CN-121997677-A - Structural displacement response topology optimization design method and device

CN121997677ACN 121997677 ACN121997677 ACN 121997677ACN-121997677-A

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 steps of establishing a structure finite element model, applying boundary conditions and external load excitation, constructing an optimization model taking displacement amplitude minimization as a target, volume fraction and anti-resonance frequency as constraints, iteratively calculating the sensitivity of the displacement amplitude and the volume fraction after parameter initialization is completed, solving an anti-resonance frequency characteristic value sequence through a modal acceleration method, tracking the constrained anti-resonance frequency by combining a modal confidence criterion, solving the sensitivity of the constrained anti-resonance frequency to design variables by utilizing Moore-Penrose generalized inverse, inputting all parameters and the sensitivity into an MMA optimization algorithm, judging convergence, and terminating iteration to obtain an optimal design variable vector if the optimal design variable vector meets the requirement, thereby realizing structural displacement response topology optimization. The method solves the problem that when displacement minimization topology optimization is carried out in the prior art, anti-resonance points are prone to being trapped and converged in advance to form a middle density gray area.

Inventors

ZHANG LISHENG
HOU JIE
MENG FANWEI
SONG GUANGRUI
ZHU JIHONG
GU XIAOJUN
ZHOU YING
ZHANG WEIHONG

Assignees

西北工业大学

Dates

Publication Date: 20260508
Application Date: 20260408

Claims (9)

1. The structural displacement response topology optimization design method is characterized by comprising the following steps of: Step 101, establishing a finite element model of a structure and applying boundary conditions and external load excitation; 102, establishing an optimization model taking displacement amplitude minimization as a target and taking volume fraction and anti-resonance frequency as constraints based on a finite element model of the structure; step 103, initializing parameters of an optimization model, taking the upper limit value of the volume fraction as an initial value of a design variable, taking the excitation frequency as the upper limit value of the antiresonance frequency, and recording a feature vector corresponding to the initial antiresonance frequency; Step 104, iteratively calculating the displacement amplitude and the sensitivity thereof to the design variable, the volume fraction and the sensitivity thereof to the design variable based on an optimization model, solving a characteristic value sequence of the anti-resonance frequency based on a modal acceleration method, tracking the constrained anti-resonance frequency based on characteristic vectors corresponding to characteristic values in the characteristic value sequence through a modal confidence criterion, and solving the sensitivity of the constrained anti-resonance frequency to the design variable by combining Moore-Penrose generalized inverse; Step 105, optimizing a design variable vector, a displacement amplitude, sensitivity to a design variable, a volume fraction, sensitivity to the design variable, a constrained antiresonance frequency, and sensitivity to the design variable of the current iteration step by using an MMA optimization algorithm of the input package, wherein the design variable vector is a set of all single design variables; And step 106, judging whether the design variable vector meets the convergence condition, if so, terminating iteration to obtain an optimal design variable vector, and if not, executing the steps 104 to 106 in an iteration mode until the convergence condition is met to obtain the optimal design variable vector so as to realize the topological optimization of the structural displacement response.
2. The structural displacement response topology optimization design method according to claim 1, wherein the specific process of building the finite element model of the structure is as follows: Given material properties, including Young's modulus, poisson's ratio, and density, and discretizing the structural geometric model into finite element elements based on the material properties, a finite element model of the structure is obtained.
3. The structural displacement response topology optimization design method of claim 2, wherein the expression of the optimization model is: find: ; min: ; s.t.: ; ; ; Wherein find represents a search, and, To design variable vectors, elements thereof For a single design variable, each One-to-one correspondence with the finite element elements, and updated after each iteration, For the lower design variable limit, N represents the total number of design variables, For the transpose operation, For the purpose of the index, Is the first The number of design variables, min, represents the minimum, For the degree of freedom in the kth iteration The displacement amplitude at the position, s.t. is a constraint condition, As a volume fraction of the liquid to be processed, As an upper limit to the volume fraction, For the kth iteration in the key position shift frequency response function The frequency of the anti-resonance is chosen, For excitation angular frequency.
4. The structural displacement response topology optimization design method of claim 3, wherein degrees of freedom are calculated using a concomitant vector method Amplitude of displacement For the first Design variables The sensitivity of (2) is: wherein, the method comprises the steps of, Represent the first In a plurality of iterations, degrees of freedom Amplitude of displacement For the first Design variables Is used for the detection of the sensitivity of (a), Represent the first In a number of iterations, the real part of the displacement amplitude, Represent the first In a number of iterations, the imaginary part of the displacement amplitude, Representing the displacement amplitude versus the first Design variables The real part of the partial derivative, Representing the displacement amplitude versus the first Design variables The imaginary part of the partial derivative, Is the reciprocal of the displacement amplitude; Based on Calculating a volume fraction of the volume fraction, wherein, Is the first The volume fraction in the number of iterations, Represent the first The volume of the individual units is such that, Representing the total volume; Based on Calculate the volume fraction to the first Design variables Wherein, the sensitivity of the sensor is equal to that of the sample, Is the first In multiple iterations, volume fraction For the first Sensitivity of the individual design variables.
5. The structural displacement response topology optimization design method of claim 4, wherein the solving the eigenvalue sequence of the antiresonance frequency based on the modal acceleration method comprises: Will solve the generalized eigenvalue problem All the obtained characteristic value sets are used as characteristic value sequences of the anti-resonance frequency of the current iteration, and the characteristic value sequences are recorded as Wherein, the method comprises the steps of, In the form of a generalized stiffness matrix, , Is a zero space matrix of load column vectors, satisfies the relation , As a vector of the modal forces, In the form of a generalized force vector, For converting displacement response in modal coordinates into degrees of freedom A vector of displacement magnitudes at which, In order to extract the vector quantity, Is a pseudo static force compensation term in a modal acceleration method, In the form of a modal stiffness matrix, In order to excite the angular frequency of the wave, In the form of a generalized quality matrix, , In the form of a modal mass matrix, Is a modal coordinate vector.
6. The structural displacement response topology optimization design method of claim 5, wherein tracking the constrained antiresonance frequency by a modal confidence criterion based on the eigenvectors corresponding to each eigenvalue in the eigenvalue sequence comprises: Combine with the first First iteration Eigenvectors corresponding to anti-resonance frequencies Calculating the MAC value of the feature vector corresponding to each feature value in the feature value sequence of the current iteration by adopting a mode confidence criterion, finding out the feature vector corresponding to the maximum MAC value, and taking the positive square root of the corresponding feature value as the constrained anti-resonance frequency ; The expression of the MAC function is: wherein, the method comprises the steps of, For the MAC value of the feature vector corresponding to each feature value in the sequence of feature values, Is the first First iteration The eigenvectors corresponding to the anti-resonance frequencies, For the transpose operation, For the kth iteration, the sequence of eigenvalues Feature vectors corresponding to the s-th feature value of (c).
7. The structural displacement response topology optimization design method of claim 6, wherein said solving the sensitivity of the constrained anti-resonance frequency to the design variable in combination with Moore-Penrose generalized inverse comprises: wherein, the method comprises the steps of, In the kth iteration, the th At the antiresonance frequency For the first Design variables Is used for the detection of the sensitivity of (a), In the kth iteration, the th At the antiresonance frequency Corresponding characteristic value , For the kth iteration, the eigenvalues The corresponding feature vector is used to determine the feature vector, For the kth iteration, the eigenvalue problem is followed Is used for the feature vector of (a), For the transpose operation, Is a generalized stiffness matrix Transposed matrix pair of (2) Design variables Is used for the partial derivative of (a), Is a generalized quality matrix Transposed matrix pair of (2) Design variables Is a partial derivative of (c).
8. The structural displacement response topology optimization design method of claim 1, wherein the convergence condition comprises: And calculating the maximum absolute value of the element difference value corresponding to the design variable vector before and after updating, and meeting the convergence condition when the maximum absolute value is smaller than the threshold value.
9. A structural displacement response topology optimization design device, characterized in that the device performs the method of any one of claims 1 to 8, comprising: The first building module is used for building a finite element model of the structure and applying boundary conditions and external load excitation; The second building module is used for building an optimization model taking the displacement amplitude as a target and taking the volume fraction and the antiresonance frequency as constraints based on the finite element model of the structure; The initialization module is used for initializing parameters of the optimization model, taking the upper limit value of the volume fraction as an initial value of a design variable, taking the excitation frequency as the upper limit value of the anti-resonance frequency, and recording a feature vector corresponding to the initial anti-resonance frequency; The iteration module is used for iteratively calculating the displacement amplitude and the sensitivity of the displacement amplitude to the design variable, the volume fraction and the sensitivity of the displacement amplitude to the design variable, solving a characteristic value sequence of the anti-resonance frequency based on a modal acceleration method, tracking the constrained anti-resonance frequency through a modal confidence criterion based on characteristic vectors corresponding to all characteristic values in the characteristic value sequence, and solving the sensitivity of the constrained anti-resonance frequency to the design variable by combining Moore-Penrose generalized inverse; The optimization module is used for optimizing the design variable vector, the displacement amplitude and the sensitivity thereof to the design variable, the volume fraction and the sensitivity thereof to the design variable of the current iteration step, and the constrained antiresonance frequency and the sensitivity thereof to the design variable of the current iteration step by using an MMA optimization algorithm of the input package, wherein the design variable vector is a set of all single design variables; And the judging module is used for judging whether the design variable vector meets the convergence condition, if so, ending the iteration to obtain an optimal design variable vector, and if not, executing the steps 104 to 106 in an iteration mode until the convergence condition is met, and obtaining the optimal design variable vector so as to realize the topological optimization of the structural displacement response.

Description

Structural displacement response topology optimization design method and device Technical Field The application relates to the technical field of structural dynamics, in particular to a structural displacement response topology optimization design method and device. Background In the field of structural dynamics, the displacement response of a structural key position is an important index for measuring the dynamic performance of the structural key position, and the structural displacement response is usually minimized as an objective function to perform topological optimization so as to obtain a light-weight structure with excellent dynamic performance. In the prior art, a better optimization result can be obtained under a low-frequency excitation condition that the excitation frequency is lower than the fundamental frequency of the initial structure, but under a high-frequency excitation condition that the excitation frequency is higher than the fundamental frequency of the initial structure, a topological optimization problem of displacement response minimization can cause a large number of gray areas with middle density to appear in the design result, and a clear available structure cannot be obtained. In summary, the prior art lacks an effective solution to the problem of structural topology optimization of displacement minimization of a low-damping structure under a single high-frequency excitation condition. Disclosure of Invention In the embodiment of the application, the technical problem that anti-resonance points are easy to be trapped to converge in advance to form a middle density gray area when displacement minimization topology optimization is carried out in the prior art is solved by providing the structural displacement response topology optimization design method. In a first aspect, an embodiment of the present application provides a structural displacement response topology optimization design method, including step 101, building a finite element model of a structure and applying boundary conditions and external load excitation; 102, establishing an optimization model taking displacement amplitude minimization as a target and taking volume fraction and anti-resonance frequency as constraints based on a finite element model of the structure; step 103, initializing parameters of an optimization model, taking the upper limit value of the volume fraction as an initial value of a design variable, taking the excitation frequency as the upper limit value of the anti-resonance frequency, recording a feature vector corresponding to the initial anti-resonance frequency, step 104, iteratively calculating a displacement amplitude and the sensitivity thereof to the design variable, the volume fraction and the sensitivity thereof to the design variable, solving a feature value sequence of the anti-resonance frequency based on a modal acceleration method, tracking the constrained anti-resonance frequency through a modal confidence rule based on feature vectors corresponding to feature values in the feature value sequence, solving the sensitivity of the constrained anti-resonance frequency to the design variable by combining with a Moore-Penrose generalized inverse, step 105, inputting the design variable vector, the displacement amplitude and the sensitivity thereof to the design variable, the volume fraction and the sensitivity thereof to the design variable and the constrained anti-resonance frequency and the sensitivity thereof to MMA of the design variable of the package optimization algorithm, wherein the design variable vector is a set of all single design variable, step 106, judging whether the optimization meets a convergence condition or not, if the optimization meets the final design configuration, stopping the iteration step 104 until the convergence condition is met, the optimal design variable is obtained, to achieve topological optimization of the structural displacement response. In one possible implementation, the specific process of building the finite element model of the structure is to give material properties including Young's modulus, poisson's ratio and density, and to discrete the geometric model of the structure into finite element units based on the material properties, so as to obtain the finite element model of the structure. In one possible implementation, the expression of the optimization model is find:;min:;s.t.:;; Wherein find represents a seek, and wherein, To design variable vectors, elements thereofFor a single design variable, eachOne-to-one correspondence with the finite element elements, and updated after each iteration,For the lower design variable limit, N represents the total number of design variables,For the transpose operation,For the purpose of the index,Is the firstThe number of design variables, min, represents the minimum,For the degree of freedom in the kth iterationThe displacement amplitude at the position, s.t. is a constraint condition,As a volume fra