Optimization method

Abstract

To obtain topology of a structure satisfying a target load displacement relation.SOLUTION: An optimization device 10 sets an existence range distance vector indicating that an element of the structure exists within a range represented by a distance to a reference point. The optimization device 10 determines a candidate of topology of the structure on the basis of an initial value of the existence range distance vector or a distance represented by each component of the updated existence range distance vector. The optimization device 10 calculates the load displacement relation vector of the candidate of the topology of the structure by executing structure analysis simulation on the basis of the candidate of the topology of the structure. The optimization device 10 calculates an error vector between the load displacement relation vector and the target load displacement relation vector. The optimization device 10 updates the existence range distance vector so that the error vector becomes smaller. The optimization device 10 repeats the determination of the candidate of the topology of the structure, the calculation of the error vector, and the calculation of the new existence range distance vector to obtain the topology of the structure.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] This invention relates to an optimization method. [Background technology]

[0002] Conventionally, methods for optimizing structural topology based on material yard reduction series expansion are known (see, for example, Patent Document 1). This method solves the problem of reduced computational efficiency in conventional density-based topology optimization, which requires relative density and sensitivity filtering measures due to the large number of design variables.

[0003] Furthermore, topology evolution optimization methods for structural design are known (see, for example, Patent Document 2). This method can overcome the mesh dependency problem present in known optimized structural design methods, and the optimized structure has smooth geometric boundaries.

[0004] Furthermore, methods are known for designing structures having deployable surfaces using surface deployability constraints (see, for example, Patent Document 3).

[0005] Furthermore, topology optimization techniques known include topology optimization based on the homogenization method (see, for example, Non-Patent Document 1), topology optimization based on the density method (see, for example, Non-Patent Document 2), and topology optimization based on the level set method (see, for example, Non-Patent Document 3).

[0006] Furthermore, techniques for optimizing the dimensions and shape of dampers to target load-displacement relationships are known (see, for example, Non-Patent Documents 4 and 5). [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Special Publication No. 2021-516801 [Patent Document 2] Japanese Patent Publication No. 2008-186440 [Patent Document 3] Japanese Patent Publication No. 2021-125257 [Non-patent literature]

[0008] [Non-Patent Document 1] Bendsoe, Martin Philip, Kikuchi, Noboru Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering Open Access Volume 71, Issue 2, Pages 197 - 224November 1988 [Non-Patent Document 2] Bendsoe, Martin Philip: Optimal shape design as a material distribution problem; Structural Optimization, Vol.1, No.4, pp.193-202, 1989 [Non-Patent Document 3] JA Sethian, A. Wiegmann: Structural boundary design via level-set and immersed interface methods; Journal of Computational Physics, Vol.163, No.2, pp.489-528, 2000 [Non-Patent Document 4] Sumi Inaba, Takuya Suzuki, "Control of Plastic Deformation Performance of Shear Panel Type Dampers by Introducing Web Openings," Proceedings of the Architectural Institute of Japan Annual Conference, pp. 329-330, 2021. [Non-Patent Document 5] Takuya Suzuki, "Analytical Study on Control of Mechanical Properties of Shear Panel Damper by Introduction of Out-of-Plane Irregular Shape", Structural Engineering Papers, Architectural Institute of Japan, Vol.84, No.765, pp.1401-1409, November 2019 [Summary of the Invention] [Problem to be Solved by the Invention]

[0009] When designing the shape of a structure, it is necessary to search for an optimal shape that maximizes the performance of the structure. As a method for searching for the shape of a structure, topology optimization as disclosed in the above Patent Documents 1 to 3 is known.

[0010] This topology optimization is different from "size optimization" that uses the dimension itself representing the width of a member or the like as a design variable, or "shape optimization" that uses the outline of a member as a design variable, and is a highly flexible optimization method that uses the distribution of elements in a space to be designed as a design variable.

[0011] FIG. 11 is a diagram for explaining the difference among size optimization, shape optimization, and topology optimization.

[0012] As shown in FIG. 11(A), in size optimization, the dimension of the member B1 of the structure is set as a design variable, and the dimension of the member B1 included in the structure is optimized by adjusting the design variable.

[0013] Further, as shown in FIG. 11(B), in shape optimization, a parameter representing the shape of the member B2 is set as a design variable, and the shape of the member B2 included in the structure is optimized by adjusting the design variable.

[0014] On the other hand, as shown in FIG. 11(C), in topology optimization, the distribution itself of elements constituting the member B3 of the structure is searched, and it is also possible to search for a shape such as providing a hole or a void in the member B3. For this reason, topology optimization has been widely used for weight reduction of members in recent years.

[0015] On the other hand, the objective function of topology optimization is often a single target value, such as maximizing stiffness or maximizing material efficiency. This can be described as optimization based on the assumption that the member is within its elastic range. However, in the design of members that allow for plastic deformation, such as dampers, there are design requirements not only for stiffness but also for the load-displacement relationship, and efficient shape search is necessary while satisfying these requirements.

[0016] The technologies described in Patent Documents 1-2 and Non-Patent Documents 1-3 relate to topology optimization, but do not consider load-displacement relationships. Furthermore, the technologies described in Non-Patent Documents 4-5 relate to shape optimization that considers load-displacement relationships, and are not technologies related to topology optimization.

[0017] This invention has been made in view of the above facts, and aims to obtain a structural topology that satisfies the target load-displacement relationship. [Means for solving the problem]

[0018] To achieve the above objective, the present invention provides an optimization method for optimizing the topology of a structure that satisfies a target load-displacement relationship, comprising: setting a plurality of reference points within the target design space; setting an initial value for an existence range distance vector having a variable representing the distance between each of the plurality of reference points as its components, and indicating that the elements of the structure exist within the range represented by the distance between the reference points; determining a candidate topology of the structure based on the initial value of the existence range distance vector or the distance represented by each component of the updated existence range distance vector; and performing a predetermined structural analysis simulation based on the candidate topology of the structure to express the load-displacement relationship of the candidate topology of the structure. This is an optimization method in which a computer performs the following steps: calculate a load-displacement relationship vector, which is a vector and has loads corresponding to displacements as its components; calculate an error vector between the load-displacement relationship vector and a target load-displacement relationship vector that represents a target load-displacement relationship; calculate a new existence range distance vector by updating the existence range distance vector so that the error vector becomes smaller; repeatedly determine candidate topology of the structure, calculate the error vector, and calculate the new existence range distance vector; and when predetermined conditions are met, obtain the topology of the structure in which the elements of the structure exist within the range of the distance from the reference point represented by each component of the existence range distance vector. This makes it possible to obtain a topology of a structure that satisfies the target load-displacement relationship.

[0019] In the present invention, when updating the existing range distance vector to reduce the error vector, a partial derivative matrix of the error vector with respect to the existing range distance vector is generated, a singular value decomposition result is generated by performing singular value decomposition of the partial derivative matrix, a submatrix corresponding to a predetermined low-order mode is generated from the submatrix of the singular value decomposition result, a first correction vector for the existing range distance vector for error reduction is generated based on the generated submatrix and the error vector, a submatrix corresponding to a predetermined high-order mode is generated from the submatrix of the singular value decomposition result, a second correction vector for the existing range distance vector for noise removal is generated based on the generated submatrix and the existing range distance vector, and a new existing range distance vector is calculated based on the existing range distance vector, the first correction vector and the second correction vector. This makes it possible to obtain a structural topology that satisfies the target load-displacement relationship while removing noise included in the candidate structural topology. [Effects of the Invention]

[0020] According to the present invention, the topology of a structure that satisfies the target load-displacement relationship can be obtained. [Brief explanation of the drawing]

[0021] [Figure 1] This block diagram shows an example of the configuration of the optimization apparatus according to this embodiment. [Figure 2] This figure shows an example of the computer configuration of the optimization device according to this embodiment. [Figure 3] This figure illustrates the design space and the existence range distance vector in this embodiment. [Figure 4] This is a diagram illustrating the processing flow of this embodiment. [Figure 5] This figure shows an example of the optimization processing routine according to this embodiment. [Figure 6] This is a diagram used to explain the details of the simulation experiment. [Figure 7] This figure shows the results of a simulation experiment. [Figure 8] This figure shows the results of a simulation experiment. [Figure 9] This figure shows the results of a simulation experiment. [Figure 10] This figure shows the results of a simulation experiment. [Figure 11] This diagram illustrates the differences between dimensional optimization, shape optimization, and topology optimization. [Modes for carrying out the invention]

[0022] Embodiments of the present invention will be described in detail below with reference to the drawings.

[0023] <Configuration of the optimization device according to this embodiment>

[0024] Figure 1 shows an example of the configuration of an optimization device 10 according to an embodiment of the present invention. Functionally, the optimization device 10 can be represented as a configuration including a data receiving unit 12, a computer 14, and an output unit 16, as shown in Figure 1.

[0025] The optimization device 10 of this embodiment assists designers in designing structures by performing topology optimization of the structure.

[0026] In this embodiment, when expressions such as "optimize," "optimized design variables," or "optimal solution" are used, it should be noted that these expressions of "optimal" refer to something obtained by approaching the optimal state. Therefore, when trying to obtain parameters that minimize a certain error, it should be noted that the parameters obtained through optimization may not be the global solution that minimizes the error, but rather a local solution.

[0027] The following provides a detailed explanation.

[0028] The data reception unit 12 receives various types of data. Specifically, the data reception unit 12 receives data related to the structure, data representing the structural simulation model for performing structural simulations, and data representing the target load-displacement relationship. This data is pre-set by the user.

[0029] Computer 14 is composed of a CPU (Central Processing Unit), ROM (Read Only Memory) which stores programs for implementing each processing routine, RAM (Random Access Memory) which temporarily stores data, memory as a storage means, a network interface, etc. As shown in Figure 2, computer 14 includes a CPU 51, memory 52 as a temporary storage area, and a non-volatile storage unit 53. Computer 14 also includes an input / output interface (I / F) 54 to which input / output devices such as a data receiving unit 12 and an output unit 16 are connected, and a read / write (R / W) unit 55 which controls the reading and writing of data to the recording medium 59. Computer 14 also includes a network I / F 56 which is connected to a network such as the Internet. The CPU 51, memory 52, storage unit 53, input / output I / F 54, R / W unit 55, and network I / F 56 are connected to each other via a bus 57.

[0030] The storage unit 53 can be implemented using a Hard Disk Drive (HDD), Solid State Drive (SSD), flash memory, etc. The storage unit 53, as a storage medium, stores programs that enable the computer to function. The CPU 51 reads the programs from the storage unit 53, loads them into memory 52, and sequentially executes the processes contained within the programs.

[0031] As shown in Figure 1, the computer 14 functionally comprises a data storage unit 20, a setting unit 24, a calculation unit 26, and a result acquisition unit 28.

[0032] The data storage unit 20 stores various types of data received by the data reception unit 12. Specifically, the data storage unit 20 stores data related to the structure, data representing the structural simulation model for performing structural simulations, and data representing the target load-displacement relationship vector.

[0033] Figure 3 is a diagram illustrating the design space and existence range distance vector in this embodiment. Figure 3(A) shows the design space of the structure. The rectangular areas in Figure 3(A) represent the elements of the structure. In this embodiment, the existence range distance vector, which indicates whether or not the elements of the structure exist, is optimized. Multiple reference points are set on the design space shown in Figure 3(A), and the structure model is set according to the existence range distance of the structure set for each reference point. In this embodiment, a grid-type element mesh is set.

[0034] Figure 3(B) is a diagram illustrating the existence range distance vector of this embodiment. As shown in Figure 3(B), in this embodiment, a plurality of reference points S1, S2, S3, S4, ... are set in the design space. These reference points may be set regularly or randomly in the design space. In this embodiment, distances L1, L2, L3, L4, ... are set from these plurality of reference points S1, S2, S3, S4, ... Then, in this embodiment, elements of a structure are treated as existing within the range represented by these distances L1, L2, L3, L4 from the reference points. Various methods can be used to determine whether an element of a structure exists. For example, as shown in Figure 3(B), elements whose center position (not shown) is within the existence range distance from the reference points are modeled as existing elements.

[0035] Specifically, as shown in Figure 3(B), elements E1 whose center is within a distance L1 from reference point S1 are treated as existing. Also, as shown in Figure 3(B), elements E2, E3, E4, E5, E6, and E7 whose centers are within a distance L2 from reference point S2 are treated as existing. Also, as shown in Figure 3(B), elements E8, E9, E10, E11, and E12 whose centers are within a distance L3 from reference point S3 are treated as existing. Also, as shown in Figure 3(B), elements E13 and E14 whose centers are within a distance L4 from reference point S4 are treated as existing. On the other hand, elements within the above design space whose center is not within a predetermined distance from a reference point are treated as not existing.

[0036] In this embodiment, an existence range distance vector {L1, L2, L3, L4, ...} is set, with the above-mentioned distances L1, L2, L3, L4, ... as its components. Then, this existence range distance vector {L1, L2, L3, L4, ...} is optimized by the processes described later.

[0037] Figure 4 is a diagram illustrating the overview of the processing in this embodiment. As shown in Figure 4, in this embodiment, first, an existence range distance vector {Li} is set. Next, the presence or absence of elements constituting the structure is set according to the distances represented by each component of the existence range distance vector {Li}. Next, candidate structural topologies are set according to the presence or absence of elements constituting the structure. These candidate structural topologies are set as structural models, and a structural analysis simulation is performed. As a result of the structural analysis simulation, a load-displacement relationship vector {Pj} of the candidate structural topology is output. This load-displacement relationship vector {Pj} is a vector whose components are loads corresponding to displacements. Specifically, the load-displacement relationship vector {Pj} has loads "load" (values ​​of the plotted points of the black circles in Figure 4) corresponding to each displacement "disp" shown in Figure 4 as its components.

[0038] The setting unit 24 refers to the data on the structure stored in the data storage unit 20 and sets the design space.

[0039] Next, the setting unit 24 sets multiple reference points within the target design space.

[0040] Next, the setting unit 24 sets the initial value of the existence range distance vector. As described above, the existence range distance vector is a vector in which each component is a variable representing the distance between each of the multiple reference points, and which represents that the elements of the structure exist within the range represented by the distance between the reference points.

[0041] The calculation unit 26 determines candidate structures for topology based on the initial value of the existence range distance vector set by the setting unit 24 or the existence range distance vector updated in the previous processing. Specifically, as shown in Figure 3(B), the calculation unit 26 determines candidate structures for topology based on the existence range distance vector {L1, L2, L3, L4, ...}, assuming that elements of the structure exist within the range represented by the distances L1, L2, L3, L4, ... from multiple reference points S1, S2, S3, S4, ....

[0042] Next, the calculation unit 26 calculates the load-displacement relationship vectors for the candidate structural topology by performing a predetermined structural analysis simulation based on the candidate structural topology. Note that known methods may be used for the structural analysis simulation here.

[0043] Next, the calculation unit 26 calculates an error vector between the load-displacement relationship vector obtained by the structural analysis simulation and the target load-displacement relationship vector representing the target load-displacement relationship. Specifically, the calculation unit 26 calculates an error vector representing the error between the load-displacement relationship vector obtained by the structural analysis simulation and the target load-displacement relationship vector stored in the data storage unit 20.

[0044] The calculation unit 26 calculates a new existence range distance vector by updating the existence range distance vector so that the error vector becomes smaller.

[0045] For example, the existence range distance vector can be updated to reduce the error vector using the MIEC (Modal Iterative Error Correction) (registered trademark) method, which is one example of an error correction method. The MIEC (registered trademark) method is disclosed, for example, in the following references 1-2.

[0046] Reference 1: Takuya Suzuki, "Dynamic Inversion of Basement Input in an Elastoplastic Ground Model Using Modal Iterative Error Correction Method," Journal of Structural Engineering, Architectural Institute of Japan, Vol. 83, No. 749, 2018, pp. 1021-1029, https: / / doi.org / 10.3130 / aijs.83.1021 Reference 2: Takuya Suzuki, "Function Identification Using Modal Iterative Error Correction Method," The Japanese Society for Artificial Intelligence, Conference Name: 2021 Annual Conference of the Japanese Society for Artificial Intelligence (35th), https: / / doi.org / 10.11517 / pjsai.JSAI2021.0_4G3GS2l05

[0047] For example, the following describes the case where the existence range distance vector is updated to minimize the error vector using the MIEC® method disclosed in References 1 and 2.

[0048] First, the calculation unit 26 generates a partial derivative matrix with respect to the range distance vector of the error vector. Next, the calculation unit 26 generates a singular value decomposition result by performing singular value decomposition on the generated partial derivative matrix. The calculation unit 26 generates a submatrix corresponding to a predetermined low-order mode from the submatrixes of the singular value decomposition result.

[0049] The calculation unit 26 generates a first correction vector for the existence range distance vector for error reduction, as disclosed in Reference 2, based on the generated submatrix and error vector.

[0050] Furthermore, the calculation unit 26 generates a submatrix corresponding to a predetermined higher-order mode from the submatrix of the singular value decomposition result, and generates a second modification vector for the existence range distance vector for noise reduction, as disclosed in Reference 2, based on the generated submatrix and the existence range distance vector.

[0051] Then, the calculation unit 26 calculates a new existence range distance vector based on the existence range distance vector, the first correction vector, and the second correction vector.

[0052] Furthermore, the determination of candidate structural topologies, calculation of error vectors, and calculation of new existence range distance vectors are repeated until predetermined conditions related to the error vector are met.

[0053] The predetermined conditions related to the error vector may include, for example, whether the number of corrections has reached a predetermined number, whether the value of each component of the error vector has fallen below a predetermined threshold, or whether the norm of the error vector has fallen below a predetermined threshold.

[0054] The result acquisition unit 28 acquires the topology of a structure in which the elements of the structure exist within the distance range from the reference point represented by each component of the existence range distance vector, when predetermined conditions related to iteration are met. Specifically, the result acquisition unit 28 determines whether the error vector satisfies predetermined conditions related to the error vector. If the predetermined conditions related to the error vector are met, the correction of the existence range distance vector is terminated. If the predetermined conditions related to the error vector are not met, the correction of the existence range distance vector is repeated.

[0055] The result acquisition unit 28 then outputs the topology of the structure corresponding to the existence range distance vector {L1, L2, L3, L4, ...} obtained by modifying each component of the existence range distance vector.

[0056] The output unit 16 outputs the topology of the structure output by the result acquisition unit 28 as the result. For example, the output unit 16 can be implemented by a display.

[0057] <Operation of Optimization Device 10>

[0058] Next, the operation of the optimization device 10 will be explained. When the data receiving unit 12 of the optimization device 10 receives various data inputs, it stores them in the data storage unit 20. Then, when the computer 14 of the optimization device 10 receives a processing execution instruction signal, it executes the optimization processing routine shown in Figure 5.

[0059] In step S100, the setting unit 24 refers to the data on the structure stored in the data storage unit 20 and sets the design space.

[0060] In step S102, the setting unit 24 sets multiple reference points within the target design space set in step S100.

[0061] In step S104, the setting unit 24 sets the initial value of the existence range distance vector. For example, the setting unit 24 sets the initial value of the existence range distance vector by setting each component of the existence range distance vector to 0.

[0062] In step S106, the calculation unit 26 determines candidate structures based on the initial values ​​of the existence range distance vector set in step S104 or the new existence range distance vector updated in the previous step S114.

[0063] In step S108, the calculation unit 26 reads the structural simulation model stored in the data storage unit 20 and performs a known structural simulation based on the structural simulation model and the candidate structural topology determined in step S106. This structural simulation generates a load-displacement relation vector {P c1 ,P c2, P c3 , ···} is obtained.

[0064] In step S110, the calculation unit 26 calculates the load-displacement relationship vector {P c1 , P c2 , P c3 , ···} obtained in step S108 and the target load-displacement relationship vector {P T1 , P T2 , P T3 , ···} stored in the data storage unit 20, calculates the error vector {P c1 -P T1 , P c2 -P T2 , P c3 -P T3 , ···}.

[0065] In step S112, the calculation unit 26 determines whether the error vector {P c1 -P T1 , P c2 -P T2 , P c3 -P T3 , ···} calculated in step S110 satisfies a predetermined condition related to the error vector. If the predetermined condition related to the error vector is satisfied, the process proceeds to step S116. On the other hand, if the predetermined condition related to the error vector is not satisfied, the process proceeds to step S114.

[0066] In step S114, the calculation unit 26 updates the existing range distance vector such that the error vector {P c1 -P T1 , P c2 -P T2 , P c3 -P T3 , ···} calculated in step S110 becomes smaller, thereby calculating a new existing range distance vector, and the process proceeds to step S106.

[0067] For example, the calculation unit 26 uses the aforementioned MIEC (registered trademark) method to obtain the error vector {P c1 -P T1 , P c2-P T2 ,P c3 -P T3 A new existence range distance vector is calculated by updating the existence range distance vector so that ,···} becomes smaller.

[0068] In step S116, the result acquisition unit 28 acquires the topology of the structure, which is determined by the distance range from the reference point represented by each component of the existence range distance vector. The result acquisition unit 28 then outputs the final topology of the structure.

[0069] The output unit 16 outputs the final structure topology obtained by the result acquisition unit 28 as the result.

[0070] As described in detail above, the optimization device of this embodiment optimizes the topology of a structure that satisfies the target load-displacement relationship. Specifically, the optimization device sets a plurality of reference points within the target design space. The optimization device sets an initial value for the existence range distance vector, which has a variable representing the distance between each of the plurality of reference points as its component, and which represents that the elements of the structure exist within the range represented by the distance between the reference points. The optimization device determines a candidate structure topology based on the initial value of the existence range distance vector or the distances represented by each component of the updated existence range distance vector. Based on the candidate structure topology, the optimization device calculates a load-displacement relationship vector, which is a vector representing the load-displacement relationship of the candidate structure topology and has loads corresponding to the displacements as its components, by performing a predetermined structural analysis simulation. The optimization device calculates an error vector between the load-displacement relationship vector and the target load-displacement relationship vector, which represents the target load-displacement relationship. The optimization device calculates a new existence range distance vector by updating the existence range distance vector so that the error vector becomes smaller. The optimization device then repeats the process of determining a candidate structure topology, calculating the error vector, and calculating a new existence range distance vector. The optimization device obtains the topology of a structure in which, when predetermined conditions are met, the elements of the structure exist within the distance range from the reference point represented by each component of the existence range distance vector. This allows the device to obtain the topology of a structure that satisfies the target load-displacement relationship.

[0071] Furthermore, the optimization device of this embodiment can also use the MIEC® method, which is an example of an error correction method. Specifically, when the optimization device updates the existing range distance vector to reduce the error vector, it generates a partial derivative matrix of the error vector with respect to the existing range distance vector, performs singular value decomposition of the partial derivative matrix to generate the singular value decomposition result, and generates a submatrix corresponding to a predetermined low-order mode from the submatrix of the singular value decomposition result. Based on the generated submatrix and the error vector, the optimization device generates a first correction vector for the existing range distance vector for error reduction, generates a submatrix corresponding to a predetermined high-order mode from the submatrix of the singular value decomposition result, and generates a second correction vector for the existing range distance vector for noise removal based on the generated submatrix and the existing range distance vector. Then, the optimization device calculates a new existing range distance vector based on the existing range distance vector, the first correction vector, and the second correction vector. This makes it possible to obtain a structural topology that satisfies the target load-displacement relationship while removing noise included in the candidate structural topology.

[0072] <Simulation Experiment>

[0073] Next, we set up an example problem and confirmed the effectiveness of the optimization method according to this embodiment by conducting a simulation experiment on that example problem. In the simulation experiment, the structural optimization problem of a beam was used as the example problem. Figure 6 shows the design space of the beam used as the example problem in the simulation experiment. As shown in Figure 6, in this simulation experiment, we consider the case in which a forced displacement load is applied to the upper center of a beam that is pin-supported at both lower ends. In this simulation experiment, we explored where to place elements within the entire beam, which is enclosed by a dashed line in the design space. A two-dimensional model was used for the beam analysis model.

[0074] In this simulation experiment, similar to the embodiment described above, the presence or absence of structural elements is first determined according to the existence range distance for each reference point set as input. Then, a model representing the structure is created based on the presence or absence of elements, numerical analysis is performed, and the resulting load-displacement relation vector is output. By solving this inverse problem, an existence range distance vector that satisfies the target load-displacement relation vector is searched for. In this example, the MIEC (registered trademark) method was used as the error correction method.

[0075] Figures 7 to 10 show the results of the simulation experiment. In graph (A), the horizontal axis represents the number of iterations (Iteration Number (times)), and the vertical axis represents the norm of the error vector (RSS Error (kN)). In graph (B), the horizontal axis represents the displacement (Disp (mm)), and the vertical axis represents the load (RF (kN)). Also, in graph (B), T represents the target load relationship, and I represents the load-displacement relationship of the candidate structural topology. Figure (C) shows the candidate structural topology represented in the design space.

[0076] As shown in Figures 7 to 10, in areas where the norm of the error vector is small, the load-displacement relationship I of the candidate structural topology approaches the target load-displacement relationship T. The final topology shown in Figure 10(C) can be seen to satisfy the target load-displacement relationship while eliminating elements that are considered unnecessary. From the above, it has been confirmed that topology optimization that satisfies the target load-displacement relationship can be performed according to this embodiment.

[0077] It should be noted that the present invention is not limited to the embodiments described above, and various modifications and applications are possible without departing from the spirit of the invention.

[0078] For example, the above embodiment describes the case where the MIEC® method is used as the error correction method, but it is not limited to this. For example, other error correction methods such as the nonlinear least squares method, Newton's method, or the steepest descent method may be used.

[0079] Furthermore, although the above embodiment describes the optimization of the topology of a structure in two-dimensional space as an example, it is not limited to this. The optimization method according to the above embodiment can also be extended to the topology of a structure in three dimensions. For this reason, the optimization method according to the above embodiment may also be used when optimizing the topology of a structure in three-dimensional space.

[0080] Furthermore, although the above describes a configuration in which the program is pre-stored (installed) in a storage unit (not shown), the program can also be provided in a form recorded on any of the recording media such as a CD-ROM, DVD-ROM, or microSD card. [Explanation of Symbols]

[0081] 10 Optimization device 12 Data Reception Department 14 Computer 16 Output section 20 Data storage unit 24. Settings Section 26 Calculation section 28 Result acquisition part

Claims

1. An optimization method for optimizing the topology of a structure that satisfies a target load-displacement relationship, By setting multiple reference points within the target design space, The system has variables as its components that represent the distance between each of the aforementioned multiple reference points, and sets an initial value for the existence range distance vector that indicates that the elements of the structure exist within the range represented by the distance between the reference points. Based on the initial value of the existence range distance vector or the distance represented by each component of the updated existence range distance vector, a candidate topology for the structure is determined. Based on the candidate topology of the structure, a predetermined structural analysis simulation is performed to calculate a load-displacement relationship vector that represents the load-displacement relationship of the candidate topology of the structure, and in which each component is a load corresponding to the displacement. The error vector between the aforementioned load-displacement relationship vector and the target load-displacement relationship vector representing the target load-displacement relationship is calculated. By updating the existence range distance vector so that the error vector becomes smaller, a new existence range distance vector is calculated. The determination of candidate topologies for the structure, the calculation of the error vector, and the calculation of a new existence range distance vector are repeated. When predetermined conditions are met, the topology of the structure is obtained in which the elements of the structure exist within the range of the distances from the reference point represented by each component of the existence range distance vector. An optimization method used by computers to perform processing.

2. When updating the new existence range distance vector so that the error vector becomes smaller, A partial derivative matrix of the error vector with respect to the existence range distance vector is generated, By performing singular value decomposition on the aforementioned partial differential matrix, the singular value decomposition results are generated. A submatrix corresponding to a predetermined low-order mode is generated from the submatrix of the singular value decomposition results. Based on the generated submatrix and the error vector, a first correction vector is generated for the existence range distance vector for error reduction. From the submatrices of the singular value decomposition results, a submatrix corresponding to a predetermined higher-order mode is generated, Based on the generated submatrix and the existence range distance vector, a second modification vector for the existence range distance vector for noise reduction is generated. Based on the aforementioned existence range distance vector, the first modification vector, and the second modification vector, a new existence range distance vector is calculated. The optimization method according to claim 1.

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