目标函数含有边界切向导数的有限一维声子结构边界元拓扑优化

A topology optimization for finite 1D phononic structures with objective function involving tangential derivative quantities using TDBIE

高海峰 ¹梁建国 ²刘江林 ²李银辉 ³廉浩杰 ⁴松本敏郎⁵

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作者信息

1. College of Mechanical and Vehicle Engineering,Taiyuan University of Technology,Taiyuan 030000,China;Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering,Taiyuan 030000,China
2. College of Mechanical and Vehicle Engineering,Taiyuan University of Technology,Taiyuan 030000,China
3. College of Electronic Information and Optical Engineering,Taiyuan University of Technology,Taiyuan 030000,China
4. Key Laboratory of In-situ Property-improving Mining of Ministry of Education,Taiyuan University of Technology,Taiyuan 030000,China
5. Department of Mechanical System,Nagoya University Nagoya 464-8604,Japan
折叠

摘要

本文提出了一种针对最小化粒子速度在目标边界的切向分量最小化的一维声子结构拓扑优化方法.边界积分方程的切向导数形式被用来计算含有切向导数量的目标函数.采用伴随变量法计算了拓扑导数,同时伴随场的诺伊曼边界条件也是采用边界积分方程的切向导数形式来计算的.在拓扑更新过程中,周期设计域的拓扑导数是通过计算整体设计域的平均拓扑导数,并被用来带入水平集函数的进化方程.数值应用算例表明了该方法对于目标函数含有切向导数量的一维声子结构拓扑优化问题的有效性.

Abstract

The paper proposes a topology optimization method for 1D phononic structures to minimize the tangential component of particle velocity at the objective boundary.The tangential derivative of the boundary integral equation(TDBIE)is employed for the evaluation of the objective function involves the tangential derivative quantities.The topological derivative is derived through the adjoint method and the Neumann boundary condition of the adjoint field is obtained using the TDBIE.The average topological derivative which is obtained by calculating the average value of the topological derivative in each layer of design domains,is employed for the updating of the level set function.Numerical implementations demonstrate the proposed method is effective for the design of the 1D phononic crystals with the objective function involving tangential derivative quantities.

关键词

Boundary element method/Topology optimization/Phononic structures/Tangential derivative

Key words

Boundary element method/Topology optimization/Phononic structures/Tangential derivative

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基金项目

Fundamental Research Program of Shanxi Province(202203021221053)

Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering(2022SX-TD021)

National Natural Science Foundation of China(52075361)

National Natural Science Foundation of China(52274222)

Lvliang Science and Technology Guidance Special Key R&D Project(2022XDHZ08)

Major Science and Technology Project of Shanxi Province(20201102003)

Key Research and Development Projects in Shanxi province(201903D421030)

出版年

2024

力学学报(英文版)

CSTPCD

影响因子：0.363

ISSN：0567-7718

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