Designing Mechanical Parts Using Topology Optimization

Abstract

The present invention particularly relates to a computer-implemented method for designing a modeled object. The method includes providing a finite element mesh, data associated with the finite element mesh, and a non-uniform distribution of one or more local quantitative constraints. The data associated with the finite element mesh includes forces, boundary conditions, parameters, and global quantitative constraints. The method also includes performing topology optimization based on the finite element mesh, the data associated with the finite element mesh, and the non-uniform distribution. The method improves the design of a modeled object representing a mechanical part through topology optimization.

Description

Technical Field

[0001] The present invention relates to the field of computer programs and systems, and more particularly to methods, systems and programs for designing modeling objects representing mechanical parts. Background Art

[0002] There are many systems and programs available on the market for the design, engineering and manufacturing of objects. CAD is the abbreviation for computer-aided design, for example, it refers to software solutions for designing objects. CAE is the abbreviation for computer-aided engineering, for example, it refers to software solutions for simulating the physical behavior of future products. CAM is the abbreviation for computer-aided manufacturing, for example, it refers to software solutions for defining manufacturing processes and operations. In such computer-aided design systems, graphical user interfaces play an important role in the efficiency of the technology. These technologies can be embedded in product lifecycle management (PLM) systems. PLM refers to business strategies that help companies share product data, apply common processes, and leverage corporate knowledge throughout the concept of the extended enterprise to develop products from concept to end of life. PLM solutions provided by Dassault Systèmes (trademarks CATIA, ENOVIA and DELMIA) provide an Engineering Center (for organizing product engineering knowledge), a Manufacturing Center (for managing manufacturing engineering knowledge), and an Enterprise Center (for enabling companies to integrate and connect engineering and manufacturing centers). Together, the system provides an open object model that links products, processes, resources together to enable knowledge-based dynamic product creation and decision support to drive optimized product definition, manufacturing preparation, production and service.

[0003] Some of these systems provide functionality that employs topology optimization. Topology optimization is a computer-implemented technique that bridges the fields of product design and physical simulation. It is used to design modeled objects that represent mechanical parts formed with materials, subjected to loads in use, and having one or more constraint boundaries. The technique focuses on automatically generating optimized generative designs based on modifying physical properties and behaviors typically simulated by finite element analysis (FEA). More specifically, topology optimization works by providing a finite element mesh (FEM), such as by discretizing the design space in small elements and data associated with the mesh. The technique then finds the optimal distribution and layout of material in a given discrete space by iteratively finding the most efficient elements with respect to a given objective function (e.g., related to the stiffness of the design) and a set of constraints (e.g., related to the total amount of material allowed).

[0004] In this context, there is a need for an improved solution for designing a modeled object representing a mechanical part formed of a material, subjected to loads in use, and having one or more constraint boundaries. Summary of the invention

[0005] Therefore, a computer-implemented method for designing a modeled object is provided. The modeled object represents a mechanical part. The mechanical part is formed of a material. The mechanical part is subjected to a load in use, and the mechanical part has one or more constraint boundaries. The method includes providing a finite element mesh, data associated with the finite element mesh, and a non-uniform distribution of one or more local quantitative constraints. The data associated with the finite element mesh includes forces, boundary conditions, parameters, and global quantitative constraints. The forces represent portions of the loads. The boundary conditions represent at least portions of the one or more constraint boundaries. The parameters are related to the material. The global quantitative constraints are relative to the global quantitative of the material in the finite element mesh. Each local quantitative constraint of the non-uniform distribution is relative to the corresponding local quantitative of the material in the corresponding local region of the finite element mesh. The method also includes performing topology optimization based on the finite element mesh, the data associated with the finite element mesh, and the non-uniform distribution.

[0006] The method forms an improved solution for designing a modeled object, the modeled object representing a mechanical part formed of a material, subjected to loads in use and having one or more constraint boundaries. It is noteworthy that, based on the finite element mesh and the data associated with the finite element mesh, the method performs a topology optimization, thereby achieving a design optimized from a mechanical point of view given constraints relative to the global material quantity in an efficient manner. In particular, the method produces an optimization result for the portion of the loads that the mechanical part is subjected to in use and represented by the forces included in the data associated with the mesh. In addition, the method provides for integrating one or more local material quantity constraints into the topology optimization, thereby allowing the local material quantity and its mechanical effect to be controlled in each local area with respect to such local constraints. In addition, since the distribution of the one or more local quantity constraints is non-uniform, the method allows for the differentiation of the mechanical effects by location. Therefore, the one or more local material quantity constraints provide a means to compensate for the fact that the forces contained in the data associated with the mesh cannot and do not represent all the loads that the mechanical part is subjected to in use. In particular, the method can improve mechanical robustness in view of future actual loads that will be applied to the mechanical part but will not be directly integrated as forces in the formulation of the topology optimization problem.

[0007] The method may include one or more of the following:

[0008] Each local quantitative constraint represents a respective upper limit for the respective local quantitative;

[0009] The mesh has a set of elements, each element has a corresponding relative density of a material that varies during iterations of the topology optimization, the non-uniform distribution includes a plurality of local quantitative constraints, each local quantitative constraint is on a corresponding element, a corresponding local region of each corresponding local quantitative constraint is a corresponding neighborhood of the corresponding element, and a corresponding local quantitative of each corresponding neighborhood is a corresponding average value of the material in the corresponding neighborhood;

[0010] The method includes aggregating the plurality of local volume constraints into a single aggregate constraint;

[0011] The aggregate constraint represents a constant bound defining an extreme value of a difference between the respective means and the respective upper bound on a set of elements;

[0012] The extremum is a maximum value, and the aggregate constraint approximates the maximum value with a differentiable function, and performing the topology optimization includes performing a gradient-based optimization;

[0013] The differentiable function is a P-norm;

[0014] The gradient-based optimization is a method of moving asymptotes;

[0015] The method includes, before performing the topology optimization: performing another topology optimization based on the finite element mesh and data associated with the finite element mesh, and determining a non-uniform distribution based on a result of the another topology optimization;

[0016] The result of the another topology optimization includes a density field, a strain field, a stress field and / or a compression field, and determining the non-uniform distribution includes automatically determining one or more local quantitative constraints based on the density field, the strain field, the stress field and / or the compression field, and / or displaying a graphical representation of the density field, the strain field, the stress field and / or the compression field, and determining the one or more local quantitative constraints via user interaction; and / or

[0017] The mechanical part is an additively manufactured part having one or more functional outer regions and one or more inner regions and / or a vehicle part.

[0018] Also provided is a modeling object that can be designed or obtained by the method. Due to the non-uniform distribution of one or more local quantitative constraints, each local quantitative constraint in a corresponding local area of ​​the finite element mesh relative to the corresponding local quantitative of the material, the modeling object exhibits a non-uniform distribution / layout of porous, alveolar, and / or complex structures, for example, an organic appearance with a varying material / void ratio.

[0019] A computer program is also provided, comprising instructions for executing the method.

[0020] A computer-readable storage medium having recorded thereon a modeling object and / or a computer program is also provided.

[0021] A system is also provided that includes a processor coupled to a memory having recorded thereon a modeling object and / or a computer program and a graphical user interface. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Embodiments of the invention will now be described by way of non-limiting examples and with reference to the accompanying drawings, in which:

[0023] Figure 1 An example of a system is shown; and

[0024] Figure 2-Figure 20 The method is shown. DETAILED DESCRIPTION

[0025] The method is computer-implemented. This means that the steps (or substantially all steps) of the method are performed by at least one computer or any similar system. Therefore, the steps of the method can be performed by a computer, which may be fully automatic, or semi-automatic. In an example, the triggering of at least some steps of the method can be performed by user-computer interaction. The required level of user-computer interaction may depend on the foreseen level of automation and be balanced with the need to implement the user's wishes. In an example, the level can be user-defined and / or predefined.

[0026] A typical example of a computer implementation of a method is to perform the method using a system suitable for this purpose. The system may include a processor and a graphical user interface (GUI) coupled to a memory, on which a computer program is recorded, the computer program including instructions for performing the method. The memory may also store a database. The memory is any hardware suitable for such storage, and may include several physically distinct parts (e.g., a part for the program, and a part that may be used for the database).

[0027] The method generally manipulates modeling objects. A modeling object is any object defined by data stored, for example, in a database. By extension, the expression "modeling object" represents the data itself. Depending on the type of system, the modeling object may be defined by different kinds of data. The system may indeed be any combination of a CAD system, a CAE system, a CAM system, a PDM system and / or a PLM system. In those different systems, the modeling object is defined by corresponding data. Thus, CAD objects, PLM objects, PDM objects, CAE objects, CAM objects, CAD data, PLM data, PDM data, CAM data, CAE data may be mentioned. However, these systems are not mutually exclusive, since the modeling object may be defined by data corresponding to any combination of these systems. It will be apparent from the definition of such a system provided below that the system may therefore very well be a CAD and PLM system.

[0028] By CAD system, it is further meant any system, such as CATIA, which is at least suitable for designing modeled objects based on a graphical representation of the modeled objects. In this case, the data defining the modeled objects include data allowing the representation of the modeled objects. The CAD system can, for example, use edges or lines (with faces or surfaces in some cases) to provide representations of CAD modeled objects. Lines, edges or surfaces can be represented in various ways, such as non-uniform rational B-spline curves (NURBS). In particular, CAD files contain specifications from which geometric figures can be generated and thus representations can be generated. The specifications of the modeled objects can be stored in a single CAD file or in multiple CAD files. The typical size of a file representing a modeled object in a CAD system is in the range of 1MB per part. Modeled objects can typically be assemblies of thousands of parts.

[0029] In the context of CAD, a modeled object may typically be a 3D modeled object, which for example represents a product, such as a part or an assembly of parts, or possibly an assembly of products. By "3D modeled object", it is meant any object modeled by data that allows its 3D representation. The 3D representation allows the part to be viewed from various angles. For example, when a 3D modeled object is represented in 3D, the 3D modeled objects can be manipulated and rotated around any of their axes or around any axis in the screen where the representation is displayed. In particular, this does not include 2D icons that are not 3D modeled. The display of a 3D representation facilitates design (i.e., increases the speed at which designers can statistically complete tasks). Since the design of a product is part of the manufacturing process, the industrial manufacturing process can be accelerated.

[0030] The 3D modeled object may represent a product designed after its virtual design has been completed using, for example, a CAD software solution or a CAD system, such as a (e.g., mechanical) part or an assembly of parts (or equivalently, an assembly of parts, since from the method's point of view, an assembly of parts can be considered as a part itself, or the method can be applied independently to each part of the assembly), or more generally, any rigid body assembly (e.g., a moving mechanism). CAD software solutions allow the design of products in a variety of and unlimited industrial fields, including: aerospace, architecture, construction, consumer goods, high-tech equipment, industrial equipment, transportation, ships and / or offshore oil and gas production or transportation. Thus, the 3D modeled object designed by the method may represent an industrial product, which may be any mechanical part, such as a land vehicle (including, for example, automobile and light truck equipment, racing cars, motorcycles, trucks and motor equipment equipment, trucks and buses, trains), parts of air vehicles (including, for example, fuselage equipment, aerospace equipment, propulsion equipment, defense products, aviation equipment, space equipment), parts of naval vehicles (including, for example, naval equipment, commercial ships, offshore equipment, yachts and workboats, parts of marine equipment), general mechanical parts (including, for example, industrial manufacturing machinery, heavy mobile machinery or equipment, installed equipment, industrial equipment products, metal products, tire manufacturing products), electromechanical or electronic parts (including, for example, consumer electronics, safety and / or control and / or instrumentation products, computing and communication equipment, semiconductors, medical devices and equipment), consumer products (including, for example, furniture, home and garden products, leisure products, fashion products, products of hard goods retailers, products of soft goods retailers), packaging (including, for example, food and beverage and tobacco, beauty and personal care, household product packaging).

[0031] Figure 1 An example of the system is shown, where the system is a client computer system, such as a user's workstation.

[0032] The client computer of 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 is also provided with a graphics processing unit (GPU) 1110, which is associated with a video random access memory 1100 connected to the bus. Video RAM 1100 is also known in the art as a frame buffer. A mass storage device controller 1020 manages access to mass storage devices such as a hard disk drive 1030. Mass storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including, for example, semiconductor memory devices such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks 1040. Any of the above may be supplemented or incorporated by specially designed ASICs (application specific integrated circuits). A network adapter 1050 manages access to a network 1060. The client computer may also include a tactile device 1090, such as a cursor control device, a keyboard, and the like. A cursor control device is used in the client computer to allow the user to selectively position the cursor at any desired location on the display 1080. In addition, the cursor control device allows the user to select various commands and input control signals. The cursor control device includes a plurality of signal generating devices for inputting control signals to the system. Typically, the cursor control device may be a mouse, the buttons of which are used to generate signals. Alternatively or additionally, the client computer system may include a sensitive pad and / or a sensitive screen.

[0033] The computer program may include instructions executable by a computer, the instructions including means for causing the above-mentioned system to perform the method. The program may be recorded on any data storage medium, including the memory of the system. The program may be implemented, for example, in digital electronic circuits or computer hardware, firmware, software, or a combination thereof. The program may be implemented as a device, such as a product tangibly embodied in a machine-readable storage device to be executed by a programmable processor. The method steps may be performed by a programmable processor executing an instruction program to perform the functions of the method by operating on input data and generating output. Thus, the processor may be programmable and coupled to receive data and instructions from a data storage system, at least one input device, and at least one output device, and to transmit data and instructions to a data storage system, at least one input device, and at least one output device. If desired, the application program may be implemented in a high-level procedural or object-oriented programming language or in an assembly or machine language. In any case, the language may be a compiled language or an interpreted language. The program may be a complete installer or updater. In any case, the application of the program on the system result results in the execution of the instructions of the method.

[0034] "Designing a 3D modeled object" specifies any action or series of actions that is at least part of a process of elaborating a 3D modeled object. Thus, the method may comprise creating a 3D modeled object from scratch. Alternatively, the method may comprise providing a previously created 3D modeled object and then modifying the 3D modeled object.

[0035] The method may be included in a manufacturing process, which may include, after performing the method, producing a physical product corresponding to the modeled object. In any case, the modeled object designed by the method may represent a manufactured object. Therefore, the modeled object may be a modeled solid (i.e., a modeled object representing a solid). The manufactured object may be a product, such as a part or an assembly of parts. Because the method improves the design of the modeled object, the method also improves the manufacture of the product, thereby increasing the productivity of the manufacturing process.

[0036] The method is for designing a modeled object, such as a 2D modeled object or a 3D modeled object, representing a mechanical part via topology optimization. Therefore, the method comprises providing an input for the topology optimization, such as via user interaction.

[0037] The input to topology optimization includes a FEM. The FEM represents a space containing a modeling object to be designed. Depending on whether a 2D modeling object or a 3D modeling object is to be designed, the FEM can be 2D or 3D. The FEM can be regular or irregular. Conventional FEMs can allow simplified calculations during topology optimization. The FEM can be of any type, for example, each finite element is a tetrahedron or a hexahedron. Providing the FEM can include defining a design space and meshing the design space. The method can include displaying the FEM to a user, and defining other inputs to the topology optimization by the user, for example, including through graphical user interaction on the displayed FEM.

[0038] "Graphical user interaction" with respect to defining an element refers herein to any user interaction by the designer employing a tactile system (e.g., a mouse or a touch device such as a sensitive / touch screen or a sensitive / touch pad) to activate one or more locations of the display unit and where the element is to be positioned. Activating a location of the scene may include positioning a cursor of a mouse thereon or performing a touch thereon. Substantially in real time after activation, a representation of the defined element may be displayed.

[0039] The input for topology optimization also includes data associated with FEM and depends on the mechanical part that the user wants to design.

[0040] These associated data include parameters related to the material, in other words, data representing the material used to form the mechanical part. These material parameters can particularly represent the mechanical properties of the material. The material parameters can, for example, include the Young's modulus of the material and / or the Poisson's ratio of the material. In an example, the user can specify the material, for example, by selecting from a list, and / or the system can automatically determine the material parameters and / or suggest its selection to the user, for example, based on one or more formulas and / or based on a database. The material can be any material, for example a solid and / or isotropic material, such as a metal (e.g., steel, silver, gold, titanium), a plastic (e.g., nylon, ABS, polycarbonate, resin), a ceramic or a composite material.

[0041] The associated data also includes global quantitative constraints. Global quantitative constraints are relative to the global quantification of materials in the FEM. In other words, the global quantitative constraints limit the value of the total amount of material in the entire FEM. The global quantitative constraint can, for example, be provided as a boundary of the fraction of the (entire) FEM that can be filled with material, such as an upper limit of the fraction. Alternatively, the global quantitative constraint can provide a value that must be reached instead of a boundary value. However, topology optimization can optimize an objective function that tends to use as much material as is available in the optimal result, making the equality constraint equivalent to an upper limit constraint. In all cases, the fraction can be a volume fraction (also called GVC in this case, as described in "Global Volume Constraint"). In other examples, the global quantitative constraint may involve a value representing the weight of the material.

[0042] As is known per se from the field of topology optimization, the associated data also include data representative of the conditions of use of the mechanical part, and the topology optimization is able to optimize the mechanical part model taking into account this foreseeable use based on these data.

[0043] The associated data include forces in particular. In other words, the associated data include vectors (e.g., whose magnitude is in Newtons or multiples thereof), each of which is applicable and linked to one or more finite elements of the FEM. These forces partially represent the loads that the mechanical part will bear when in use. In other words, for each of the one or more finite elements of the FEM for which there is a corresponding force in the data, the data represents the fact that the material of the mechanical part will bear the corresponding load at the position corresponding to the one or more finite elements. However, since the mechanical part may theoretically bear an infinite number of loads, not all loads are represented by the forces present in the data. The force only represents the limit of the entire load set, such as the most important load and / or the most representative load. The force can be determined for each modeling problem and can be selected as the maximum (i.e., maximum magnitude) force that the object can bear during its life, because these forces tend to cause the greatest deformation and mechanical stress. These forces can be grouped in a set called a load case. In the example, an industrial problem may have between 1 and 12 load cases. In the example, a user can select a finite element of the FEM via a graphical user interaction and then specify the force applied to it.

[0044] The associated data also includes boundary conditions. Each boundary condition is applicable and linked to one or more finite elements of the mesh, and represents the corresponding constraints on the boundaries to which the mechanical part is subjected. In other words, each boundary condition represents the fact that the material of the mechanical part is subject to constraints on its displacement at the position corresponding to the one or more finite elements, such as using Dirichlet boundary conditions. The displacement of the element may be (especially) along a plane, along a curve, along an axis / around an axis or to a point / around a point, and / or its displacement can only be restricted in translation, rotation, or translation and rotation. If the displacement is restricted to a translation and rotation point, the element is fixed in 3D space and is called "clamped". However, the displacement of the element may be freer translation along a plane but on the plane (for example, if it belongs to an object mounted on a bearing), freer translation along an axis but on the axis (for example, in a piston), or rotation around an axis (for example, a joint of a manipulator).

[0045] In the example, the boundary conditions represent all constraint boundaries. In other words, for each finite element of the FEM that is intended to ultimately contain material that is constrained (e.g., held fixed), a boundary (e.g., clamping) condition can be associated to integrate this fact into the topology optimization. In the example, the user can select the finite elements of the FEM via graphical user interaction and then specify the boundary conditions that apply to them.

[0046] In an example, one or more constraining boundaries of a mechanical part include or consist of one or more fixed boundaries (ie, material at the one or more boundaries cannot move), and the corresponding one or more boundary conditions are clamping conditions.

[0047] As is well known, topology optimization includes automatically optimizing an objective function based on an input. The objective function may represent any mechanical property to be optimized. Topology optimization can, in particular, maximize stiffness. To this end, the objective function may be a compliance function. Compliance is the inverse of structural stiffness for a structure. Therefore, compliance takes into account specified load conditions and fixed boundary conditions, thereby encapsulating the amount of deformation of the structure. Therefore, when the optimization process minimizes compliance, this corresponds to maximizing the design stiffness for a given mass. The free variables of the objective function may be the distribution (i.e., layout) of the quantitative (e.g., volume fraction) of the material on the FEM. Therefore, topology optimization may change the amount of material (e.g., volume fraction) in each finite element of the mesh to optimize the objective function. The objective function may depend on material parameters (i.e., the fixed variables of the objective function may involve material parameters), and the optimization may be performed under constraints including global quantitative constraints. The optimization may be performed according to any algorithm (e.g., an iterative algorithm). In the case where the material quantitative is the volume fraction of the material, the optimization process will produce a distribution of the material volume fraction by finite element. In this case, the topology optimization or method may include a further filtering step (e.g., automatically), i.e., based on such a volume fraction distribution, determining whether each finite element is (completely) filled with material. For example, this can be based on a comparison with a (e.g., predetermined) threshold value (e.g., above 0.1 or 0.2 and / or below 0.9 or 0.8, e.g., of the order of 0.5), if the volume fraction resulting from the optimization is above (below) the threshold value, the finite element is considered to be completely filled with material (equal to completely empty). In an example, the method may further include calculating (e.g., automatically) a 3D modeled object based on the result, such as a boundary representation (B-Rep) model. For example, the method may calculate a swept volume based on and along a series of finite elements resulting from the optimization and / or filtering.

[0048] As is known, based on the FEM, forces, boundary conditions, material parameters and global quantitative constraints, a topology optimization may have been performed to determine the distribution of the material in the FEM. The method goes beyond this general topology optimization by adding a non-uniform distribution of one or more local quantitative constraints to the optimization problem. Thus, the method may not perform a general topology optimization at all, but only a topology optimization with a non-uniform distribution, or, as will be discussed later, first perform a general topology optimization and then a topology optimization with a non-uniform distribution. In both cases, the method integrates the steps of a general topology optimization workflow, which will now be discussed with the example of a general topology optimization workflow.

[0049] As an example of the specification of the topology optimization solution Figure 2 As shown, a generic topology optimization workflow requires as input a design space 22 (here subdivided into small square elements), a set of load cases 24 (forces that will be applied to the design), and boundary conditions 26 (locations where the design is subject to deformation constraints, such as locations that are "clamped", here located on the entire left side of the design space 22). Other parameters may be defined, such as the shell that must be preserved, the mechanical constituent properties of the selected material, the target mass, the maximum allowed deformation, or any other constraints. Since the goal of topology optimization is to generate an optimized design from a blank canvas (i.e., the design space), the design workflow may exclude the possibility of providing an initial geometry from the design space definition.

[0050] The output of a general topology optimization workflow is an optimized design geometry that conforms to the input specifications as closely as possible. Figure 3 An optimized design is shown, which shows the design developed during the optimization process. In this example, the global volume fraction is set to 30%. Figure 3 An initial design 32, a design 34 after five optimization iterations, a design 36 after ten optimization iterations, and a final converged design 38 after twenty-five optimization iterations are shown.

[0051] like Figure 4 As shown, the general topology optimization workflow can follow the eight steps described below in the example:

[0052] 1. Gridding of design space

[0053] like Figure 2 As shown, a discretization of the design space is created. This means that the space is subdivided into small simple connected elements, such as tetrahedrons, hexahedrons. These small elements can later be used both as FEM for simulation and as design variables for optimization.

[0054] 2. Apply load conditions and boundary conditions

[0055] Here, a general topology optimization workflow can take the forces and boundary conditions of a given input specification and apply them to the nodes of the FEM. Figure 2 A grid that subdivides the design space into regular square elements is shown. The nodes on the left are clamped (fixed in 2D space) and a downward force is applied in the middle of the right-hand side of the design space.

[0056] 3. Initialize design variables

[0057] Each element has a given relative density value, which defines whether it is empty or filled with material, defined by the values ​​"0" and "1", respectively. Additionally, in order to make the optimization problem continuous, a general topology optimization workflow may allow elements to take on any value between 0 and 1. This may be called "relaxation". Since the interpretation of elements with intermediate densities may be ambiguous, a general topology optimization workflow may introduce a penalty method that forces the intermediate element density to be less efficient for the overall behavior of the structure than elements with lower and upper bounds of 0 or 1, respectively. This has the effect of driving the optimizer to produce a final design with few intermediate densities, while still maintaining the Figure 3 The continuous formulation shown.

[0058] 4. Solve the balance

[0059] At this point, a general topology optimization workflow might have a fully defined finite element model meshed and attached with forces and boundary conditions, and with relative density values ​​for each element. From there, a general topology optimization workflow can assemble a global stiffness matrix and solve for the nodal displacements for structural equilibrium. In other words, a general topology optimization workflow can calculate the deformation of the structure in its current state for the applied forces and boundary conditions.

[0060] 5. Calculate the objective function value and its derivative

[0061] The objective function that can be used in any topology optimization is the flexibility of the structure. It is the inverse of the stiffness and therefore encapsulates the amount of deformation of the structure taking into account the specified load cases and boundary conditions. Therefore, when the optimization process minimizes the flexibility, this is equivalent to maximizing the stiffness of the design for a given mass. In addition, due to the large number of design variables in the process, the optimization can be performed using gradient-based methods. Therefore, a general topology optimization workflow can also calculate the derivatives of the objective function with respect to each design variable. In other words, a general topology optimization workflow can calculate how the relative density of each element should be changed to improve the flexibility and satisfy the constraints. For flexibility, the well-known and classic "adjoint sensitivity analysis" can be used. In addition, after calculating the derivatives, these derivatives can be smoothed by filtering to improve numerical stability. Conventional topology optimization workflows can reduce erroneous checkerboard patterns and introduce length scales in the optimization so that they are well defined.

[0062] 6. Calculate constraint values ​​and derivatives

[0063] A constraint function in a common topology optimization workflow can be the global volume fraction of the structure. Such a GVC defines the maximum volume of material allowed to be used, and therefore the maximum mass of material that makes up the design. Therefore, the optimizer must find the best distribution of mass in the design space to maximize stiffness. Figure 3 Intermediate designs 34 and 36 in the optimization workflow are shown where the global volume fraction is the same, but the distribution of the material changes during the optimization iterations in the process. The derivative of this constraint is equal to the element volume, and if the elements are of equal size, the derivative is constant for each element, so it is simple to calculate.

[0064] 7. Use mathematical programming to update design variables

[0065] When the values ​​of the objective function and constraints and their derivatives are known, the general topology optimization workflow can use gradient-based mathematical programming to modify the relative density of each element to improve the flexibility of the structure without violating the specified GVC. Once the relative density values ​​of each element have been modified by mathematical programming, and the given modified design in the optimization process has not converged, the general topology optimization workflow can loop back to step 4. A simple mathematical programming for this problem is the so-called optimal criterion (OC). However, in the general topology optimization workflow and method example, a more general mathematical programming algorithm can be used: the moving asymptote method (MMA, first described in "The method of moving asymptotes—a new method for structural optimization", Krister Svanberg, International Journal of Numerical Methods in Engineering, February 1987). It has been observed that in the case of this method, MMA is particularly effective because it can handle multiple nonlinear constraints and the method has the specificity of presenting a large number of variables and only having few constraints. However, any other mathematical programming algorithm can also be used.

[0066] 8. Output the final design

[0067] Once convergence is achieved, the general topology optimization workflow can present the final design in the design space, where each element has an optimized relative density value. Through simple thresholding, the general topology optimization workflow can extract the geometry defined by the set of elements with relative density values ​​above a certain threshold (e.g., chosen to be 0.5). The general topology optimization workflow can now present the geometry of the optimized design, which is the output of the general topology optimization workflow. Figure 3 shows the steps described in step 2 and Figure 2 The final design 38 is optimized on the specifications shown.

[0068] The method can implement all the steps of this general topology optimization workflow and deviate from the method only by providing an additional input to the topology optimization, which is a non-uniform distribution of one or more local quantitative constraints, each constraint relative to a corresponding local quantitative of the material in a corresponding local region of the finite element mesh. The topology optimization is then based on such local quantitative constraints in addition to the other inputs.

[0069] Each local quantitative constraint is relative to the local quantity of material in the FEM of the corresponding local area. In other words, the local quantitative constraint limits the value of the total amount of material in each local area. "Local area" refers to any sub-portion of the FEM, for example including less than 10% or 1% of the number of finite elements of the FEM, or even as low as 2 or 3 elements. Local quantitative constraints can, for example, be provided as boundaries of the fractions of each local area that can be filled with material, such as an upper limit on the fraction. The fraction can be a volume fraction (also called LVC in this case, as shown in "Local Volume Constraint"). In other examples, the global quantitative constraint can involve a value representing the weight of the material.

[0070] Upper limit constraints improve the robustness of mechanical parts by prohibiting material concentration. In particular, local quantitative constraints can be provided for respective local regions, which together cover an area forming a sub-portion of the FEM, for example, including less than 90% of the number of finite elements of the FEM, for example, about 80%. Each local region can be relatively small, for example, each local region can include less than 10% or 1% of the number of finite elements of the FEM. In this case, the method allows to enhance robustness in this region by prohibiting the concentration of material from exceeding the corresponding upper limit in the corresponding region forming the region. Therefore, the method forces the material to be spread out in the region, while reducing all loads of a part of it when formulating the optimization problem will bias the optimization towards a solution that is optimized for this part but not for other loads that may occur in use. This further allows to define a reduced number of load cases as inputs for the topology optimization, while still ensuring the robustness of the structure taking into account the loads corresponding to the undefined forces. In the example, less than 10 or 5 forces are provided as input in the method, each of which is applicable to one or more corresponding finite elements.

[0071] Each local region may include at least two finite elements of the FEM. Each local region may form a connected space (from a topological point of view). One or more local quantitative constraints may provide at least two different local regions (i.e., each local region corresponds to a different local quantitative constraint) to at least overlap (i.e., have a non-void intersection).

[0072] In an example, each finite element of the FEM may be associated (i.e. linked) in a data structure with corresponding data dedicated to local constraint information relative to a corresponding neighborhood comprising the finite element. Each neighborhood may include or consist of all finite elements within a sphere centered at the finite element. The sphere may present a radius of a predetermined size (e.g., the same for all spheres), for example, less than 20, 10, or 2 times the size of the finite element of the FEM (e.g., the FEM is regular and the size of the finite element is the length of the edge of the FEM finite element, for example, all edges of all, e.g., hexahedral or tetrahedral finite elements, have the same length). Alternatively, the neighborhood may include or consist of all finite elements within an oriented ellipse or another predetermined shape. The data may indicate that there are no constraints in the corresponding neighborhood (e.g., by providing an upper limit equal to 1 for the volume fraction of material present in the corresponding neighborhood, which is equivalent to no constraints). The data may alternatively indicate that there are corresponding (truly restrictive) constraints (e.g., by providing an upper limit greater than 0 and less than 1 for the volume fraction). The corresponding neighborhood of each finite element may be determined according to a predetermined scheme. Alternatively, a respective neighborhood of each finite element may be defined within the data representing the local constraints.

[0073] Now, the distribution of one or more local quantitative constraints is non-uniform. "Non-uniform" here means that the FEM includes at least two non-overlapping local regions, which are differently constrained (with respect to the amount of material in the local regions). "Differently constrained" means that one of the two regions is not constrained (i.e., respectively corresponding to the local quantitative constraints) while the other region is constrained (i.e., corresponding to the local quantitative constraints), or both regions are constrained (i.e., each region with respect to the local quantitative constraints), but the two local quantitative constraints are different. Two local quantitative constraints are called "different" if their corresponding local regions have different sizes and / or shapes, and / or the quantitative values ​​involved in the constraints are different (e.g., the two constraints involve different upper limits on volume fractions).

[0074] In examples, one or more local quantitative constraints may each be provided as an upper limit (e.g., between 0 and 1) on the fraction of a respective local region that may be filled with material. In these examples, the "non-uniform" distribution may be achieved by a FEM that includes one or more finite elements that do not belong to any local region with respect to the local quantitative constraints (i.e., unconstrained finite elements, e.g., equal to at least 5% of the total number of finite elements, and / or by one or more local quantitative constraints that include at least two local quantitative constraints, each of which is provided as a different upper limit value (in other words, the one or more local quantitative constraints include a first upper limit on the volume fraction of the material in one or more first local regions and a second upper limit on the volume fraction of the material in one or more second local regions, the first upper limit and the second upper limit being different from each other and each being strictly between 0 and 1).

[0075] Thus, the method adds a new type of constraint, the LVC, to the topology optimization formulation, which leads to the apparition of so-called "bone-like" porous structures in the region containing the local region with respect to the local constraint. These lightweight infill structures show useful properties with respect to robustness.

[0076] Furthermore, the method adds this new constraint non-uniformly. In a naive approach that applies this new constraint uniformly, the lack of control would limit the applicability of the method in an industrial setting. In particular, implementing a uniform LVC would result in increased stresses in certain areas of the design, increasing the risk of structural failure.

[0077] Therefore, the method enables fine control of LVC in the topology optimization formulation without affecting the convergence of the process. Moreover, the method can automatically exploit this new level of control over LVC.

[0078] In the example, the method can formulate the LVC so that a different value can be defined for each point in space. Thus, allowing it to vary across the design space. This may also result in modifications to the calculation of local volume derivatives, and these derivatives may be involved in the optimization process.

[0079] Now, with full control over the LVC value throughout the design space, the method can automatically create a domain of appropriate and non-uniform (also called "dynamic") scalar values ​​to control the current constraint. In a specific example, this threshold may be the result of another topology optimization where the so-called penalty has been deactivated, resulting in intermediate design variables in many locations and no LVC was implemented.

[0080] This new approach allows one to benefit from the robustness and reliability of lightweight porous structures while also automatically adjusting the LVC in areas of high stress and deformation. Potentially, it is also a useful tool for manually controlling and customizing designs and mechanical properties. Moreover, this new approach adds almost no additional computational cost to the workflow for generating optimized designs.

[0081] To make it easier to understand the method, the following discusses examples of simple uniform LVC topology optimization (hereinafter referred to as "uniform LVC optimization") and explains how these examples fit into the general topology optimization workflow described above. Subsequently, with reference to the discussion of uniform LVC optimization, examples of how the method implements LVC non-uniformly are introduced.

[0082] Adding the concept of LVC to the optimization workflow may be equivalent to, based on Figure 4In the workflow in , in step 6 an additional constraint is provided for the optimization and its corresponding derivatives are calculated for the design. Furthermore, in step 7, the uniform LVC optimization in the example can specifically use the MMA optimizer to handle this additional nonlinear constraint (for the same reason that the example in the method uses MMA). Everything else in the overall workflow can remain the same.

[0083] LVC can be intuitively explained in a similar way to GVC. GVC defines the maximum amount of material allowed in the design space. Therefore, setting GVC to 30% means that the final design will have at most 30% of the elements filled with solid material and at least 70% of the elements empty representing voids (assuming the ideal case that no design elements have intermediate relative densities in the design space).

[0084] LVC works exactly the same way, except that instead of applying the maximum allowed amount of material to a smaller partition (i.e., a local neighborhood) of the design space, LVC applies the maximum allowed amount of material to the entire design space. This means that if one sets LVC to 40% and GVC to 30%, then the final design can have at most 30% solid material elements, and if one zooms in on a small partition of a defined size within the design space, then there can only be at most 40% solid material elements.

[0085] Figure 5 Several designs are shown that utilize uniform LVC optimization and optimize for various sizes and magnitudes of partitions of local neighborhoods and local volume fractions, respectively. In particular, Figure 5 Six converged designs using LVCs for different sets of design parameters are shown: radius R and local volume fraction α, which is constantly distributed on the regular FEM via one LVC per finite element for each design. Figure 5 The compliance C achieved in each case is also provided. Application Figure 5 The design of the design is separated by Figure 2 The design shown in .

[0086] It is worth mentioning that LVC is more constrained (i.e., more constraints on material layout) than GVC. Moreover, if LVC-like constraints are defined on the partition size of a local neighborhood covering the entire design space, then it will be strictly equivalent to GVC.

[0087] Calculation and implementation

[0088] For any given element in the design space, uniform LVC optimization can sum the densities in its local neighborhood to obtain the local volume fraction for a given partition. However, having only one local volume fraction per finite element creates too many constraints to be easily solved by standard mathematical programming algorithms. Instead, uniform LVC optimization can consider constraints on the maximum local volume fraction of any element, thereby converting the maximum function into a single aggregate constraint that is easy to solve for the final design. Since the local maximum function is non-differentiable, it may also be more efficient to approximate it using a continuous and differentiable aggregate function, such as the P-norm. However, other continuous and differentiable aggregate functions can also be used.

[0089] The derivative of this constraint can be calculated and implemented. Now, the uniform LVC optimization has evaluated the new constraint in step 6 of the workflow and can be directly applied to the mathematical programming algorithm, similar to GVC, to update the relative density of the design elements in step 7. As mentioned before, the rest of the general topology optimization workflow can remain unchanged.

[0090] Examples of methods that build upon the uniform LVC optimization but differ are now discussed.

[0091] Non-uniform / dynamic local volume constraints

[0092] Perhaps one of the main key points for introducing LVC is to enforce optimizations to implicitly build more robust structures.

[0093] robustness

[0094] The stiffness and stress of a structure are well-defined measures that describe the resistance to deformation and failure under specified load conditions. Robustness, on the other hand, refers to the ability of a structure to resist a variety of conditions or unforeseen events. Such unforeseen events are unavoidable and could be, for example, changes in load conditions (e.g. force direction, abuse load conditions, manufacturing defects, buckling or other events that make the specifications prescribed by theory not completely match their real life.

[0095] Since it is very complex to perfectly describe every event that a designed mechanical part will encounter during its service life, it may be effective to optimize the design so that it performs well in the expected and most common situations, while also being somewhat robust to unforeseen events. Therefore, the design process of this method can form a balance between optimization for expected situations and robustness to unforeseen events.

[0096] Uniform LVC optimization creates porous structures, which leads to redundancy in the structure, which tends to implicitly have a positive impact on its robustness. However, since the constraints are applied non-uniformly on the design space, it also prevents the optimization from creating strong, bulky and solid sub-components in highly deformable and highly stressed areas (e.g., near boundary conditions, forces or geometric restrictions in the design space).

[0097] Based on this consideration, the method can obtain the benefits of a design that benefits from the robustness of the porous structure obtained using one or more LVCs, while also allowing certain important structural regions of the design space to be 100% filled with material. This leads to a non-uniform distribution of local quantitative constraints (hereinafter also referred to as "dynamic" LVC).

[0098] We now discuss implementations of dynamic LVC, where each local quantitative constraint represents a respective upper bound on the respective local volume fraction of a material. These implementations converge relatively robustly and quickly.

[0099] As mentioned earlier, the local volume fraction is a metric that can be defined for each finite element in the design space. This means that the method can consider applying constraints to only a subset of elements, while leaving other elements free. The method generalizes this idea by allowing any arbitrary LVC for each element and its corresponding partition of the design space. In other words, the method can restrict the local volume fraction of a given element to be lower than any value (e.g. 40%) and lower than any other value of its nearby elements (e.g. 45%), and so on for each element in the design space. Alternatively, the method can also modulate the size of the local neighborhood considered for each element (the size of the partition). In the example, the method can modulate the local neighborhood size and the local volume fraction within a given neighborhood for each design element.

[0100] In the simple case of a uniform LVC, constraints are easy to formulate because they are the same for every element and are therefore simple to apply using a given aggregation function (e.g., P norm). However, in the case of a dynamic LVC, constraints may have different values ​​for each element. This means that the method can modify the constraint formulation to accommodate these local variations.

[0101] Now for the discussion.

[0102] Let Ω be the set of elements in FEM, e be a given element in the design space, and ρ e is the relative density of a given element (i.e., the volume fraction of the material inside a given element), ω e the set of elements in the realm selected for a given element, and is the average relative density in the local neighborhood of a given element, i.e., its local volume fraction. This method can consider:

[0103]

[0104] Let α e is the LVC value for a given element. Implementing dynamic LVC means that for any element in the design space, the method takes the following set of constraints as input to the topology optimization:

[0105]

[0106] In α e In the strictly positive case, it can be reordered as:

[0107]

[0108] In the example, the method can aggregate the set of constraints into a single constraint using a maximum function:

[0109]

[0110] As now explained, the method can constrain the topology optimization via G or alternatively by converting it into a differentiable function.

[0111] Let p be the exponential value selected by the P norm (p is greater than or equal to 2 and / or less than or equal to 20 or 10, for example p=6), then the method can estimate the aggregation constraint G using the following approximation in the example:

[0112]

[0113] To clarify the differentiation step, we introduce A as:

[0114]

[0115] In gradient-based optimization, the gradient of the constraint G′ can be calculated by using the chain rule as follows:

[0116]

[0117]

[0118]

[0119]

[0120] Using gradient-based mathematical programming methods (such as the MMA optimizer) in conjunction with the dynamic LVC and its gradient, this approach allows designs to be optimized in a computationally efficient manner to have varying LVC throughout the design space.

[0121] Note that by following similar steps as above, in other examples the constraints can be formulated as follows:

[0122]

[0123] Furthermore, the above equation can also be formulated using other differentiable aggregate functions.

[0124] New constraints with different properties for each element of the design space can be represented by the field ω e or field α e or these two fields. These can be called constraint fields. These fields define the required local volume fraction at each point in space for the optimization setup.

[0125] We now discuss the workflow for integrating this approach.

[0126] In the workflow, a non-uniform distribution of local quantitative constraints can be manually set by a user on the FEM without using any information other than data associated with the FEM (eg, without any information about individual finite element features except for their positions).

[0127] In other workflows, the method may alternatively or alternatively include performing another initial topology optimization based on the FEM and the generic data associated with the FEM (i.e., when there is no non-uniform LVC distribution) before the topology optimization under non-uniform LVC distribution. In this case, the method may include manually, semi-automatically or fully automatically determining the non-uniform distribution based on the results of the other topology optimization. The initial topology optimization thus forms a pre-processing that allows setting local quantitative constraints.

[0128] As is known per se from the field of topology optimization, the initial topology optimization may thus provide a density field (i.e. the value of the volume fraction of the material of each FEM finite element) as a result and optionally, as other results, a (corresponding) strain field associated with the density field, a stress field associated with the density field and / or a compression field associated with the density field. In this case, the method may comprise determining the non-uniform distribution based on any one or any combination of such result fields.

[0129] In an example, the method may include automatically determining one or more local quantitative constraints based on density, strain, stress and / or compression fields. The initial topology optimization may provide an initial distribution / layout of materials optimized in the form of fields for simplified forces / loads of the problem formulation and their mechanical properties. The method may rely on this information to establish where LVC needs to be applied.

[0130] This automation can be achieved in different ways.

[0131] As an example, the method may use the values ​​provided for one or more corresponding finite elements of the FEM by the density field or by any normalized function (i.e., having a value between 0 and 1) of any one or any combination of density, strain, stress and / or compression fields directly as upper limits for the LVC constraints provided for said corresponding finite elements of the FEM. In this case, the local region may be defined in any of the ways discussed above, for example as a neighborhood having a predetermined and constant radius.

[0132] As an alternative example, the method may comprise thresholding the density field or the normalization function. In other words, the method may cluster the values ​​of the field resulting from the initial topology optimization, thereby dividing the FEM into different regions of the finite element. The number of clusters may be strictly higher than 1 and / or strictly lower than 20 or 10, for example equal to 2, 3, 4 or 5. A respective upper limit may then be defined for each region based on the value of the field in the region.

[0133] In an example, the method may alternatively or additionally include: displaying a graphical representation of the density field (e.g., using grayscale or color intensity), and determining one or more local quantitative constraints via (e.g., graphical) user interaction. In this case, the constraint differentiation may depend on factors such as: areas with forces, areas with clamping, or areas that are desired to be narrow areas of the modeled object.

[0134] In an industrial setting, it may be practical to accommodate constraints on high strain or high stress regions. Therefore, to locate these regions, the proposed method can first perform a full (general) topology optimization without any LVC or penalty for enforcing solid / void designs, applying only GVC.

[0135] The result of this very simple optimization can be a relative density field where the relative density of each element can freely choose any relative density value in the range [0-1] between voids and solid material, without penalty forcing these values ​​close to 0 or 1. However, at some locations relative density values ​​of 0 or 1 may still be observed.

[0136] The method may include using the relative density field to create the constraint field required to perform a second full topology optimization with penalty and using dynamic LVC.

[0137] As mentioned above, this can be done simply by using the relative element density field from the first converged optimization as the constraint field for the second optimization. However, numerical tests on specific examples have shown that better results can be obtained for these examples by automatically thresholding the relative density field to define partitions of regions and then choosing a local volume fraction parameter for each region.

[0138] Figure 6 Optimized designs without penalty and threshold fields are shown. The figure shows the relative density field and its processed version with thresholds and selected local volume fraction upper limits associated with different regions. The initial topology optimization provides a design 60 without LVC (or penalty) optimization, which includes elements 61 with relative density of about 0.5, elements 62 with relative density > 0.9 and elements 63 with relative density < 0.1. Design 64 with a simple threshold at a relative density value of 0.9 results in the local volume fraction upper limit of region 65 being selected to be equal to 100%, while the local volume fraction upper limit of region 66 is selected to be equal to 50%. Another design 67 with multiple thresholds at relative density values ​​of 0.9, 0.7, 0.3 and 0.1 results in finer partitioning of the FEM in different such regions.

[0139] Note that in this example, the method keeps the local neighborhood size constant across the design space. However, the method can also modulate it, as shown in the mathematical formula described earlier.

[0140] Reference Figure 7 To validate the method, a test (femoral head model) with a 3D scenario of clamping side 70 and force 72 was run. The rotation axis 74 of force 72 was used for robustness testing. The test generated three different optimized designs:

[0141] Design A with GVC only.

[0142] Design B with GVC and uniform LVC.

[0143] Design C with GVC and dynamic (ie, non-uniform) LVC.

[0144] Each design has the same quality (error margin is 0.1%) and is shown in slice view in the figure. As shown in the figure, while design A occupies most of the bulk area and design B occupies most of the porous area, design C forms a mixture of bulk and porous areas.

[0145] For each design, compliance and maximum stress were tested under loads that gradually deviated from the initial operating specifications. Figure 7 As shown, the force deviation is controlled by rotating the force about axis 74. This allows the performance of each design to be evaluated and how these performances degrade with changes in load, thereby showing their robustness to unexpected events.

[0146] Results from Figure 8-Figure 9 The curve graph in shows that Figure 8 and Fig. 9The following examples illustrate: the compliance of each design considering the varying loads, where high compliance means larger structural deformations and thus lower stiffness; and the maximum stress of each design under the varying loads, where high maximum stress means a higher risk of structural failure. As shown, design A performs best without deviating from the initial specifications, but its performance decreases rapidly with the force variation due to unexpected events caused by the change in the direction of the force. On the other hand, design B has a worse performance, but, due to its better robustness, becomes better than design A as the change in the direction of the force increases. Finally, design C shows almost the same characteristics as design A with low deviations in the direction of the force, while approaching design B with high deviations. This means that dynamic LVC allows optimization to produce a hybrid design that benefits from the stiffness of the traditional design method and the robustness of the porous design method. The method is able to automatically generate design C.

[0147] Examples of mechanical parts that can be designed by this method are now discussed.

[0148] In the example, the mechanical part is an additively manufactured part. In other words, the mechanical part is a part that can be manufactured via an additive manufacturing type 3D printing process. As previously mentioned, the local area corresponding to the local quantitative constraint may present a honeycomb or porous structure. The size of each honeycomb may be lower than the diameter of the local area (i.e., the maximum size). Therefore, the mechanical part can present a complex structure, i.e., "lattice-like". Such a complex structure may be difficult to produce via traditional manufacturing, but can be achieved via additive manufacturing. Therefore, the method in such an example may be followed by one or more implemented additive manufacturing processes for producing mechanical parts. The additive manufacturing process can take the designed modeling object as input.

[0149] In other examples, the mechanical part may alternatively or additionally be a part having one or more functional external regions and one or more internal regions. An "external" region refers to any region of a mechanical part including the outer surface of the mechanical part (i.e., the surface visible when viewed from the perspective of the mechanical part). A "functional" region refers to a region configured to physically interact with another part and / or directly receive a load condition. The design part and other parts may be elements of the same component. The method may be included in a process for designing a component (including the design of each part of the component). An "internal region" refers to a region that does not include any external surface. In such an example, the internal region may be covered with local quantitative constraints, while the functional external region may not have any local quantitative constraints. Therefore, the method may allow materials to be gathered in the functional external region and force the honeycomb structure to be located in the internal region. The concentration of the material remainder may produce an overall structure of materials that make the functional external region resistant, which is useful for their function of physically interacting with other parts. On the other hand, the honeycomb structure of the internal region may make the component lighter and / or present improved thermal conductivity. In a specific example, the external functional region forms the outer shell of the mechanical part (completely surrounding the mechanical part).

[0150] In other examples, the mechanical part may alternatively or additionally be a vehicle part. For example, the mechanical part may be a ground, air, or aerospace vehicle part. In this case, the area that is subjected to the action (e.g., through physical interaction with another part of the vehicle) may be more constrained than the area that is only subjected to vibration and / or turbulence. The area that is subjected to the action may be associated with forces in the data associated with the FEM. The area that is subjected to vibration and / or turbulence may be subject to local quantitative constraints to ensure its robustness.

[0151] Figure 10-Figure 20 A diagram showing such an example of a mechanical part is shown.

[0152] Fig.10 A FEM 100 for designing a structural frame part of a helicopter is shown. The regions of the FEM 102 are not locally constrained. Such regions 102 correspond to the active areas of the mechanical parts, here the prescribed shell areas for fixing bolts, electrical and mechanical components. The figure shows different levels of porosity 104 controlled by local constraints, resulting in a porous structure 106 throughout the design. The porous structure fits and provides support for the prescribed shell area where other components will be assembled and positioned. Moreover, the properties of the porous structures are such that they effectively dampen vibrations, thereby protecting the components. The designed modeled object 111 resulting from the optimization is shown in FIG. Fig.11 Shown above. Figure 11-Figure 12 It is shown how the modeled object 111 can be assembled to other parts of the helicopter.

[0153] Fig.14 An aircraft wing that can be designed using this method is shown with a cutaway showing its internal structure. The wing has a central axis 142 with no local constraints, allowing a strong wall structure to be created to carry the main aerodynamic loads. The wing also has areas 144 with local constraints near the front and rear of the airfoil to create a sparse truss structure to handle smaller torsional forces.

[0154] Fig.15 Another helicopter part is shown, which is a motor mount and heat exchanger. The part has a structure 152 with a modified porosity to facilitate heat exchange and has local constraints. The part also has solid areas 154 for fixing electrical components and solid areas 156 for bolting, where no local constraints are set.

[0155] Figures 16 to 18 An example of a connecting rod that can be designed by this method with manual region selection for local constraints is shown. The rod has a region 162 near the load and fixture. The manual method may disable local constraints here. The rod also has a region 172 with high mechanical stresses as calculated by finite element analysis. The manual method may disable local constraints here. The rod also has a region 182 at a safe distance from the active region (i.e., a non-functional internal region). The user can choose to add local constraints only in this region.

[0156] Fig.19 A car front bumper for shock absorption is shown. Due to its high redundancy, the porous structure will gradually break and collapse, while the solid structure will break suddenly. The porous structure is very effective in suppressing the energy of the collision. Therefore, the part can be designed to have region 192 without local volume constraints to allow the solid front stop to appear, and region 194 with strong local volume constraints to produce redundant porous structure.

[0157] Fig. 20 An industrial part with a hybrid solid and porous structure is shown. The part is an optimized industrial part, comprising a solid outer shell 202 with functional areas and a porous lightweight inner area 204.

Claims

1. A computer-implemented method for designing a modeled object, the modeled object representing a mechanical part to be manufactured and formed of a material, comprising one or more local regions, each local region representing a porous structure, the material being load-bearing in use and having one or more constraining boundaries, the method comprising: supply: Finite element mesh, Data associated with the finite element mesh and including: represents the force of the portion of the load, a boundary condition representing at least a portion of the one or more constraint boundaries, a parameter related to the material, the parameter representing the mechanical properties of the material and comprising Young's modulus of the material and / or Poisson's ratio of the material, a global quantitative constraint relative to a global quantitative amount of the material in the finite element mesh, the global quantitative constraint limiting the value of the total amount of material throughout the finite element mesh, and a non-uniform distribution of one or more local quantitative constraints, each local quantitative constraint relative to a respective local quantitative quantity of the material in a respective local region of the finite element mesh; and performing a topology optimization based on the finite element mesh, data associated with the finite element mesh, and the non-uniform distribution, Among them, each local quantitative constraint represents the corresponding local quantitative The corresponding upper limit α e , so that, as a result of the topology optimization, the robustness of the area covered by one or more corresponding local areas is achieved by prohibiting the concentration of the material in the area from exceeding the corresponding upper limit, whereby the topology optimization forces the material to spread in the area, thereby causing a porous structure to be created in the area.

2. The method according to claim 1, wherein: The mesh has a set Ω of elements e, each element having a corresponding relative density ρ of the material that varies during iterations of the topology optimization e , the non-uniform distribution includes multiple local quantitative constraints Each local quantitative constraint is on a corresponding element e, and the corresponding local region of each corresponding local quantitative constraint is the corresponding neighborhood ω of the corresponding element e. e , each corresponding neighborhood ω e The corresponding local quantity is the corresponding neighborhood ω e The relative density of the material ρ e The corresponding average 3. The method according to claim 2, wherein: The method comprises constraining the plurality of local volumes Aggregated into a single aggregate constraint.

4. The method according to claim 3, wherein: The aggregation constraint satisfies the corresponding average The corresponding upper limit α e The difference between the two is defined as the extreme value of the set Ω of elements e constant limit, where the corresponding average The corresponding upper limit α e The difference between or The constant limit is 0 or 1.

5. The method according to claim 4, wherein: The extremum is a maximum value, and the aggregation constraint approximates the maximum value using a differentiable function, and performing the topology optimization includes performing a gradient-based optimization.

6. The method according to claim 5, wherein: The aggregation constraints include and the differentiable function is the P-norm, Wherein, p is the exponent value selected for the P-norm.

7. The method according to claim 5 or 6, wherein: The gradient-based optimization is a method of moving asymptotes.

8. The method according to any one of claims 1 to 6, wherein: The method comprises, before performing the topology optimization: performing another topology optimization based on the finite element mesh and data associated with the finite element mesh, and The non-uniform distribution is determined based on a result of the further topology optimization.

9. The method according to claim 8, wherein: The result of the other topology optimization includes a density field, a strain field, a stress field and / or a compression field, and determining the non-uniform distribution includes: Automatically determining one or more local quantitative constraints based on the density field, the strain field, the stress field and / or the compression field; and / or A graphical representation of the density field, the strain field, the stress field, and / or the compression field is displayed, and one or more local quantitative constraints are determined via user interaction.

10. The method according to any one of claims 1 to 6, wherein: The mechanical part is an additively manufactured part, a part having one or more functional exterior regions and one or more interior regions, and / or a vehicle part.

11. A modeled object that can be designed by a method according to any one of claims 1 to 10.

12. A computer program product comprising a computer program for executing the method according to any one of claims 1 to 10.

13. A computer-readable storage medium having recorded thereon the modeling object according to claim 11 and / or the computer program according to claim 12.

14. A system comprising a processor and a graphical user interface coupled to a memory having recorded thereon the modeling object according to claim 11 and / or the computer program according to claim 12.

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