Method of modeling variations of repetitive components of an assembly
By using the parametric superelement method, the accuracy and efficiency problems of modeling the variation of repetitive components in existing technologies are solved, enabling rapid simulation and optimization of complex structures such as crystal lattice structures and reducing computational costs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SIEMENS IND SOFTWARE NV
- Filing Date
- 2022-03-03
- Publication Date
- 2026-07-10
AI Technical Summary
Existing technologies suffer from insufficient accuracy and low computational efficiency in modeling repetitive component variations of components, especially junctions in lattice structures, making it difficult to achieve fast and detailed simulation and optimization, particularly in industrial applications.
The Parametric Superelement (PSE) method is employed to construct component models and perform interpolation by providing parameter sets for each component configuration, thereby generating approximators for rapid and accurate simulation and optimization of variations of repetitive components, including junctions of lattice structures.
It enables fast and accurate simulation and optimization of components, reduces computational costs, is applicable to structures with complex geometries, and improves the efficiency of simulation and optimization.
Smart Images
Figure CN115017631B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a computer-implemented method for modeling variations of repetitive parts of a component. Background Technology
[0002] When performing engineering tasks, it is often necessary to model variations of repetitive parts of components. For example, lattice structures (preferably lightweight types of lattice structures) have become increasingly popular, especially due to new manufacturing technologies such as additive manufacturing, which make it easier to create lightweight structures, for example, variations of repetitive parts of the component to be generated.
[0003] In a narrower sense, a lattice structure contains beams connected at junctions, most commonly by repeating unit cells.
[0004] More generally, the present invention applies to lattice structures that also include porous three-dimensional spatial structures formed and interlocked by unit cells with different topological geometries. Such lattice structures can be considered, for example, cellular structures (including foam structures, honeycomb structures, and lattice structures).
[0005] For example, if a lattice structure with nodes is considered as a component, these nodes can be provided as variations of repeating parts, and they can have complex geometries. Such nodes are often difficult to accurately simulate without a large amount of computational work. The models required for industrial applications may be very detailed and may quickly become infeasible in terms of the availability of computing power.
[0006] Lattice structures are typically simulated using the finite element method (FEM). In this method, the structure is subdivided (“meshed”) into a mesh of simpler geometries called finite elements. These elements are easier to discretize and capture the complete geometry after assembly. During post-processing, the performance of the design can be measured by examining the simulation results. In the topology optimization framework, total stiffness and mass are typically used, stress concentration determines the fatigue life of the structure, and eigenvalue analysis reveals the dynamic behavior of the structure.
[0007] There are two types of meshes used, for example, crystal lattices.
[0008] The first type is the three-dimensional lattice: the lattice structure is subdivided into a large number of three-dimensional (3D) elements (e.g., Simcenter Nastran's CTETRA). Due to the geometric complexity of the lattice, many of these elements are typically required. Therefore, this approach can be considered "accurate but slow".
[0009] The second type of mesh is a one-dimensional (1D) mesh: each beam in the mesh is replaced by a beam element (e.g., Simcenter Nastran's CBAR). Therefore, fewer elements are needed, resulting in shorter computation time. One problem with this approach is that these beam elements are based on beam theory (Euler-Bernoulli beam theory, Timoshenko-Ehrenfest beam theory), which becomes inaccurate as the beam becomes thicker.
[0010] Various aspects of lattice modeling are known from the following literature: M. Helou and S. Kara, “Design, Analysis and Fabrication of Lattice Structures: An Overview.” International Journal of Computer Integrated Manufacturing, 31(3):243–261, 2018. ISSN 13623052. doi:10.1080 / 0951192X.2017.1407456.
[0011] Another existing technical document is: “Research on modeling of lattice structures manufactured by additive manufacturing” by G. Dong, Y. Tang and YF Zhao. Journal of Mechanical Design, ASME Transactions, 139(10), 2017. ISSN 10500472. doi:10.1115 / 1.4037305.
[0012] Some of the teachings in these documents can be summarized regarding the field of this invention as follows. A major problem is that by replacing the beam with one-dimensional elements, each joint is replaced by a single point. However, these joints contain considerable stiffness and mass. In a predominantly bending lattice, they also have a significant impact on fatigue life, as they are where stress is highest. Some techniques in the literature attempt to mitigate this problem by increasing the beam thickness near the joints, but this is a more practical but less accurate solution. Furthermore, there is no universally accepted method to determine how much the thickness should subsequently be changed. Therefore, this approach can be considered "fast but inaccurate."
[0013] Currently, methods exist for modeling variations of repeating components in components, particularly for modeling junctions in lattice structures. These methods could potentially benefit from improvements. One object of this invention is to improve the design process for components with variations of repeating components. Summary of the Invention
[0014] Based on the aforementioned prior art and related problems, the present invention is based on an improved design process for components (e.g., lattice structures) that include variations of repeating parts.
[0015] The objective of this invention is achieved by the independent claims. The dependent claims describe advantageous developments and modifications of the invention.
[0016] According to the present invention, a solution to the above-mentioned problem is provided by a method initially defined, the method comprising the following additional steps:
[0017] A) Provide parameter sets for component configurations of multiple different components, where the parameters in each parameter set define the component configuration of each component.
[0018] B) Select the component configuration.
[0019] C) Provide a component model for each selected component, where the component model associates forces and displacements with the position of the corresponding component.
[0020] D) Construct an approximator, wherein the approximator is provided for interpolating the part model to approximate the part model of a part configuration that is not part of the selected part configuration.
[0021] The components according to the invention may include lattice structures, porous three-dimensional spatial structures formed and embedded by unit cells with different topological geometries, such as foam structures, honeycomb structures, etc.
[0022] In this invention, a variation of a repeating component refers to a structure comprising elements having similar functions and similar geometries. These elements may be partially identical or partially different and can be defined by a set of parameters defining the configuration of the respective components. The method according to the invention uses these variations of repeating components as a novel type of element, which can be referred to as a "parametric superelement," and can be more broadly applied to any structure containing a large number of components with similar (but slightly varied) geometries.
[0023] Force can include linear forces (such as tensile force, compressive force, and shear force) and rotational equivalents of linear forces, commonly referred to as moments, torques, rotational forces or rotational effects, and torsional forces. Force can also include pressure, area forces, tensile stress, shear stress, and compressive stress.
[0024] Meanwhile, for lattice design, using a topology optimization framework that determines the correct placement of the lattice in the correct location is very attractive. However, optimization is an order of magnitude more complex than simulation, and therefore more expensive. Consequently, the highly detailed models required for optimization in industrial applications quickly become impractical.
[0025] This invention opens up the possibility of rapid and accurate simulation, such as of crystal lattices, and even their subsequent optimization. This is accomplished through the method steps defined in the claims—in other words, by employing reduction and interpolation techniques, which simulate, for example, lattice junctions using so-called parameterized components (referred to as “parameterized superelements (PSEs)”). Furthermore, this invention can be applied to structures containing numerous slightly varied structures.
[0026] Currently available finite element methods can be extended using the method according to the invention. Some examples of corresponding components of the structure according to the invention can be applied to the following (but are not limited to):
[0027] - Truss bridges and tower cranes, because they can be viewed as macroscopic-scale lattices;
[0028] - Gas turbine rotors, because their blades are not designed to prevent resonance; and
[0029] - The hull is made possible by its numerous different configurations of plates, rivets, welds, and beams.
[0030] According to a preferred embodiment of the present invention, the steps are as follows:
[0031] (This is step C) providing a component model for each selected component, where the component model associates forces and displacements with the position of the corresponding component.
[0032] The configuration for each selected component includes the following steps:
[0033] a. Mesh the component's mesh using solid elements.
[0034] b. By using the stiffness matrix of the first component, forces and displacements are associated with the positions of defined solid elements, thereby generating a preliminary component model of the meshed component.
[0035] c. Identify constraints that reduce the number of external degrees of freedom that would otherwise restrict the number of degrees of freedom for movement.
[0036] d. By eliminating the constraint degrees of freedom of the stiffness matrix of the first component, a reduced stiffness matrix is obtained, reducing the model order of the initial component model to the remaining external degrees of freedom, thereby generating the component model.
[0037] And step D) includes constructing an approximator by interpolating the reduced stiffness matrix to extract the reduced stiffness matrix of the component that is not part of the component configuration selection.
[0038] According to another preferred embodiment of the invention, the repeating component may be a junction of a lattice structure.
[0039] According to another preferred embodiment of the invention, the selection in step B) can be accomplished by selecting all types of variants or by selecting only a subset of the entire variant multivariate. In the case of subset selection, this can be done randomly or systematically. A systematic approach can be used by systematically changing the parameters of the parameter set. This variation can be performed incrementally, and if the range is limited by upper and lower limits, it can be performed along the range of the corresponding parameter in equal-interval steps. As an alternative to equal-interval steps, logarithmic steps or other steps can be used, especially when one parameter is unrestricted. The number of variants can be limited to a predefined number per parameter, and the step width can be defined by dividing the parameter range by the number of steps. The resulting number of variants can be the product of all the numbers of the corresponding parameter variables.
[0040] According to another preferred embodiment of the invention, the step of reducing the model order is accomplished using Guyan reduction, thereby producing a reduced stiffness matrix. In computational mechanics, Guyan reduction, also known as static condensation, is a dimensionality reduction method that reduces the number of degrees of freedom by ignoring the inertial terms of the equilibrium equations and by representing the unloaded degrees of freedom as loaded degrees of freedom. (GUYAN, J., Reduction of stiffness and mass matrices, R., AIAA Journal 3380-380 (1965) https: / / doi.org / 10.2514 / 3.2874).
[0041] According to yet another preferred embodiment of the invention, the interpolation in step D) uses a canonical multifactor decomposition. This tensor rank decomposition is a generalization applied to the matrix singular value decomposition of tensors [FL Hitchcock (1927), “Representing tensors or multifactors as the sum of products,” Journal of Mathematics and Physics (6: 164-189).].
[0042] This invention also relates to a computer-implemented method for optimizing a component, comprising repeatedly executing optimization steps via a computer-implemented method for modeling variations of repeating parts of the component according to features defined by the foregoing description and / or claims for several variations of the component, and subsequently comparing the modeling results with respect to predefined performance factors to determine the starting configuration for the next optimization step. Such optimization can be performed as long as the predefined target performance factors are achieved. The optimization can also follow parallel tracking with different starting variations of the component and can exchange variation features according to a predefined optimization strategy.
[0043] The present invention also relates to an additive manufacturing method for generating a variant of an assembly having repeating parts, wherein the design step includes the method of the present invention according to one of its embodiments, wherein subsequent generation steps are completed based on the design generated by the design step. Attached Figure Description
[0044] Embodiments of the present invention are described by way of example only with reference to the accompanying drawings, wherein:
[0045] Figure 1 A flowchart of the method according to the present invention is shown.
[0046] Figure 2 A flowchart illustrating a method for modeling components according to the present invention is shown.
[0047] Figure 3 A flowchart of a method for generating an approximator according to the present invention is shown.
[0048] The illustrations in the accompanying drawings are schematic. It should be noted that similar or identical elements may have the same reference numerals in different drawings. Detailed Implementation
[0049] Figure 1 The following is a schematic illustration of a computer-implemented method according to the present invention for modeling variations of repeating components VRP of a component CMP, comprising the following steps:
[0050] A) Provide parameter sets (PRMs) for configuring CFGs of multiple different component VRPs, where the parameter PRMs of each parameter set PRM define the component VRP configuration CFG of each component VRP.
[0051] B) Select the SCT for the VRP configuration CFG of the component.
[0052] C) For each component VRP selected for SCT, the configuration CFG provides a component VRP model MDL, where the component VRP model MDL associates the force FRC and displacement DPL with the corresponding component VRP's position LCT.
[0053] a. Mesh the VRP component's mesh MSH using Solid Element Type (SOE) elements.
[0054] b. By associating the force FRC and displacement DPL with the position LCT of the defined solid element SOE through the first component VRP stiffness matrix SMX, a preliminary component VRP model PPM of the meshed component VRP is generated.
[0055] c. Identify the constraint CTS that reduces the number of external degrees of freedom (EDF) that will move the constraint degrees of freedom (CDF).
[0056] d. By eliminating the constraint degrees of freedom (CDF) of the first component's VRP stiffness matrix SMX, a reduced stiffness matrix (RSM) is obtained. This reduces the model order (ORD) of the initial component VRP model PPM to the remaining external degrees of freedom (RDF), thereby generating the component VRP model MDL.
[0057] Furthermore, step D) includes constructing the approximator APX by interpolating the reduced stiffness matrix RSM to extract the reduced stiffness matrix of the selected SCT of the component VRP that does not belong to the component VRP configuration CFG.
[0058] E) By applying the approximator APX to multiple component VRPs of the component CMP and combining the resulting reduced stiffness matrices of these component VRPs with the other element models of the component CMP, a reduced component model RCP is generated.
[0059] The approximator APX can be considered as a parameterized superelement PSE.
[0060] Figure 2 A simplified illustration of some steps of a method for modeling a component CMP according to the present invention is shown, where the component is a lattice structure LTS. During lattice simulation, approximators APX, each representing a parameterized superelement PSE according to the present invention, are used to efficiently and accurately simulate, for example, a diamond lattice DIA. The illustration shows the diamond lattice DIA structure simplified to a beam BMS and junction JNTs (one junction JNT is shown exemplarily). Junction JNTs, as samples of a general component PRT according to the present invention, are modeled as parameterized superelement PSEs, and after doing so for all junction JNTs, the initial diamond lattice DIA structure is modeled. Finally, by combining all the parameterized superelement PSEs of the component CMP with the other elements of the component, a reduced overall model OVM is obtained for the component CMP. For applications of lattice structure simulation, the method according to the present invention can be part of a process that simulates a beam BMS with 1D elements but models the junction JNTs according to the present invention as parameterized superelement PSEs.
[0061] Due to the large number and complex geometry of the junction JNTs, this invention is suitable for lattice structure design. This invention can also be applied to, for example, truss bridges (because such bridges contain a large number of beams and junction JNTs), and more generally, to any structure containing many components with complex geometries (cars, airplanes, etc.), which are similar to but include variations defined by the parameter set PRM for the component VRP configuration CFG. The basic steps of the illustrated process include:
[0062] 1. The JNT contact is modeled by meshing it with solid elements.
[0063] 2. Add constraint CTS to reduce the number of external degrees of freedom (EDF).
[0064] According to a preferred embodiment, it can be assumed that the connection surfaces of the JNTs in the lattice structure remain straight, which may result in a reduction in the number of remaining external degrees of freedom (RDFs), for example, six degrees of freedom per surface. Subsequent reduction steps can reduce the model order ORD to external degrees of freedom (EDFs). This is preferably accomplished using Guyan reduction (also known as substructuring, static condensation, etc.), which yields a reduced stiffness matrix similar to that implemented by an analytical element but applicable to more complex geometries. Due to the reduced computational cost, a fast approximator APX based on the selected SCT of the component VRP configuration CFG can be constructed to extract the reduced stiffness matrix of the component VRP that is not part of the selection. For a large number of node configurations, reduced matrices are generated. They are then interpolated to be able to extract the reduced stiffness matrix of nodes with previously unsimulated parameters. In this case, canonical multifactor decomposition can be used because it eliminates all parameter dimensions, thus allowing 1D-to-1D interpolation (e.g., https: / / www.tensorlab.net / doc / cpd.html).
[0065] Preferably, the combination of the above steps enables the efficient calculation of the reduced stiffness matrix RSM, which depends on the parameters of the complex geometry it represents.
[0066] Figure 3 The steps of this method are shown below:
[0067] A) Provide the parameter set PRM for configuring the CFG of the component VRP and B) Select the selection SCT for configuring the CFG of the component VRP as the input IPT for the next step.
[0068] C) a. & b.: By meshing with solid element SOE, a component VRP model MDL is provided for each component VRP by configuring CFG. The force FRC and displacement DPL are associated with the position LCT defined by the solid element SOE through the first component VRP stiffness matrix SMX, thereby generating the preliminary component VRP model PJM of the meshed component VRP (steps a. (meshing the component VRP mesh MSH with solid element SOE), b. (generating the preliminary component VRP model PJM of the meshed component VRP as the first component VRP stiffness matrix SMX)).
[0069] C) c. & d. Use, for example, the vertical surface assumption for constraints and reduce to the remaining external degrees of freedom (RDF). Typically, higher-order surface constraints can also be used to create the parametric hyperelement PSE. For example, 8 external nodes (EXN) and the corresponding 6 degrees of freedom (DoF) of the remaining RDF yield a 48×48 stiffness matrix for the parametric hyperelement PSE.
[0070] D) A fast approximator APX is constructed by repeating the preceding steps and interpolating the reduced stiffness matrix RSM using IPL to extract the reduced stiffness matrix of at least one component VRP that does not belong to the selected SCT of the component VRP configuration CFG. One technique used may preferably be static condensation, also known as the superelement method or substructuring. An interpolation step is then required to construct the approximator APX of the reduced stiffness matrix RSM provided as the output OPT of this method. A preferred embodiment uses canonical multifactorial decomposition CPD.
[0071] Although the invention has been described in detail with reference to preferred embodiments, it should be understood that the invention is not limited to the disclosed examples, and those skilled in the art can make many additional modifications and changes to it within the scope of the claims without departing from the scope of the invention.
[0072] It should be noted that the use of "a" or "an" throughout this application does not exclude a plurality, and "comprising" does not exclude other steps or elements. Furthermore, elements described in different embodiments may be combined. It should also be noted that the reference numerals in the claims should not be construed as limiting the scope of the claims.
Claims
1. A computer-implemented method for simulating the lattice structure of a component to be generated by modeling variations of repeating parts of the component, comprising: A) Provide parameter sets for component configurations of multiple different components, wherein the parameters of each parameter set define the component configuration of the component. B) Selecting a configuration for the component, wherein the selection can be accomplished by choosing only a subset of the entire variant multivariate, wherein the selection can be accomplished by systematically changing the parameters of the parameter set and the number of variants can be limited to a predefined number for each parameter. C) Provide a component model for each selected component, wherein the component model associates forces and displacements with the position of the corresponding component. D) Constructing an approximator, wherein the approximator is provided for interpolating the component model to approximate a component model of the selected component configuration that does not belong to the component configuration. The repeating components are the junctions of the lattice structure, which are modeled as parameterized superelements. After all junctions are modeled as parameterized superelements, the initial lattice structure is modeled, wherein the approximator is considered as the parameterized superelement. A reduced overall model of the component is obtained by combining all the parameterized superelements of the component with the other elements of the component.
2. The method according to claim 1, wherein, Step C) Configuring each selected component includes the following steps: a. Mesh the component using solid elements. b. By associating forces and displacements with the positions of the defined solid elements using the first component stiffness matrix, a preliminary component model of the meshed component is generated. c. Identify constraints that reduce the number of external degrees of freedom that would otherwise restrict the number of degrees of freedom for movement. d. By eliminating the constrained degrees of freedom in the stiffness matrix of the first component, a reduced stiffness matrix is obtained, reducing the model order of the preliminary component model to the remaining external degrees of freedom, thereby generating the component model. Furthermore, step D) includes constructing the approximator by interpolating the reduced stiffness matrix to extract the selected reduced stiffness matrix of the component that does not belong to the component configuration.
3. The computer-implemented method according to claim 1 or 2, wherein, The selection in step B) is random.
4. The computer-implemented method according to claim 2, wherein, The step of reducing the model order is accomplished by using Guyan reduction to obtain a reduced stiffness matrix.
5. The method according to claim 1 or 2, wherein, The interpolation in step D) uses canonical multifactor decomposition.
6. The method according to claim 1 or 2, further comprising the additional step of: E) generating a reduced component model by using the approximator on a plurality of parts of the component and combining the resulting reduced stiffness matrices of these parts with other element models of the component.
7. An additive manufacturing method for generating a variant assembly with repeating parts, wherein, The design steps include the method according to any one of claims 1 to 6, wherein subsequent generation steps are performed based on the design generated by the design steps.
8. A computer system suitable for performing the method according to any one of claims 1 to 5.