摘要
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.
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.
作者
Haifeng Gao
Jianguo Liang
Jianglin Liu
Yinhui Li
Haojie Lian
Toshiro Matsumoto
高海峰;梁建国;刘江林;李银辉;廉浩杰;松本敏郎(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;College of Electronic Information and Optical Engineering,Taiyuan University of Technology,Taiyuan 030000,China;Key Laboratory of In-situ Property-improving Mining of Ministry of Education,Taiyuan University of Technology,Taiyuan 030000,China;Department of Mechanical System,Nagoya University,Nagoya 464-8604,Japan)
基金
supported by the Fundamental Research Program of Shanxi Province(Grant No.202203021221053)
the Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering(Grant No.2022SX-TD021)
the National Natural Science Foundation of China(Grant Nos.52075361,and 52274222)
the Lvliang Science and Technology Guidance Special Key R&D Project(Grant No.2022XDHZ08)
the Major Science and Technology Project of Shanxi Province(Grant No.20201102003)
the Key Research and Development Projects in Shanxi province(Grant No.201903D421030).
