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Nonlinear eigenvalue topological optimization method and system considering frequency correlation material

A nonlinear feature and topology optimization technology, applied in design optimization/simulation, CAD numerical modeling, special data processing applications, etc., can solve problems such as large eigenvector errors, inability to explain the degree of influence of frequency-related items, and difficulty in convergence. Achieve stable iterations, promote dynamic performance research, and achieve further upgrade effects

Active Publication Date: 2021-09-07
SHANDONG UNIV
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Problems solved by technology

[0005] A solution method for nonlinear eigenvalues ​​is proposed in the prior art, but this method omits the frequency-dependent term. Although it can be solved directly, it cannot explain the degree of influence of the frequency-dependent term on the result, resulting in inaccurate results
The existing technology also proposes an asymptotic numerical method for solving nonlinear eigenvalue problems. Although this method considers frequency-related items, the eigenvector error of the solution using this method is relatively large, and it is applied to topology optimization. During the iterative process, there will be Difficulty in convergence
In addition, so far, the solution process of nonlinear eigenvalues ​​has not formed a complete set of methods in the field of topology optimization.

Method used

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  • Nonlinear eigenvalue topological optimization method and system considering frequency correlation material
  • Nonlinear eigenvalue topological optimization method and system considering frequency correlation material
  • Nonlinear eigenvalue topological optimization method and system considering frequency correlation material

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Embodiment 1

[0052] As mentioned in the background technology, most of the methods for solving nonlinear equations disclosed in the prior art omit frequency-related items, or the eigenvectors solved by traditional asymptotic numerical methods have large errors, resulting in convergence in the iterative process after being applied to topology optimization difficult phenomenon. Therefore, the present invention provides a nonlinear eigenvalue topology optimization method and system considering frequency-dependent materials.

[0053] Such as figure 1 As shown, this embodiment provides a nonlinear eigenvalue topology optimization method that considers frequency-dependent materials. This embodiment uses the example of applying this method to a server. It can be understood that this method can also be applied to a terminal. It can also be applied to a terminal, a server and a system, and is realized through the interaction between the terminal and the server. The server can be an independent ph...

Embodiment 2

[0122] This embodiment provides an application of a nonlinear eigenvalue topology optimization method considering frequency-dependent materials in structural design.

[0123] Nonlinear eigenvalue topology optimization methods for frequency-dependent materials, including:

[0124] According to the actual working conditions, the structure is meshed and boundary conditions are added, and the corresponding overall stiffness matrix and overall mass matrix in the structure are obtained through finite element analysis;

[0125] Based on the corresponding overall stiffness matrix and overall mass matrix in the structure, the nonlinear eigenvalue equation is constructed, and the continuous asymptotic numerical method and inverse iteration method are used to solve the nonlinear eigenvalue equation to obtain the structural eigenfrequency and the corrected eigenvector;

[0126] With the goal of maximizing the fundamental frequency of the structure and satisfying the volume constraint as t...

Embodiment 3

[0137] This embodiment provides a nonlinear eigenvalue topology optimization system considering frequency-dependent materials.

[0138] Nonlinear eigenvalue topology optimization systems considering frequency-dependent materials, including:

[0139] a matrix acquisition module configured to: divide the structure into grids and add boundary conditions according to actual working conditions, and obtain the corresponding overall stiffness matrix and overall mass matrix in the structure through finite element analysis;

[0140] The structural eigenfrequency and corrected eigenvector acquisition module is configured to construct nonlinear eigenvalue equations based on the corresponding overall stiffness matrix and overall mass matrix in the structure, and use continuous asymptotic numerical methods and inverse iteration methods to solve nonlinear eigenvalue equations Eigenvalue equations to obtain structural eigenfrequencies and corrected eigenvectors;

[0141] The material consum...

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Abstract

The invention belongs to the technical field of structural topological optimization, and provides a nonlinear eigenvalue topological optimization method and system considering a frequency correlation material. The method comprises the steps of according to actual working conditions, dividing a structure into grids, adding boundary conditions, and through finite element analysis, obtaining a corresponding total stiffness matrix and a corresponding total mass matrix in the structure; constructing a non-linear eigenvalue equation based on the corresponding total stiffness matrix and the total mass matrix in the structure, and solving the non-linear eigenvalue equation by adopting a continuous asymptotic numerical method and an inverse iteration method to obtain a structural feature frequency and a corrected feature vector; and establishing a topological optimization model by taking the fundamental frequency maximization of the structure as a target and meeting the volume constraint as a constraint condition and combining the structural feature frequency and the corrected feature vector, inputting the material components containing the frequency correlation material structure into the model, and obtaining the material consumption meeting the requirement through topological optimization.

Description

technical field [0001] The invention belongs to the technical field of structural topology optimization, and in particular relates to a nonlinear eigenvalue topology optimization method and system considering frequency-dependent materials. Background technique [0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art. [0003] Structural eigenvalue topology optimization is a research hotspot in the field of dynamic optimization, and it has a wide range of applications in the fields of improving structural fundamental frequency, avoiding resonance, and bandgap material design. However, most of the existing studies assume that the material is an elastic material, and the eigenfrequency of the structure is obtained by solving the linear eigenvalue equation. However, the elastic modulus of many engineering materials has a frequency dependence, that is, the elastic modulus of the mat...

Claims

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Application Information

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IPC IPC(8): G06F30/23G06F30/18G06F17/13G06F111/04G06F111/10
CPCG06F30/23G06F30/18G06F17/13G06F2111/10G06F2111/04
Inventor 李取浩吴强波刘书田朱向前张风同曲泳鑫
Owner SHANDONG UNIV
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