Structural displacement response topology optimization design method and device

Abstract

The application discloses a structural displacement response topology optimization design method and device, and relates to the technical field of structural dynamics. The method comprises the following steps: a finite element model of a structure is established, boundary conditions and external load excitation are applied, an optimization model with the minimum displacement amplitude as the target and the volume fraction and the anti-resonance frequency as the constraints is constructed, after the parameter initialization is completed, the sensitivities of the displacement amplitude and the volume fraction are iteratively calculated, the anti-resonance frequency eigenvalue sequence is solved by using the modal acceleration method, the constrained anti-resonance frequency is tracked in combination with the modal assurance criterion, the sensitivities of the anti-resonance frequency to the design variables are solved by using the Moore-Penrose generalized inverse, all the parameters and the sensitivities are input into the MMA optimization algorithm, the convergence is judged, and if the convergence is satisfied, the iteration is terminated to obtain the optimal design variable vector, and the structural displacement response topology optimization is realized. The method solves the problem that the existing technology is prone to falling into the anti-resonance point and converging in advance to form an intermediate density gray area when displacement minimization topology optimization is performed.

Description

Technical Field

[0001] This application relates to the field of structural dynamics technology, and in particular to a method and apparatus for topology optimization design of structural displacement response. Background Technology

[0002] In the field of structural dynamics, the displacement response at critical locations of a structure is a crucial indicator of its dynamic performance. Topology optimization is typically performed with the goal of minimizing the structural displacement response to obtain lightweight structures with excellent dynamic performance. Existing techniques achieve good optimization results under low-frequency excitation conditions (excitation frequencies lower than the initial structural fundamental frequency). However, under high-frequency excitation conditions (excitation frequencies higher than the initial structural fundamental frequency), the topology optimization problem of minimizing the displacement response leads to numerous gray areas of intermediate density in the design results, making it impossible to obtain a clearly usable structure.

[0003] In summary, existing technologies lack effective solutions for the structural topology optimization problem of minimizing displacement of low-damped structures under a single high-frequency excitation condition. Summary of the Invention

[0004] In this embodiment of the application, a structural displacement response topology optimization design method is provided, which solves the technical problem that the existing technology is prone to getting trapped in the anti-resonance point premature convergence and forming an intermediate density gray region when performing displacement minimization topology optimization.

[0005] In a first aspect, embodiments of this application provide a structural displacement response topology optimization design method, which includes: Step 101, establishing a finite element model of the structure and applying boundary conditions and external load excitation; Step 102, establishing an optimization model based on the finite element model of the structure with the objective of minimizing displacement amplitude and with volume fraction and anti-resonance frequency as constraints; Step 103, initializing the parameters of the optimization model, taking the upper limit of volume fraction as the initial value of the design variable, taking the excitation frequency as the upper limit of the anti-resonance frequency, and recording the eigenvector corresponding to the initial anti-resonance frequency; Step 104, based on the optimization model, iteratively calculating the displacement amplitude and its sensitivity to the design variable, the volume fraction and its sensitivity to the design variable, solving the eigenvalue sequence of the anti-resonance frequency based on the modal acceleration method, and based on each feature in the eigenvalue sequence... The eigenvector corresponding to the value is used to track the constrained anti-resonance frequency through the modal confidence criterion, and the sensitivity of the constrained anti-resonance frequency to the design variables is solved by combining the Moore-Penrose generalized inverse; Step 105, the design variable vector, displacement amplitude and its sensitivity to the design variables, volume fraction and its sensitivity to the design variables, and the constrained anti-resonance frequency and its sensitivity to the design variables are input into the encapsulated MMA optimization algorithm for optimization; where the design variable vector is the set of all individual design variables; Step 106, it is determined whether the optimization meets the convergence condition. If it does, the iteration is terminated to obtain the final design configuration. If it does not meet the condition, steps 104 to 106 are executed iteratively until the convergence condition is met to obtain the optimal design variables, so as to realize the topology optimization of the structural displacement response.

[0006] In one possible implementation, the specific process of establishing the finite element model of the structure is as follows: given material properties, including Young's modulus, Poisson's ratio and density, the geometric model of the structure is discretized into finite element elements based on the material properties to obtain the finite element model of the structure.

[0007] In one possible implementation, the expression for the optimization model is: find: min: ;st: ; ; ; where find means to search, To design a variable vector, its elements For a single design variable, each It corresponds one-to-one with finite element elements and is updated after each iteration. To design the lower bound of variables, N This represents the total number of design variables. For transpose operation, For indexing, For the first There are 1 design variable, where min represents minimizing. For the first k Degrees of freedom in the next iteration The displacement amplitude at point st is a constraint condition. It is the volume fraction. This is the upper limit of volume fraction. For the first k In the frequency response function of the key position displacement in the iteration, the first... One anti-resonance frequency, The excitation angular frequency.

[0008] In one possible implementation, the degrees of freedom are calculated using the adjoint vector method. Displacement amplitude For the Design variables The sensitivity is: ;in, Indicates the first In the next iteration, the degrees of freedom Displacement amplitude For the Design variables Sensitivity, Indicates the first In the next iteration, the real part of the displacement amplitude... Indicates the first In the next iteration, the imaginary part of the displacement amplitude Indicates the displacement amplitude relative to the first Design variables The real part of the partial derivative, Indicates the displacement amplitude relative to the first Design variables The imaginary part of the partial derivative, It is the reciprocal of the displacement amplitude; based on Calculate the volume fraction; where, For the first Volume fraction in the next iteration Indicates the first Volume of each unit Represents the total volume; based on Calculate the volume fraction for the first Design variables The sensitivity; among which, For the first In the next iteration, the volume fraction For the Sensitivity of each design variable.

[0009] In one possible implementation, the step of solving the eigenvalue sequence of anti-resonance frequencies based on the modal acceleration method includes: solving a generalized eigenvalue problem. The set of all obtained eigenvalues ​​is taken as the eigenvalue sequence of the anti-resonance frequency in the current iteration, and the eigenvalue sequence is denoted as... ;in, For generalized stiffness matrix, , Let be the null space matrix of the load column vectors, satisfying the relation , For modal force vectors, It is a generalized force vector. This is used to convert displacement response in modal coordinates into degrees of freedom. The vector of displacement magnitude at that point To extract vectors, This is the quasi-static compensation term in the modal acceleration method. Here is the modal stiffness matrix. For the excitation angular frequency, For the generalized mass matrix, , Here is the modal mass matrix. This is the modal coordinate vector.

[0010] In one possible implementation, the step of tracking the constrained anti-resonance frequency based on the eigenvectors corresponding to each eigenvalue in the eigenvalue sequence using a modal confidence criterion includes: combining the first... The iteration of the ... Eigenvectors corresponding to each anti-resonance frequency The modal confidence criterion is used to calculate the MAC value of the eigenvector corresponding to each eigenvalue in the current iteration's eigenvalue sequence. The eigenvector corresponding to the maximum MAC value is found, and the positive square root of its corresponding eigenvalue is used as the constrained anti-resonance frequency. The expression for the MAC function is: ;in, The MAC value is the eigenvector corresponding to each eigenvalue in the eigenvalue sequence. For the first The iteration of the ... The eigenvectors corresponding to the anti-resonance frequencies For transpose operation, For the first k In the next iteration, the eigenvalue sequence The s The eigenvectors corresponding to each eigenvalue.

[0011] In one possible implementation, the combination of Moore-Penrose generalized inverse solving for the sensitivity of the constrained anti-resonance frequency to the design variables includes: ;in, For the first k In the nth iteration, the 1st Anti-resonance frequency Design variables Sensitivity, For the first k In the nth iteration, the 1st Anti-resonance frequency Corresponding eigenvalues , For the first k In the next iteration, the eigenvalues The corresponding feature vector, For the first k In the next iteration, the accompanying eigenvalue problem eigenvectors, For transpose operation, Generalized stiffness matrix The transpose of the matrix for the first Design variables The partial derivatives, Generalized mass matrix The transpose of the matrix for the first Design variables The partial derivatives of .

[0012] In one possible implementation, the convergence condition includes: calculating the maximum absolute value of the difference between corresponding elements of the design variable vector before and after the update; when the maximum absolute value is less than a threshold, the convergence condition is satisfied.

[0013] Secondly, embodiments of this application provide a structural displacement response topology optimization design device, which includes: a first establishment module for establishing a finite element model of the structure and applying boundary conditions and external load excitation; a second establishment module for establishing an optimization model based on the finite element model of the structure with the objective of minimizing displacement amplitude and with volume fraction and anti-resonance frequency as constraints; an initialization module for initializing the parameters of the optimization model, using the upper limit of volume fraction as the initial value of the design variable, the excitation frequency as the upper limit of the anti-resonance frequency, and recording the eigenvector corresponding to the initial anti-resonance frequency; and an iteration module for iteratively calculating the displacement amplitude and its sensitivity to the design variable, the volume fraction and its sensitivity to the design variable, and solving the eigenvalue sequence of the anti-resonance frequency based on the modal acceleration method, and calculating the eigenvalues ​​based on each eigenvalue in the eigenvalue sequence. The corresponding eigenvectors are used to track the constrained anti-resonance frequencies using modal confidence criteria, and the sensitivity of the constrained anti-resonance frequencies to design variables is solved using the Moore-Penrose generalized inverse. The optimization module is used to optimize the MMA optimization algorithm encapsulated with the current iteration step's design variable vector, displacement amplitude and its sensitivity to design variables, volume fraction and its sensitivity to design variables, and constrained anti-resonance frequencies and their sensitivity to design variables. The design variable vector is the set of all individual design variables. The judgment module is used to determine whether the design variable vector satisfies the convergence condition. If it does, the iteration terminates and the optimal design variable vector is obtained. If it does not, steps 104 to 106 are executed iteratively until the convergence condition is met and the optimal design variable vector is obtained, thereby achieving topology optimization of the structural displacement response.

[0014] The one or more technical solutions provided in this application have at least the following technical effects: This application provides a structural displacement response topology optimization design method. By introducing anti-resonance frequency constraints to construct an optimization model, it fundamentally avoids the problem of low-damped structures falling into the anti-resonance point and prematurely converging in the early stage of high-frequency excitation optimization, eliminating the appearance of the intermediate density gray area in the design results, and obtaining a clear and usable topology configuration. At the same time, it allows the excitation frequency to gradually approach the resonance point in the later stage of optimization, causing the displacement amplitude at key positions of the structure to converge to an extremely low value close to zero, breaking through the lower limit of displacement amplitude in traditional methods and significantly improving the displacement minimization optimization effect. Combined with the sensitivity of the constrained anti-resonance frequency to design variables by Moore-Penrose generalized inverse solution, it effectively improves the iterative solution efficiency of topology optimization, with particularly obvious advantages in large-scale multi-degree-of-freedom structural optimization. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 A flowchart of a structural displacement response topology optimization design method provided in an embodiment of this application.

[0017] Figure 2 This is a schematic diagram illustrating the geometric model of a planar cantilever beam structure provided in an embodiment of this application.

[0018] Figure 3 A schematic diagram of the optimization results obtained by the existing method provided in this application embodiment after 220 iterations at an excitation frequency of 350Hz.

[0019] Figure 4 A schematic diagram of the optimization results obtained by the method of this application after 220 iterations at an excitation frequency of 350Hz, as provided in the embodiments of this application.

[0020] Figure 5 Frequency response curves of the optimized results of the existing method provided in the embodiments of this application.

[0021] Figure 6 Frequency response curves of the optimized results of the method of this application provided in the embodiments of this application.

[0022] Figure 7 A schematic diagram of the structural displacement response topology optimization design device provided in the embodiments of this application.

[0023] Figure 8 A schematic diagram of a structural displacement response topology optimization design server provided in an embodiment of this application. Detailed Implementation

[0024] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0025] The following description of some technologies involved in the embodiments of this application is provided to aid understanding and should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, some descriptions of well-known functions and structures are omitted in the following description.

[0026] This application provides a structural displacement response topology optimization design method, such as... Figure 1 As shown, the method includes steps 101 to 106. Wherein, Figure 1 This is merely one execution order shown in the embodiments of this application and does not represent the only execution order of a structural displacement response topology optimization design method. Where the final result can be achieved, Figure 1 The steps shown can be performed in parallel or in reverse order.

[0027] Step 101: Establish the finite element model of the structure and apply boundary conditions and external load excitation.

[0028] It should be noted that the structure of this application is a low-damping structure.

[0029] The specific process of establishing the finite element model of the structure is as follows: given material properties, including Young's modulus, Poisson's ratio and density, the geometric model of the structure is discretized into finite element elements based on the material properties to obtain the finite element model of the structure.

[0030] Specifically, Figure 2 This is a schematic diagram illustrating the geometric model of a planar cantilever beam structure provided in an embodiment of this application. The structure is discretized into 100 × 50 = 5000 planar 4-node stress elements, each element being 400 mm in size, resulting in 10302 degrees of freedom. Given material properties: Young's modulus E = 210 GPa, Poisson's ratio μ = 0.3, and density ρ = 7860 kg / m³. The left end of the structure is set as a fixed boundary, and a vertically downward harmonic excitation force is applied at the midpoint of the right end as an external load excitation. In the figure, x represents the horizontal direction, and y represents the vertical direction. o The origin of the coordinate system is denoted as .

[0031] Step 102: Based on the finite element model of the structure, establish an optimization model with the goal of minimizing displacement amplitude and with volume fraction and anti-resonance frequency as constraints.

[0032] The expression for the optimization model is: find: .

[0033] min: .

[0034] st: .

[0035] .

[0036] .

[0037] Here, find means to search. To design a variable vector, its elements For a single design variable, each It corresponds one-to-one with finite element elements and is updated after each iteration. To design the lower bound of variables, N This represents the total number of design variables. For transpose operation, For indexing, For the first There are 1 design variable, where min represents minimizing. For the first k Degrees of freedom in the next iteration The displacement amplitude at point st is a constraint condition. It is the volume fraction. This is the upper limit of volume fraction. For the first k In the frequency response function of the key position displacement in the iteration, the first... One anti-resonance frequency, The excitation angular frequency.

[0038] Specifically, please refer to Figure 2 This application uses the midpoint of the right end of the structure (direction of the excitation force, degree of freedom number) as the reference point. With the objective of minimizing the displacement amplitude, and constrained by the volume fraction and anti-resonance frequency, an optimization model as described in step 102 is established; and lower limits for design variables are set. Volume fraction upper limit Four excitation frequencies were selected: 350Hz, 500Hz, 1200Hz, and 1450Hz (except for 350Hz, all others are higher than the initial structure's fundamental frequency of 362Hz). The excitation angular frequency... It is obtained by converting the excitation frequency.

[0039] Step 103: Initialize the parameters of the optimization model, take the upper limit of the volume fraction as the initial value of the design variable, take the excitation frequency as the upper limit of the anti-resonance frequency, and record the eigenvector corresponding to the initial anti-resonance frequency.

[0040] Specifically, set the iteration steps Design variables The initial values ​​were uniformly set to an upper limit of 0.4 for the volume fraction. The displacement frequency response curve of the initial structure was calculated in the frequency range of 0-2500Hz, and the first anti-resonance frequency of the initial structure was found to be 988.09Hz and the second anti-resonance frequency was 1870.22Hz. The four excitation frequencies were used as the upper limits of the anti-resonance frequency to constrain the first anti-resonance frequency of the structure, and the first anti-resonance frequency of the initial structure was recorded. corresponding feature vector .

[0041] Step 104: Based on the optimization model, iteratively calculate the displacement amplitude and its sensitivity to design variables, the volume fraction and its sensitivity to design variables, solve the eigenvalue sequence of the anti-resonance frequency based on the modal acceleration method, track the constrained anti-resonance frequency through the modal confidence criterion based on the eigenvectors corresponding to each eigenvalue in the eigenvalue sequence, and solve the sensitivity of the constrained anti-resonance frequency to design variables by combining the Moore-Penrose generalized inverse.

[0042] Specifically, degrees of freedom are calculated based on the concept of modal superposition. To determine the displacement amplitude, first establish the steady-state motion equations in modal coordinates: ;in, Here is the modal stiffness matrix. , The modal matrix, The overall stiffness matrix of the structure. For transpose operation, Here is the modal mass matrix. , The overall mass matrix of the structure. For modal coordinate vectors, For modal force vectors, , This is the vector of external forces on the structure.

[0043] The degrees of freedom are approximated by linear superposition. Displacement amplitude at: .in, For degrees of freedom Displacement amplitude at point, To extract vectors, used to extract specified degrees of freedom. The displacement amplitude at that point, which has only one degree of freedom in the vector. (as in this application) The element corresponding to ) has a value of 1, and all other elements have a value of 0. , This is used to convert displacement response in modal coordinates into degrees of freedom. The vector of displacement magnitude at a given location.

[0044] Degrees of freedom are calculated using the adjoint vector method. Displacement amplitude For the Design variables The sensitivity is: .in, Indicates the first In the next iteration, the degrees of freedom Displacement amplitude For the Design variables Sensitivity, Indicates the first In the next iteration, the real part of the displacement amplitude... Indicates the first In the next iteration, the imaginary part of the displacement amplitude Indicates the displacement amplitude relative to the first Design variables The real part of the partial derivative, Indicates the displacement amplitude relative to the first Design variables The imaginary part of the partial derivative, It is the reciprocal of the displacement amplitude.

[0045] based on Calculate the volume fraction. Wherein, For the first Volume fraction in the next iteration Indicates the first Volume of each unit Indicates the total volume.

[0046] based on Calculate the volume fraction for the first Design variables The sensitivity. Among them, For the first In the next iteration, the volume fraction For the Sensitivity of each design variable.

[0047] The eigenvalue sequence of anti-resonance frequency is solved based on the modal acceleration method, including the following content.

[0048] Modal acceleration method is an improvement on the traditional modal superposition method (by adding quasi-static components to improve calculation accuracy). The formula for calculating the steady-state displacement response of the structure in the next iteration is: .in, For the first The steady-state displacement response vector calculated based on the modal acceleration method in the next iteration. The modal matrix, For modal coordinate vectors, This is the quasi-static compensation term in the modal acceleration method. It is the inverse of the overall structural stiffness matrix. The modal order involved in the calculation. For the first The first-order mode shape represents the mode matrix. List, For the first Transpose of the first mode shape It is the first r The natural frequency of the order, This is the vector of external forces on the structure.

[0049] The core physical meaning of anti-resonance is the target degree of freedom. Since the displacement amplitude is 0, a zero displacement equation is established based on the above steady-state displacement response: .in, To extract the vector.

[0050] Steady-state equations of motion in modal coordinates With zero displacement equation To eliminate the influence of load-related terms, the simultaneous equations are multiplied on the left by the null space matrix of the load column vectors. The problem of obtaining generalized eigenvalues .

[0051] Solving the generalized eigenvalue problem The set of all obtained eigenvalues ​​is taken as the eigenvalue sequence of the anti-resonance frequency in the current iteration, and the eigenvalue sequence is denoted as... .in, For generalized stiffness matrix, , Let be the null space matrix of the load column vectors, satisfying the relation , For modal force vectors, It is a generalized force vector. This is used to convert displacement response in modal coordinates into degrees of freedom. The vector of displacement magnitude at that point To extract vectors, This is the quasi-static compensation term in the modal acceleration method. Here is the modal stiffness matrix. For the excitation angular frequency, For the generalized mass matrix, , Here is the modal mass matrix. This is the modal coordinate vector.

[0052] Based on the eigenvectors corresponding to each eigenvalue in the eigenvalue sequence, the constrained anti-resonance frequency is tracked using the modal confidence criterion, including the following:

[0053] Combined with the The first anti-resonance frequency of the next iteration corresponding feature vector The modal confidence criterion is used to calculate the MAC value of the eigenvector corresponding to each eigenvalue in the current iteration's eigenvalue sequence. The eigenvector corresponding to the maximum MAC value is found, and the positive square root of its corresponding eigenvalue is taken as the first constrained anti-resonance frequency. .

[0054] The expression for the MAC function is: .in, The MAC value is the eigenvector corresponding to each eigenvalue in the eigenvalue sequence. For the first The eigenvector corresponding to the first anti-resonance frequency in the next iteration. For transpose operation, For the first k In the next iteration, the eigenvalue sequence The s The eigenvectors corresponding to each eigenvalue.

[0055] The sensitivity of the constrained anti-resonance frequency to design variables is solved by combining the Moore-Penrose generalized inverse method, including the following:

[0056] Specifically, due to the constrained first anti-resonance frequency Its corresponding eigenvalues Satisfying Relationships ,but .in, For the first k In the nth iteration, the 1st Anti-resonance frequency For the Design variables Sensitivity, For the first k In the next iteration, the first anti-resonance frequency Corresponding eigenvalues , For the first k In the next iteration, the eigenvalues The corresponding feature vector, For the first k In the next iteration, the accompanying eigenvalue problem eigenvectors, For transpose operation, Generalized stiffness matrix The transpose of the matrix for the first Design variables The partial derivatives, Generalized mass matrix The transpose of the matrix for the first Design variables The partial derivatives of .

[0057] Step 105 involves optimizing the MMA optimization algorithm by encapsulating the design variable vector of the current iteration step, the displacement amplitude and its sensitivity to the design variables, the volume fraction and its sensitivity to the design variables, and the constrained anti-resonance frequency and its sensitivity to the design variables. Here, the design variable vector is the set of all individual design variables.

[0058] Step 106: Determine whether the optimization meets the convergence condition. If it does, terminate the iteration to obtain the optimal design variable vector. If it does not meet the condition, iterate from step 104 to step 106 until the convergence condition is met and the optimal design variables are obtained to achieve topology optimization of structural displacement response.

[0059] The convergence condition includes: calculating the maximum absolute value of the difference between corresponding elements of the design variable vector before and after the update; when the maximum absolute value is less than the threshold, the convergence condition is met.

[0060] It should be noted that the convergence condition can also be met when the maximum number of iterations is reached, thus preventing the system from getting stuck in a loop due to non-convergence.

[0061] Specifically, the threshold in this application can be 0.001.

[0062] Figure 3 A schematic diagram of the optimization results obtained by the existing method provided in this application embodiment after 220 iterations at an excitation frequency of 350Hz. Figure 4 A schematic diagram of the optimization results obtained by the method of this application after 220 iterations at an excitation frequency of 350Hz, as provided in the embodiments of this application. Figure 5 Frequency response curves of the optimized results of the existing method provided in the embodiments of this application. Figure 6 The frequency response curve of the optimized result of the method of this application provided in the embodiments of this application. The existing method is specifically a method without anti-resonance constraints. Combined with... Figures 3 to 6It can be seen that although a clear and usable optimization result was obtained after 220 iterations (low-frequency excitation) at an excitation frequency of 350Hz, the displacement amplitude at 350Hz is much higher than that at anti-resonance, as can be seen from the displacement amplitude curve of the optimization result. Meanwhile, the optimization results at other excitation frequencies converged to the intermediate density prematurely after only a few iterations, failing to yield a clear and usable optimization result. In contrast, the optimization results of the method in this application all obtained usable topological configurations after 220 iterations, and the displacement amplitude at key positions of the optimization results at all excitation frequencies converged to the anti-resonance point at the end, with a response much lower than the displacement amplitude at non-resonance, all being local minima close to zero. Among these, compared to the clear and usable design results in the existing methods (excitation frequency 350Hz), the displacement amplitude of the optimization results in this application decreases at the same frequency, indicating that the method in this application achieves excellent results in the displacement minimization problem.

[0063] This application also provides a structural displacement response topology optimization design device 700, such as... Figure 7 As shown, the device includes: a first establishment module 701, a second establishment module 702, an initialization module 703, an iteration module 704, an optimization module 705, and a judgment module 706.

[0064] The first module 701 is used to establish the finite element model of the structure and apply boundary conditions and external load excitation.

[0065] The second module 702 is used to establish an optimization model based on the structure of the finite element model, with the goal of minimizing the displacement amplitude and the constraints of volume fraction and anti-resonance frequency.

[0066] The initialization module 703 is used to initialize the parameters of the optimization model, taking the upper limit of the volume fraction as the initial value of the design variable, the excitation frequency as the upper limit of the anti-resonance frequency, and recording the eigenvector corresponding to the initial anti-resonance frequency.

[0067] The iteration module 704 is used to iteratively calculate the displacement amplitude and its sensitivity to design variables, the volume fraction and its sensitivity to design variables based on the optimization model, solve the eigenvalue sequence of the anti-resonance frequency based on the modal acceleration method, track the constrained anti-resonance frequency based on the eigenvectors corresponding to each eigenvalue in the eigenvalue sequence through the modal confidence criterion, and solve the sensitivity of the constrained anti-resonance frequency to design variables by combining the Moore-Penrose generalized inverse.

[0068] The optimization module 705 is used to optimize the MMA optimization algorithm, which encapsulates the design variable vector, displacement magnitude and its sensitivity to design variables, volume fraction and its sensitivity to design variables, and constrained anti-resonance frequency and its sensitivity to design variables as inputs to the current iteration step. The design variable vector is the set of all individual design variables.

[0069] The judgment module 706 is used to determine whether the design variable vector meets the convergence condition. If it does, the iteration is terminated to obtain the optimal design variable vector. If it does not meet the condition, steps 104 to 106 are executed iteratively until the convergence condition is met and the optimal design variable vector is obtained, so as to realize the topology optimization of the structural displacement response.

[0070] Some modules in the apparatus described in this application can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc., that perform a specific task or implement a specific abstract data type. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0071] The apparatus or module described in the above embodiments can be implemented by a computer chip or physical entity, or by a product with a certain function. For ease of description, the above apparatus is described by dividing it into various modules according to their functions. When implementing the embodiments of this application, the functions of each module can be implemented in one or more software and / or hardware. Of course, a module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.

[0072] The methods, apparatus, or modules described in this application can be implemented in a computer-readable program code manner. The controller can be implemented in any suitable manner, for example, as a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. A memory controller can also be implemented as part of the control logic of a memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code manner, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included within it for implementing various functions can also be considered as structures within the hardware component. Alternatively, the device used to implement various functions can be viewed as either a software module that implements the method or a structure within a hardware component.

[0073] like Figure 8 As shown in the figure, this application embodiment also provides a structural displacement response topology optimization design server, including a memory 801 and a processor 802; the memory 801 is used to store computer-executable instructions; the processor 802 is used to execute computer-executable instructions to implement the structural displacement response topology optimization design method described above in this application embodiment.

[0074] This application also provides a computer-readable storage medium storing executable instructions, which, when executed by a computer, can implement the structural displacement response topology optimization design method described above in this application.

[0075] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary hardware. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product, or it can be embodied in the process of data migration. The computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to execute the methods described in the embodiments of this application.

[0076] The various embodiments described in this specification are presented in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. All or part of this application can be used in numerous general-purpose or special-purpose computer system environments or configurations.

[0077] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of this application.

Claims

1. A structural displacement response topology optimization design method, characterized in that, include: Step 101: Establish the finite element model of the structure and apply boundary conditions and external load excitation; Step 102: Based on the finite element model of the structure, establish an optimization model with the goal of minimizing displacement amplitude and with volume fraction and anti-resonance frequency as constraints; Step 103: Initialize the parameters of the optimization model, take the upper limit of the volume fraction as the initial value of the design variable, take the excitation frequency as the upper limit of the anti-resonance frequency, and record the feature vector corresponding to the initial anti-resonance frequency. Step 104: Based on the optimization model, iteratively calculate the displacement amplitude and its sensitivity to design variables, the volume fraction and its sensitivity to design variables, solve the eigenvalue sequence of the anti-resonance frequency based on the modal acceleration method, track the constrained anti-resonance frequency through the modal confidence criterion based on the eigenvectors corresponding to each eigenvalue in the eigenvalue sequence, and solve the sensitivity of the constrained anti-resonance frequency to design variables by combining the Moore-Penrose generalized inverse. Step 105: Optimize the MMA optimization algorithm by encapsulating the design variable vector, displacement amplitude and its sensitivity to design variables, volume fraction and its sensitivity to design variables, and constrained anti-resonance frequency and its sensitivity to design variables in the current iteration step; wherein, the design variable vector is the set of all individual design variables. Step 106: Determine whether the design variable vector satisfies the convergence condition. If it does, terminate the iteration to obtain the optimal design variable vector. If it does not, iterate from step 104 to step 106 until the convergence condition is met and the optimal design variable vector is obtained, so as to realize the topology optimization of the structural displacement response.

2. The structural displacement response topology optimization design method according to claim 1, characterized in that, The specific process for establishing the finite element model of the structure is as follows: Given material properties, including Young's modulus, Poisson's ratio, and density, the structural geometry is discretized into finite element elements based on these material properties to obtain the finite element model of the structure.

3. The structural displacement response topology optimization design method according to claim 2, characterized in that, The expression for the optimization model is: find: ; min: ; s.t.: ; ； ； Here, find means to search. To design a variable vector, its elements For a single design variable, each It corresponds one-to-one with finite element elements and is updated after each iteration. To design the lower bound of variables, N This represents the total number of design variables. For transpose operation, For indexing, For the first There are 1 design variable, where min represents minimizing. For the first k Degrees of freedom in the next iteration The displacement amplitude at point st is a constraint condition. It is the volume fraction. This is the upper limit of volume fraction. For the first k In the frequency response function of the key position displacement in the iteration, the first... One anti-resonance frequency, The excitation angular frequency.

4. The structural displacement response topology optimization design method according to claim 3, characterized in that, Degrees of freedom are calculated using the adjoint vector method. Displacement amplitude For the Design variables The sensitivity is: ;in, Indicates the first In the next iteration, the degrees of freedom Displacement amplitude For the Design variables Sensitivity, Indicates the first In the next iteration, the real part of the displacement amplitude... Indicates the first In the next iteration, the imaginary part of the displacement amplitude Indicates the displacement amplitude relative to the first Design variables The real part of the partial derivative, Indicates the displacement amplitude relative to the first Design variables The imaginary part of the partial derivative, It is the reciprocal of the displacement amplitude; based on Calculate the volume fraction; where, For the first Volume fraction in the next iteration Indicates the first Volume of each unit Indicates the total volume; based on Calculate the volume fraction for the first Design variables The sensitivity; among which, For the first In the next iteration, the volume fraction For the Sensitivity of each design variable.

5. The structural displacement response topology optimization design method according to claim 4, characterized in that, The eigenvalue sequence for solving the anti-resonance frequency based on the modal acceleration method includes: Solving the generalized eigenvalue problem The set of all obtained eigenvalues ​​is taken as the eigenvalue sequence of the anti-resonance frequency in the current iteration, and the eigenvalue sequence is denoted as... ;in, For generalized stiffness matrix, , Let be the null space matrix of the load column vectors, satisfying the relation , For modal force vectors, It is a generalized force vector. This is used to convert displacement response in modal coordinates into degrees of freedom. The vector of displacement magnitude at that point To extract vectors, This is the quasi-static compensation term in the modal acceleration method. Here is the modal stiffness matrix. For the excitation angular frequency, For the generalized mass matrix, , Here is the modal mass matrix. This is the modal coordinate vector.

6. The structural displacement response topology optimization design method according to claim 5, characterized in that, The method of tracking the constrained anti-resonance frequency based on the eigenvectors corresponding to each eigenvalue in the eigenvalue sequence and using a modal confidence criterion includes: Combined with the The iteration of the ... Eigenvectors corresponding to each anti-resonance frequency The modal confidence criterion is used to calculate the MAC value of the eigenvector corresponding to each eigenvalue in the current iteration's eigenvalue sequence. The eigenvector corresponding to the maximum MAC value is found, and the positive square root of its corresponding eigenvalue is used as the constrained anti-resonance frequency. ; The expression for the MAC function is: ;in, The MAC value is the eigenvector corresponding to each eigenvalue in the eigenvalue sequence. For the first The iteration of the ... The eigenvectors corresponding to the anti-resonance frequencies For transpose operation, For the first k In the next iteration, the eigenvalue sequence The s The eigenvectors corresponding to each eigenvalue.

7. The structural displacement response topology optimization design method according to claim 6, characterized in that, The sensitivity of the constrained anti-resonance frequency to design variables obtained by combining the Moore-Penrose generalized inverse solution includes: ;in, For the first k In the nth iteration, the 1st Anti-resonance frequency For the Design variables Sensitivity, For the first k In the nth iteration, the 1st Anti-resonance frequency Corresponding eigenvalues , For the first k In the next iteration, the eigenvalues The corresponding feature vector, For the first k In the next iteration, the accompanying eigenvalue problem eigenvectors, For transpose operation, Generalized stiffness matrix The transpose of the matrix for the first Design variables The partial derivatives, Generalized mass matrix The transpose of the matrix for the first Design variables The partial derivatives of .

8. The structural displacement response topology optimization design method according to claim 1, characterized in that, Convergence conditions include: Calculate the maximum absolute value of the difference between corresponding elements of the design variable vector before and after the update. When the maximum absolute value is less than the threshold, the convergence condition is met.

9. A structural displacement response topology optimization design device, characterized in that, The device performs the method as described in any one of claims 1 to 8, including: The first module is used to establish the finite element model of the structure and apply boundary conditions and external load excitations. The second module is used to establish an optimization model based on the finite element model of the structure, with the goal of minimizing the displacement amplitude and with volume fraction and anti-resonance frequency as constraints. The initialization module is used to initialize the parameters of the optimization model, taking the upper limit of the volume fraction as the initial value of the design variable, the excitation frequency as the upper limit of the anti-resonance frequency, and recording the eigenvector corresponding to the initial anti-resonance frequency. The iterative module is used to iteratively calculate the displacement amplitude and its sensitivity to design variables, the volume fraction and its sensitivity to design variables based on the optimization model, solve the eigenvalue sequence of the anti-resonance frequency based on the modal acceleration method, track the constrained anti-resonance frequency based on the eigenvectors corresponding to each eigenvalue in the eigenvalue sequence through the modal confidence criterion, and solve the sensitivity of the constrained anti-resonance frequency to design variables by combining the Moore-Penrose generalized inverse. The optimization module is used to optimize the MMA optimization algorithm encapsulated by the design variable vector, displacement amplitude and its sensitivity to design variables, volume fraction and its sensitivity to design variables, and constrained anti-resonance frequency and its sensitivity to design variables of the current iteration step; wherein, the design variable vector is the set of all individual design variables; The judgment module is used to determine whether the design variable vector meets the convergence condition. If it does, the iteration is terminated to obtain the optimal design variable vector. If it does not meet the condition, steps 104 to 106 are executed iteratively until the convergence condition is met to obtain the optimal design variable vector, so as to realize the topology optimization of the structural displacement response.

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