite difference scheme, but forward or backward finite differences may also be used. Finite difference approximations are very stable and reliable for this purpose. This is because in practical and industrial applications, param <<Ω meshThis is explained by the fact that each CAD parameter typically affects the values of many mesh elements, since . Therefore, aggregating the contributions of multiple elements into a CAD parameter offsets the numerical inaccuracy of the finite difference approximation. Note that analytical derivatives of CAD systems are intractable for any non-trivial CAD model, so using approximations of the derivatives is advantageous.

[0073] Derivative

number

[0074] Once calculated, the geometric and physical derivatives may be combined using the chain rule. In other words, each sensitivity

number

number

[0075] The method then performs optimization using a gradient-based optimization method (e.g., a first-order gradient-based optimization scheme such as gradient descent, moving asymptote, augmented Lagrangian, Adam's method, or LBFGS) to change (update) the values of the CAD parameters to tend to reach the optimal value of the KPI, as known in the art. This is also referred to as "parameter update," shown in step 5 of FIG. 4.

[0076] Steps 1 through 5 (see FIG. 4), i.e., calculating fields (projection step), calculating KPIs (simulation step), calculating derivative approximations (geometric and physical), and updating CAD parameters, may be iterated, with the resulting CAD parameters (step 5) being used as input to the projection step (step 1) of the next iteration. In other words, the method may include providing inputs and then applying a gradient-based optimization method to change the values of the CAD parameters, which may consist of iterating steps 1 through 5 above, where step 5 uses the optimization method to update the parameters based on the sensitivities calculated as a result of the previous steps 1 through 4. This is shown in FIG. 4. This iterative process may converge in 10 to 100 iterations using gradient-based optimization.

[0077] The method outputs a CAD model in which the values of the CAD parameters have been optimized. The method may further include saving 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, e.g., saving the CAM file, where the CAM file serves as control instructions for setting up and / or executing a manufacturing process to produce the composite part. The method may also include sending such control instructions to a factory and / or executing a manufacturing process, in which case the method is for designing and manufacturing the optimized composite part. Alternatively, the method may be included in such a manufacturing process, but the method may not include a manufacturing step, even though manufacturing is an implicit use of the output of the method.

[0078] We now describe some use cases for the method, which illustrate the above-mentioned advantages of the proposed method.

[0079] First use case: L-bracket optimization This use case particularly illustrates the importance of simultaneously considering both geometry and anisotropic material properties in the coupled optimization formulation.

[0080] The CAD model provided in this use case represents the L-shaped bracket shown in Figure 5. The bracket is fixed at the top left and loaded toward the center and bottom right. The CAD model includes 20 CAD parameters that control the bracket's shape and consist of 10 sketch control points in 2D. The bracket consists of an isotropic core wrapped with a layer of surface conformal anisotropic fiber. The one or more material anisotropic properties here consist of a density property of the foam core and an angular property, fiber orientation, that depends on the bracket's shape and is therefore affected by the CAD parameters that control its shape. The one or more CAD components here consist of one component for the foam core and one component for the constant-thickness conformal fiber layer surrounding the foam core. The one or more use and / or manufacturing performance metrics consist of a use performance metric, stiffness, to be maximized, and a use performance metric, mass, to be minimized. The optimization program consists of an objective function that identifies these two metrics, formulating a weighting between stiffness maximization and mass minimization. Anisotropic material fibers are 25 times stiffer in the fiber direction than in other directions in the anisotropic material, or compared to the stiffness of the isotropic core. Optimizing the material orientation through control point optimization allows for stiffness optimization. Note that in this 2D example, the fiber orientation is constrained to lie in a plane. Also, the fibers are along the surface of the object, meaning their orientation is entirely determined by the shape of the object's outer contour.

[0081] Figure 6 shows a model optimized using an alternative optimization method, which ignores the material anisotropy derivatives in the chain rule. Figure 7 shows a model optimized using the proposed disclosure, which includes the material anisotropy derivatives and produces consistent derivatives. Apart from this difference in the use of derivatives, both optimization setups are identical. In the figure, short segments superimposed on the object's surface indicate the fiber orientation (gray shading is set directly from the XYZ components of the direction vector).

[0082] As can be seen, ignoring the material anisotropy derivative in the chain rule optimization creates sharp re-entrant corners at the boundaries of the design domain, a typical optimization result when optimizing stiffness using a strictly isotropic material. However, this design is far from optimal for anisotropic materials because the conformal fibers create sharp re-entrant corners, significantly reducing their load-bearing capacity (concave corners are not an issue because concaves concentrate stress and convexities distribute it). The optimization results obtained by this method demonstrate that the consistent derivative of anisotropy captures the non-optimality of the sharp re-entrant corners, and therefore, the optimization produces an optimized CAD model with much smoother, more continuous fiber orientation around the re-entrant corners. In other words, the claimed method can be used to obtain new and improved bracket designs with improved load-bearing capacity, and these new and improved parts can be manufactured based on the CAD models output by this method.

[0083] The claimed method can ensure that the optimized part consists of a foam core surrounded by a layer of fibrous material with a consistent thickness and a globally consistent tangent to the part surface. Therefore, in an industrial context, this type of design is typically manufactured by CNC (Computer Numerical Control) machining one or more foam blocks according to the shape of the foam core component. Sheets of fibrous material (e.g., fiberglass or carbon fiber) are then glued around the foam core to obtain a lightweight, strong, and inexpensively manufactured object. The method may include saving the optimized method as a file of control instructions (e.g., a CAM file) for performing such a manufacturing process and / or for executing this manufacturing process consisting of CNC machining and subsequent gluing. Note that for illustrative purposes, the use case is described in 2D, but in reality, the bracket has thickness and is a 3D object, and manufacturing occurs in 3D.

[0084] This comparative example highlights the advantage of our approach, as it mathematically and consistently includes nontrivial material interactions in physical models and allows these interactions to be traced back to CAD parameters. In this case, the CAD parameters affect the shape of the outer profile, which in turn affects the orientation and curvature of the conformal laminate sheets. These CAD parameters affect local fiber orientation, ultimately affecting the load-carrying capacity and overall mechanical performance of the object.

[0085] Second Use Case: 3D Wind Turbine Blade Optimization The second use case concerns the optimization of a 3D wind turbine blade. Figure 8 shows a cross section of a 3D wind turbine blade. The 3D wind turbine CAD model is defined by an outer profile with a prescribed geometry, derived from fluid dynamics considerations, and an internal stiffening structure that is the target of optimization under multiple load cases (torsion and bending). As shown in Figure 8, the material forming the blade is a composite sandwich structure consisting of a soft, lightweight foam core sandwiched between two outer anisotropic glass fiber sheets. Note that in a real industrial model, each sheet would have a stack of various orientation layers. However, for visualization purposes, the optimization results show a single fiber orientation per sheet. This is possible without loss of generality, since the method can capture the homogenized properties of one or more orientation layers for each element's anisotropic constitutive law. The initial design (i.e., the CAD model with initial values for the CAD parameters) is shown in Figure 9, which includes anisotropic and isotropic regions. The fiber orientations are visualized as short line segments for the anisotropic regions (gray shading indicates the X, Y, and Z components of the orientation vectors).

[0086] The CAD parameters to be optimized are as follows: First, one set of CAD parameters defines the fiber orientation of the outer sheets. This set of CAD parameters consists of four angles to be optimized. The geometry of the three interior sheets is controlled by a set of 22 geometric CAD parameters. The 26 selected CAD parameters allow optimization of the foam core thickness, shear web geometry, and fiber orientation throughout the model, resulting in one or more anisotropic material properties. Note that this type of composite structure is manufactured by placing foam blocks of various thicknesses, spreading the laminated sheets, and bonding them to the surface. Therefore, to be manufacturable using this manufacturing method, the shape of the sheets must be a developable surface (i.e., zero Gaussian curvature), and the fiber orientation must be entirely along that surface. This type of geometric manufacturing constraint is very difficult to enforce using topology optimization, but is relatively easy to optimize using the CAD representation enabled by this method. The one or more CAD components in this case consist of one component for the foam core, one component for the conformal composite sheets on the outer surface of the part, and three components for the three composite sheets on the inner surface of the part.

[0087] The performance metrics include two usage performance metrics: mass (to be minimized) and compliance, which is the inverse of stiffness (also to be minimized). These usage performance metrics may be captured in an optimization program by an objective function with the goal of minimizing both mass and compliance.

[0088] The CAD parameters of the model may further include CAD parameters that constrain the model to be manufacturable by applying the following constraints: the developability of the surface formed by the sheet geometry, and the fiber orientation must be generally aligned with the surface. These CAD parameters may consist of a set of known CAD operations (e.g., sketch, extrude, fillet). As explained above, these constraints on the CAD parameters of the CAD model enable the blade to be manufactured using the manufacturing method described above. This demonstrates the aforementioned advantage of being able to optimize CAD parameters while subjecting them to constraints to enhance the manufacturability of composite parts. In other words, while formulating compliance constraints, for example, with respect to KPIs, is practically infeasible, parameterization by CAD parameters allows these constraints to be easily enforced. This demonstrates a key advantage of directly optimizing CAD parameters as explained above: guaranteed manufacturability.

[0089] The optimization convergence history shows how the optimization smoothly altered the internal structure of the airfoil turbine blade, reducing both the mass and compliance of the design compared to the mechanical performance of the design with the initial CAD parameter values. This is shown in Figures 10 and 11. Comparing the fiber orientation of the optimized model to the initial design, as shown in Figure 12, shows that the design changed from a parallel fiber configuration to an orthogonal orientation, where the fibers are at 90 degrees to each other within the composite sandwich structure. Furthermore, Figure 12 also shows that the fiber orientation generally meets the constraint of following the optimized surface.

[0090] The output of the method is therefore a CAD model of the blade, with the four aforementioned angles and 22 geometric CAD parameters optimized to minimize the blade's mass and compliance while adhering to constraints that enforce the sheet shape as a developable surface and fiber orientation generally along the surface. This optimized design, efficiently achieved by the method, can be manufactured by a manufacturing process that involves laying out foam blocks of various thicknesses and then unfolding and bonding the laminated sheet to the surface. Such a process may be directly configured and controlled according to the optimized values of the CAD parameters. The manufactured part exhibits improved performance with respect to minimum mass and minimum compliance.

[0091] Third Use Case: Optimizing Wooden Frames The composite component in this study is a wooden frame supporting the downward load of the tabletop. The frame is modeled using a CAD model with 18 straight wooden beams, with the fibers aligned along the beam length. These beams are connected at spherical hubs made of isotropic plastic. The CAD parameters consist of the hub locations. The optimization therefore controls the location of these hubs, which indirectly influences the beam length and fiber orientation throughout the design space. The beam length and fiber orientation result in one or more anisotropic material properties. The one or more CAD components consist of one component for each wooden beam and one component for each isotropic plastic hub. The optimization program optimizes the performance indicators that describe the tabletop's response to load. Specifically, the three KPIs consist of minimizing mass, minimizing the tabletop's global absolute displacement (the tabletop must remain in the same position), and minimizing the tabletop's local displacement relative to its rest shape (the tabletop must maintain its original shape). Figure 13 shows the initial design, and Figure 14 shows the optimized frame structure.

[0092] However, if the aforementioned mobile morphable component (MMC) methods were used to perform this optimization, they would have the disadvantage of having difficulty handling the optimization of "hubs." Hubs are not geometrically well-defined because connected parts at the hub often overlap, and MMCs do not adequately capture the interactions between components. In contrast, CAD parameterization can enforce global consistency and consistent placement of geometric features.

[0093] Figure 15 shows (a) the initial configuration and the resulting deformations after (b) 5 and (c) 25 iterations of optimization using the proposed method. As can be seen, the optimized structure is not only more rigid, but also provides more uniform support for the tabletop.

[0094] The optimized wood frame structure can be manufactured by cutting multiple wooden beams to length for each beam component and fabricating a plastic hub (e.g., by plastic injection molding). The beams are then inserted into the hubs to assemble the entire structure, and finally fasteners are used to secure the assembly. The method may include storing a file containing such manufacturing process and / or the optimized model as manufacturing instructions and / or transmitting the file to a factory that will perform manufacturing.

[0095] The methods generally manipulate modeled objects, such as CAD models. A modeled object is any object defined by data stored, for example, in a database. Furthermore, the term "modeled object" also refers to the data itself. Depending on the type of system, the modeled object may be defined by different types of data. The system may in fact be any combination of a CAD system, a CAE system, a CAM system, a PDM system, and / or a PLM system. In these various systems, the modeled object is 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, and CAE data. However, these systems are not mutually exclusive; a modeled object may be defined by data corresponding to any combination of these systems. Thus, a system may be both a CAD, CAE, PLM, and / or CAM system, as is clear from the system definitions provided below.

[0096] A CAD solution (e.g., CAD system or CAD software) also refers to a system, software, or hardware, such as CATIA, adapted to design at least a modeled object based on a graphical representation of the modeled object and / or its structured representation (e.g., a feature tree). In this case, data defining the modeled object includes data that allows the modeled object to be represented. A CAD system may provide a representation of the CAD modeled object, for example, using edges and lines, and possibly faces and surfaces. Lines, edges, or surfaces may be represented in various ways, for example, Non-Uniform Rational B-Splines (NURBS). Specifically, a CAD file contains specifications based on which geometry, and thus a representation, can be generated. The modeled object specifications may be stored in one or more CAD files. Typical sizes of files representing modeled objects in CAD systems are in the range of one megabyte per part. A modeled object may also typically be a collection of thousands of parts.

[0097] In the context of CAD, a modeled object typically refers to a 2D or 3D modeled object, e.g., a product, such as a part or a collection of parts, or a collection of products. The 2D or 3D modeled object may also be a manufactured product, i.e., a manufactured product. A "3D modeled object" refers to any object modeled by data capable of a 3D representation. The 3D representation allows the part to be viewed from all angles. For example, a 3D representation of a 3D modeled object can be manipulated and rotated about any of its axes or about any axis in the display on which the representation is displayed. This specifically excludes 2D icons that are not 3D modeled. Displaying 3D representations facilitates design (i.e., statistically speeds up the speed at which designers accomplish tasks). Because product design is part of the manufacturing process, this expedites the manufacturing process in the industry.

[0098] The 2D or 3D modeled object represents the geometry of a product, such as a (e.g., mechanical) part, a collection of parts (or equivalently, a collection of parts, since a collection of parts may be viewed as a single part in terms of this disclosure, or the methods may be applied independently to each part of the collection), or more generally, any collection of rigid bodies (e.g., a moving mechanism), that is manufactured in the real world after completion of the virtual design using a CAD / CAE software solution, CAD / CAE system, etc. CAD / CAE software solutions enable the design of products in various industries, including, but not limited to, aerospace, architecture, construction, consumer goods, high-tech equipment, industrial equipment, transportation, marine, and / or offshore oil and gas production, or traffic. The 3D modeled objects designed by the present method may thus represent industrial products, which may be any mechanical part, such as ground vehicle parts (e.g., including automobile and light truck equipment, racing cars, motorcycles, trucks and motor equipment, trucks, buses, trains), air vehicle parts (e.g., including airframe equipment, aerospace equipment, propulsion equipment, defense products, airline equipment, space equipment), naval vehicle parts (e.g., including naval equipment, commercial vessels, offshore equipment, yachts and workboats, marine equipment), general mechanical parts (e.g., including industrial manufacturing machinery, large mobile machinery or equipment, installation equipment, industrial machinery products, fabricated metal products, tire manufacturing products), electromechanical parts, or electronic parts (e.g., including consumer electronics, security and / or control and / or instrumentation products, computing and communications equipment, semiconductors, medical devices and equipment), consumer products (e.g., including furniture, home and garden products, leisure products, fashion products, durable consumer goods retail products, textile retail products), packaging (e.g., including food and beverage and tobacco, beauty and personal care, household product packaging), etc.

[0099] CAD systems may be history-based. In this case, the modeled object is further defined by data containing the history of its geometric features. The modeled object may actually be designed by a real person (i.e., a designer / user) using standard modeling functions (e.g., extrude, revolve, cut, and / or round) and standard surfacing functions (e.g., sweep, blend, loft, fill, deform, and / or smooth). Many CAD systems that support such modeling functions are history-based. This means that the creation history of design features is preserved, typically through acyclic data flows that link said geometric features via input and output links. The history-based modeling paradigm has been well-known since the early 1980s. The modeled object is described by two persistent data representations: its history and a B-rep (i.e., a boundary representation). The B-rep is the result of the calculations defined in the history. The shape of the part displayed on a computer screen when the modeled object is represented is its B-rep (e.g., its tessellation). The part's history is the design intent. Essentially, history collects information about operations that a modeled object has performed. B-reps may be stored with history to allow for easy viewing of complex parts. History may also be stored with B-reps to allow for design changes to the part according to design intent.

[0100] A PLM system also means a system suitable for managing modeled objects that represent physically manufactured products (or products to be manufactured). In a PLM system, modeled objects are defined by data suitable for manufacturing the physical object. These may typically be dimensional values and / or tolerances. It is indeed better to have such values to manufacture the object correctly.

[0101] CAE solution refers to any software or hardware solution suitable for analyzing the physical behavior of a modeled object. A well-known and widely used CAE technique is the finite element model (FEM), hereafter also referred to as the CAE model. FEM typically involves dividing a modeled object into elements, or finite element meshes, and then calculating and simulating their physical behavior using equations. Such CAE solutions are offered by Dassault Systèmes under the registered trademark SIMULIA. Another growing CAE technology is the modeling and analysis of complex systems consisting of multiple components from various physical disciplines without CAD geometry data. CAE solutions enable simulation, allowing the optimization, improvement, and validation of manufactured products. Such CAE solutions are offered by Dassault Systèmes under the registered trademark DYMOLA. CAE may be used to ensure that various structural requirements (such as, but not limited to, mass, stiffness, strength, and durability) are achieved by new CAD models. Some of these requirements are also known as key performance indicators (KPIs). In many industrial products (e.g., cars, airplanes, consumer goods, high-tech products), these KPIs compete with each other: for example, low mass usually means low stiffness. Therefore, optimization methods are often applied to find the best trade-off between the KPIs.

[0102] CAM solution refers to any software or hardware solution suitable for managing a product's manufacturing data. Manufacturing data typically includes data related to the product to be manufactured, the manufacturing process, and the resources required. CAM solutions are used to plan and optimize the entire manufacturing process of a product. For example, they may provide CAM users with information about the feasibility, duration, or number of resources that can be used at a particular step in the manufacturing process, such as a specific robot, thus enabling decisions regarding management or necessary investments. CAM is a subsequent process following the CAD process and potentially the CAE process. For example, a CAM solution may provide information about machining and forming parameters consistent with an extrusion function provided in a CAD model. Such CAM solutions are offered by Dassault Systèmes under the registered trademarks CATIA, Solidworks, or DELMIA.

[0103] CAD and CAM solutions are therefore closely related. In fact, CAD solutions focus on designing products or parts, while CAM solutions focus on how to manufacture them. Designing a CAD model is the first step towards computer-aided manufacturing. In fact, CAD solutions offer important capabilities such as feature-based modeling and boundary representation (B-Rep) to reduce the risk of errors and loss of precision during the manufacturing process, which is handled by CAM solutions. In fact, CAD models are intended to be manufactured. Therefore, a CAD model is a virtual twin (also known as a digital twin) of the object to be manufactured, with two purposes: -Ensuring that manufactured objects function properly in a specific environment; and -Ensuring the manufacturability of manufactured objects.

[0104] PDM stands for Product Data Management. A PDM solution refers to any software or hardware solution suitable for managing all types of data related to a specific product. PDM solutions are primarily used by engineers, but may also be used by all stakeholders involved in the product lifecycle, including project managers, finance personnel, sales personnel, and buyers. PDM solutions are generally based on a product-oriented database. PDM solutions enable stakeholders to share consistent data about the product, thus preventing them from using inconsistent data. Such PDM solutions are offered by Dassault Systèmes under the registered trademark ENOVIA.

[0105] The modeled object optimized by the method may be, for example, a CAD model that includes or consists of a feature tree and / or B-rep. Such a model may be derived from a CAE model, for example, resulting from a CAE-to-CAD conversion process that the method includes as an initial step.

[0106] The CAD model is feature-based (e.g., includes a feature tree and, optionally, a corresponding B-rep obtained by executing the feature tree). The feature-based 3D model allows for the detection and automatic resolution of geometric errors in the CAD model, such as collisions, that affect the manufacturing process (e.g., during the determination of manufacturing or CAM files, as described below). A collision is the interpenetration of two parts of the 3D model, e.g., due to relative motion. Furthermore, this collision may only be detected by a finite element analysis based on the CAD feature-based model. Thus, by iteratively changing the parameters of the features and running a finite element analysis, collision resolution can be performed with or automatically by the CAD solution.

[0107] As another example, feature-based 3D models can be used to automatically create machine tool paths via computer numerical control (CNC) (e.g., during the determination of manufacturing or CAM files, discussed below). In CNC, each manufactured object is assigned a custom computer program that is stored and executed on a machine control unit, a microcomputer connected to the machine. The program contains the instructions and parameters that the machine tool follows. Mills, lathes, routers, grinders, and lasers are some common examples of machine tools whose operations can be automated using CNC.

[0108] A key feature of CAD models is that they can be precisely and unambiguously designed by chaining together a small number of high-level, parameterized design operations (e.g., including but not limited to, sketching, extruding, chamfering, etc.), and can be edited by modifying the high-level parameters. This is their main difference from polyhedral representations, such as triangular surface meshes, which can represent any 3D shape but do not offer the modification or parameterization capabilities required in the context of industrial design.

[0109] Because CAD models are parameterized models of parts / products, they have a lighter memory footprint than other models, such as CAE models. Indeed, instead of storing a collection of discrete geometric elements, such as finite elements, CAD models can store lists of features and parameters, which are lighter in terms of storage and memory footprint. Working with CAD models not only increases the editability of the model compared to, for example, CAE models, but also reduces the memory requirements of the underlying system. In other words, the CAE-to-CAD conversion process not only converts the CAE model into a CAD model that is more easily editable, but also compresses the CAE model into a CAD model that is lighter in terms of memory requirements (e.g., footprint).

[0110] The generation of custom computer programs from CAD files may be automated. Such generation can therefore be guaranteed to be error-free and to perfectly replicate the CAD model into the manufactured product. CNC is believed to be capable of achieving greater precision, complexity, and repeatability than manual machining. Other advantages include increased accuracy, speed, and flexibility, as well as capabilities such as contouring, which allows milling of contoured shapes, including those created in 3D designs.

[0111] A B-rep (boundary representation) is a 3D representation of a mechanical part. Specifically, a B-rep is a persistent data representation that describes a 3D modeled object that represents the mechanical part. A B-rep may be the result of a calculation and / or a series of operations performed during the design phase of the 3D modeled object that represents the mechanical part. The shape of the mechanical part that appears on a computer screen when the modeled object is rendered is a B-rep (e.g., its tessellation). In one example, a B-rep represents a portion of the modeled object.

[0112] B-Rep contains topological and geometric entities. Topological entities are faces, edges, and vertices. Geometric entities are 3D objects such as surfaces, planes, curves, lines, and points. By definition, a face is a bounded portion of a surface, called a support surface. An edge is a bounded portion of a curve, called a support curve. A vertex is a point in 3D space. They are related to each other as follows: A bounded portion of a curve is defined by two points (vertices) on the curve. A bounded portion of a surface is defined by its boundary, which is a set of edges on the surface. The boundary edges of a face are connected by sharing a vertex. Faces are connected by sharing an edge. Two faces are adjacent if they share an edge. Similarly, two edges are adjacent if they share a vertex. In a CAD system, a B-Rep model collects, in an appropriate data structure, the "bounding" relationships, the relationships between topological entities and support geometry, and a mathematical description of the support geometry. By definition, an interior edge of a B-Rep is an edge that is shared by exactly two faces. By definition, a boundary edge is not shared and bounds only one face. By definition, a boundary face is bounded by at least one boundary edge. A B-Rep is said to be closed if all its edges are interior edges. A B-Rep is said to be open if it contains at least one boundary edge. Closed B-Reps are used to model 3D volumes, as they define the interior portion of a space that (virtually) surrounds a material. Open B-Reps are used to model 3D skins, which are 3D objects whose thickness is negligibly small.

[0113] The main advantage of B-Rep over other representation types used in CAD modeling is its ability to accurately represent any shape. All other representations, such as point clouds, distance fields, and meshes, are approximations of the represented shape through discretization. B-Rep, on the other hand, contains surface equations that represent the exact design, thus constituting a true "master model" for further manufacturing, such as generating CNC tool paths or discretizing to the correct sample density for a specific 3D printer technology. In other words, with B-Rep, the 3D model can be an accurate representation of the manufactured object. B-Rep is also advantageous when simulating the behavior of the 3D model. For stress, thermal, and electromagnetic analyses, it supports local refinement of the simulation mesh to capture physical phenomena, and for kinematics, it supports true contact modeling between surfaces. Finally, B-Rep allows for a small memory and / or file footprint. This is primarily because the representation contains only parametric surfaces. With other representations, such as meshes, the equivalent surface can contain up to thousands of triangles. Second, B-Rep does not contain any historical base information.

[0114] The method may be included in a production / manufacturing process, which may include, after performing the method, manufacturing a physical product corresponding to the modeled object (CAD model) optimized by the method. The production process may include the following steps: - applying the method (e.g. automatically) and thereby obtaining an optimized CAD model output by the method; - Manufacture parts / products using the acquired CAD model.

[0115] Using a CAD model for manufacturing refers to a real-world action or series of actions related to or participating in the manufacturing of a part represented by the CAD model. Using a CAD model for manufacturing may include, for example, one or more of the following steps:

[0116] - Editing the obtained optimized CAD model; - performing simulations based on the CAD model or the corresponding CAE model (e.g. the CAE model from which the CAD model was derived after the CAE-to-CAD conversion process), such as simulations for the validation of mechanical, use and / or manufacturing properties and / or constraints (e.g. structural simulation, thermodynamic simulation, aerodynamic simulation); - Edit the CAD model based on the results of the simulation; - optionally (i.e. depending on the manufacturing process used, the manufacturing of the mechanical product may or may not include this step), (e.g. automatically) determining a manufacturing file / CAM file (e.g. containing manufacturing instructions and / or control instructions for the manufacturing process and / or control instructions for instructing the manufacturing process or its manufacturing tools) based on the (e.g. edited) CAD model (e.g. the control instructions originate from the CAD model and / or a CAD file storing the specifications of the CAD model) for the production / manufacturing of the manufactured product; - Sending CAD and / or manufacturing / CAM files to factories for the purpose of manufacturing the products represented by the CAD models; and / or - Based on the determined manufacturing files / CAM files or CAD models, (e.g., automatically) produce / manufacture the machine product originally represented by the model output by the method. This may include (e.g., automatically) feeding the manufacturing files / CAM files and / or CAD files to a machine that performs the manufacturing process.

[0117] This final step of production / manufacturing is also called the manufacturing or production step. In this step, the CAD model and / or CAD file are fed to one or more manufacturing machines or computer systems that control the machines to produce / machine the part / product based on the CAD model and / or CAM file. The manufacturing step may include performing any known manufacturing process or series of manufacturing processes, such as one or more additive manufacturing steps, one or more cutting steps (e.g., laser cutting or plasma cutting), one or more stamping steps, one or more forging steps, one or more bending steps, one or more deep drawing steps, one or more forming steps, one or more machining steps (e.g., milling), and / or one or more punching steps. This design method improves the design of the model (CAE or CAD) representing the part / product, thereby improving manufacturing and its productivity.

[0118] Editing a CAD model may involve a user (i.e., a designer) performing one or more edits to the CAD model, for example, using a CAD solution. A change to a CAD model may include one or more changes to each of the CAD model's geometry and / or parameters. A change may include any change or series of changes performed to the model's feature tree (e.g., changes to feature parameters and / or specifications) and / or changes performed to the displayed CAD model representation (e.g., B-rep). A change is a change that maintains the technical functionality of the part / product; i.e., a user performs changes that may affect the model's geometry and / or parameters, but only to make the CAD model more technically compliant for downstream use and / or manufacturing of the part / product. Such changes may include any change or series of changes that make the CAD model technically compliant with the specifications of a machine used in a downstream manufacturing process. Such changes may additionally or alternatively include a change or series of changes that make the CAD model technically compliant for further use in a manufactured product / part, where such a change or series of changes is based, for example, on the results of a simulation.

[0119] The CAM file may include a manufacturing setup model obtained from a CAD model. The manufacturing setup may include all data necessary to manufacture the machined product such that a geometry and / or material distribution corresponding to that captured by the CAD model is realized, possibly up to manufacturing tolerances. Determining the production file may include applying a CAM (Computer-Aided Manufacturing) or CAD-to-CAM solution (e.g., any automatic CAD-to-CAM conversion algorithm) to (e.g., automatically) determine the production file from the CAD model. Such a CAM or CAD-to-CAM solution may include one or more of the following software solutions capable of automatically generating manufacturing instructions and tool paths for a specific manufacturing process based on a CAD model of the product to be manufactured: -Fusion360, -FreeCAD, -CATIA, -SOLIDWORKS, - Dassault Systèmes' NC Shop Floor Programmer, as described at https: / / my.3dexperience.3ds.com / welcome / fr / compass-world / rootroles / nc-shop-floor-programmer - Dassault Systèmes' NC Mill-Turn Machine Programmer, as described at https: / / my.3dexperience.3ds.com / welcome / fr / compass-world / rootroles / nc-mill-turn-machine-programmer, and / or - Dassault Systèmes' Powder Bed Machine Programmer, as described at https: / / my.3dexperience.3ds.com / welcome / fr / compass-world / rootroles / powder-bed-machine-programmer.

[0120] The product / part may be an additively manufactured part, i.e., a part manufactured by additive manufacturing (e.g., 3D printing). In this case, the manufacturing process does not include a step of determining a CAM file, but instead 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 receive a CAD model representing the mechanical product (e.g., when the 3D printer operator initiates 3D printing) and directly and automatically 3D print the mechanical product according to the CAD model. In other words, the 3D printer receives (e.g., automatically) the CAD model, reads (e.g., automatically), and prints the part by adding material layer by layer to reproduce the geometry and / or material distribution captured by the CAD model. The 3D printer adds material to accurately reproduce the geometry and / or material distribution captured by the CAD model in reality, up to the resolution of the 3D printer, with or without optional tolerances and / or manufacturing corrections. Manufacturing may include, for example, determining such manufacturing modifications and / or tolerances by a user (e.g., an operator of the 3D printer) or automatically (e.g., by the 3D printer or a computer system controlling it), e.g., modifying the CAD file to match the specifications of the 3D printer. The manufacturing process may additionally or alternatively include determining (e.g., automatically by the 3D printer or a computer system controlling it) from the CAD model, for example, the print direction to minimize the amount of overhang (as described in EP 3327593, which is incorporated herein by reference), layer slicing (i.e., the thickness of each layer, the path / trajectory for each layer, and other characteristics of the 3D printer head (e.g., in the case of a laser beam, the path, speed, intensity / temperature, and other parameters)).

[0121] The product / part may be a machined part (i.e., a part manufactured by machining), for example, a milled part (i.e., a part manufactured by milling). In such a case, the manufacturing process may include a step of determining a CAM file. This step may be performed automatically by any suitable CAM solution that automatically derives the CAM file from a CAD model of the machined part. Determining the CAM file may include (e.g., automatically) checking whether the CAD model has geometric peculiarities (e.g., errors or artifacts) that may affect the manufacturing process and (e.g., automatically) correcting such peculiarities. For example, if the CAD model still contains sharp edges, machining or milling based on the CAD model may not be performed (because the machining or milling tool cannot create sharp edges). In such a case, determining the CAM file may include (e.g., automatically) rounding or filleting such sharp edges (e.g., with a rounding or filleting radius that corresponds to the radius of the cutting head of the machining tool, e.g., approximately equal to a tolerance), thereby allowing machining or milling based on the CAD model to be performed. More generally, determining the CAM file may automatically include rounding or filleting any geometry in the CAD model that does not correspond to the radius of the machining or milling tool to allow for machining / milling. This check and possible corrections (e.g., rounding or filleting geometry) may be performed automatically as described above, or the user (e.g., a machining engineer) may manually perform the corrections in the CAD and / or CAM solution, such as a solution that constrains the user to make modifications to make the CAD model conform to the specifications of the tool used in the machining process.

[0122] In addition to checking, determining the CAM file may also include (e.g., automatically) determining a machining path or milling path, i.e., the path the machining tool will follow to machine the product. The path may include a set of coordinates and / or a parameterized trajectory followed by the machining tool for machining, and determining the path may include (e.g., automatically) calculating these coordinates and / or trajectory based on a CAD model. This calculation may be based on calculating the boundaries of a Minkowski subtraction of the CAD model with a CAD model representation of the machining tool, as described, for example, in European Patent Application EP 21306754.9 filed December 13, 2021 by Dassault Systèmes (incorporated herein by reference). It is understood that the path may be a single path, e.g., a path that the tool follows continuously without interrupting contact with the material being cut. Alternatively, the path may be a concatenation of a series of sub-paths that the tool follows in a specific order, e.g., each sub-path that the tool follows continuously without interrupting contact with the material being cut. Optionally, determining the CAM file may include (e.g., automatically) setting machine parameters such as cutting speed, cutting / piercing height, and / or die opening stroke based on the determined path and machine specifications, etc. Optionally, determining the CAM file may include (e.g., automatically) configuring nesting, in which the CAM solution determines the optimal orientation of the part to maximize machining efficiency.

[0123] In this case, for machined or milled parts, determination of the CAM file generates and outputs a CAM file containing the machining path and, optionally, the set machine parameters and / or the configured nest specifications. This output CAM file may then be (e.g., directly and automatically) sent to a machining tool, and / or the machining tool may then be (e.g., directly and automatically) programmed by reading the file, such that the production process includes a production / manufacturing step in which a machine performs machining of the product according to the production file, e.g., by directly and automatically executing the production file. The machining process includes cutting an actual block of material with a machining tool to reproduce the geometry and / or distribution of the material captured by the CAD model, e.g., to a tolerance (e.g., tens of microns in the case of milling).

[0124] Alternatively, the product / part may be a molded part, i.e., a part produced by molding (e.g., injection molding). In such cases, the manufacturing process may include a step of determining a CAM file. This step may be performed automatically by any suitable CAM solution that automatically derives the CAM file from a CAD model of the molded part. Determining the CAM file may include (e.g., automatically) performing a series of molding checks based on the CAD model to check whether the geometry and / or distribution of material captured by the CAD model is mold-compatible, and (e.g., automatically) performing appropriate modifications if the CAD model is not mold-compatible. The checks and appropriate modifications (if any) may be performed automatically, or may be performed by a CAD and / or CAM solution that allows a user (e.g., a molding engineer) to perform appropriate modifications to the CAD model, but constrains the user to modify the CAD model to conform to the molding tool specifications, for example. The checks may include verifying that the virtual product represented by the CAD model matches the dimensions of the mold and / or verifying that the CAD model includes all draft angles required for the product to be removed, as known from the mold itself. Determining the CAM file may further include determining, based on the CAD model, the amount of liquid material to use for molding and / or the time for the liquid material to cure / solidify in the mold, and outputting a CAM file containing these parameters. The manufacturing process then includes (e.g., automatically) performing molding based on the output file, where the mold molds the liquid material over the determined cure time into a shape that corresponds to the geometry and / or distribution of the material captured by the CAD model, for example, to a tolerance (e.g., incorporating or correcting a draft angle for ejection from the mold).

[0125] Alternatively, the product / part may be a pressed part (also called a "pressed part"), i.e., a part produced by a pressing process. In this case, the manufacturing process may include (e.g., automatically) determining a CAM file based on a CAD model. The CAD model represents the pressed part, e.g., when the part includes a flange, possibly including one or more flanges, and optionally, in this latter case, excess material has been removed to form an expanded state of one or more flanges of the part, as is known in pressing per se. The CAD model thus includes a portion representing the part without a flange (possibly the entire part), and possibly an outer additional patch portion (if any) representing the flange (if any), and possibly with additional material (if any). This additional patch portion may exhibit g2 continuity over a certain length, and then g1 continuity over a certain length.

[0126] In this case, determining the CAM file may include (e.g., automatically) determining the parameters of the press machine, such as the size and / or press force of the press die or punch, based on the geometry and / or material distribution of the virtual product captured by the CAD model. If the CAD model also includes a representation of excess material to be removed to form the expanded state of one or more flanges of the part, the removed excess material may be cut, for example, by machining, and determining the CAM file may include determining a corresponding machining CAM file, for example, as described above. If there are one or more flanges, determining the CAM file may include determining geometric specifications for the g2 continuity and g1 continuity portions that enable the flanges to be folded along the g2 continuity length toward the inner surface of the pressed part in the folding process after the pressing itself and the removal of the excess material. The CAM file thus determined may include the parameters of the press tool, optionally the above specifications for folding the flanges (if any), and optionally a machining production file for removing the excess material (if any).

[0127] The stamping manufacturing process may then, for example, directly and automatically output a CAM file and (e.g., automatically) perform a stamping process based on that file. The stamping process may include stamping (e.g., punching) a portion of material to form a product represented in the CAD file, possibly with an unfolded flange and excess material (if any). Where appropriate, the stamping process may include cutting off excess material based on the machining production file and folding the flange based on the flange folding specifications, thereby folding the flange at a g2 continuous length and giving the outer boundary of the part a smooth appearance. In the latter case, the shape of the manufactured part differs from the virtual shape represented by the CAD model in that the excess material has been removed and the flange has been folded, while the CAD model represents the part with the excess material and the flange unfolded.

[0128] The method is computer-implemented, meaning that the steps (or substantially all steps) are performed by at least one computer or any similar system. The method steps may thus be performed fully automatically or semi-automatically by a computer. In one example, at least some of the method steps may be triggered via user-computer interaction. The level of user-computer interaction required may depend on the level of automation envisioned, balancing the need to implement user wishes. In one example, this level may be user-defined and / or predefined.

[0129] A typical example of a computer implementation of the method is to carry out the method using a system suitable for this purpose. The system may include a processor connected to a memory having a computer program recorded thereon, the computer program including instructions for carrying out the method, and a graphical user interface (GUI). The memory may store a database. The memory is any hardware suitable for such storage, and may optionally include several physically distinct parts (e.g., one for the program and optionally one for the database).

[0130] FIG. 16 shows an example of this system, which is a client computer system, such as a user's workstation.

[0131] The client computer in this example includes a central processing unit (CPU) 1010 connected to an internal communication bus 1000, and a random access memory (RAM) 1070 also connected to the bus. The client computer further includes 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 in the art as a frame buffer. A mass storage controller 1020 manages access to mass storage devices, such as a hard drive 1030. Mass memory devices suitable for embodying computer program instructions and data include all forms of non-volatile memory, including, by way of example, semiconductor memory devices such as EPROM, EEPROM, and flash memory devices, magnetic disks, such as internal hard disks and removable disks, and magneto-optical disks. Any of the foregoing may be supplemented by, or incorporated into, specially designed ASICs (application-specific integrated circuits). A network adapter 1050 manages access to a network 1060. The client computer may also include a cursor control device, a keyboard, or other tactile device 1090. A cursor control device is used within the client computer to allow a user to selectively position a cursor at any desired location on the display 1080. Furthermore, the cursor control device allows a user to select various commands and input control signals. The cursor control device includes a number of signal generating devices for inputting control signals into the system. Typically, the cursor control device may be a mouse, with the buttons on the mouse being used to generate the signals. Alternatively, or additionally, the client computer system may include a sensitive pad and / or a sensitive screen.

[0132] The computer program may include computer-executable instructions, which include means for causing the system to perform the method. The program may be recordable on any data storage medium, including the system's memory. The program may be implemented, for example, in digital electronic circuitry, or computer hardware, firmware, software, or a combination thereof. The program may also be implemented as an apparatus, such as an article of manufacture tangibly embodied in a machine-readable storage device for execution by a programmable processor. The method steps may be performed by a programmable processor executing a program of instructions and performing the functions of the process by manipulating input data and generating output. Thus, the processor may be programmable to receive data and instructions from, or be coupled to, a data storage system, at least one input device, and at least one output device. The application program may be implemented in a high-level procedural or object-oriented programming language, or in assembly or machine language as appropriate. In either case, the language may be a compiled or interpreted language. The program may be a full installation program or an update program. In either case, instructions for performing one or more of the methods may be obtained by applying the program to a system. Alternatively, the computer program may be stored and executed on a server in a cloud computing environment, the server communicating with one or more clients over a network, in which case the processor executes the instructions contained in the program, thereby causing the method to be performed in the cloud computing environment.

Claims

1. 1. A computer-implemented method for optimizing one or more anisotropic material properties of a composite part, comprising: a CAD model representing a composite part, the CAD model including a feature tree having one or more CAD parameters, each having an initial value, at least one CAD parameter affecting the one or more anisotropic material properties of the composite part; an optimization program identified 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 Varying the initial values of the one or more CAD parameters by solving the optimization program using a gradient-based optimization method, the optimization method having the one or more CAD parameters as free variables, the optimization method using sensitivities, each sensitivity being an approximation of a derivative of a performance index with respect to a respective CAD parameter, the sensitivities being: approximate derivatives of the performance index with respect to one or more material property fields, each material property field 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 approximate derivatives of each of the one or more material property fields with respect to each CAD parameter; A method comprising:

2. The CAD model is formed by one or more CAD components, each corresponding to a region of space, and the method includes calculating one or more signed distance fields for each CAD component, and for each material property field, each local material property value of that field is obtained from a weighted combination of material properties of the components of the CAD model, weighted by the signed distance to that local material property value.

2. The method of claim 1.

3. Each weight corresponds to a projection of the signed distance value of a component by a function that maps [−∞; +∞] to [0; 1] and has a well-defined first derivative, optionally a smooth Heaviside projection.

3. The method according to claim 2.

4. The weighted combination is a weighted sum The method according to any one of claims 2 to 3, characterized in that 【Request 5】 【Number 23】 holds, where M ｉｋ is the mesh Ω of the CAD model ｍｅｓｈ of said one or more properties at element i of ｔｙｐｅ the local material property value of property k in the ｃｏｍｐ is the set of all components, H ｉｊ is the weight, m ｉｊｋ is the material property of the component 5. The method according to claim 4. 【Request 6】 【Number 24】 where α≧0 is the steepness factor of the smooth Heaviside projection, l is the average size of elements in the mesh, and the SDF ｉｊ is the signed distance value from element i to component j 6. The method according to claim 5.

7. approximate derivatives of each of the one or more material property fields with respect to each CAD parameter [Equation 25] teeth, [Equation 26] where CAD is of the type ｐ is each CAD parameter, h ｐ >0 is a small perturbation, Ω ｐａｒａｍ is the set of CAD parameters 7. The method according to claim 5 or claim 6.

8. Each sensitivity [0000] teeth, [0000] is of type, where Ω ｐｅｒｆｏ is a set of performance indicators 8. The method according to claim 7.

9. The one or more components may consist of several components. The method according to any one of claims 2 to 8, characterized in that

10. The one or more anisotropic material properties consist of several anisotropic material properties. The method according to any one of claims 1 to 9, characterized in that

11. The at least one CAD parameter affecting the one or more anisotropic material properties of the composite part satisfies a manufacturing process constraint for producing the composite part. The method according to any one of claims 1 to 10, characterized in that

12. A CAD model obtained by the 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 carry out the method according to any one of claims 1 to 11.

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

15. A computer system including a processor connected to a memory in which the computer program of claim 13 and / or the CAD model of claim 12 is stored.

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