Topology optimization in coupled structural-acoustic systems based on a piecewise constant level set method
MIAO Xiaofei,ZHAO Wenchang,CHEN Haibo
CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
摘要针对结构与无限大声场的声振耦合系统中结构的双材料拓扑优化问题进行了研究。采用有限元与边界元方法分别对结构和声场进行离散。基于分段常数水平集(piecewise constant level set ,PCLS)方法,构造了结构的刚度阵、质量阵与阻尼阵。优化目标选为最小化结构指定位置的振幅平方,采用伴随变量法进行灵敏度分析。引入二次罚函数方法来实现体积约束,基于灵敏度信息对优化参数进行重新定义,克服了参数的问题依赖性。数值结果表明优化设计可以显著降低结构的振幅,证实了优化方法的有效性。不同算例下体积约束在相同优化参数下均得到很好满足,说明了重新定义参数的优越性。
Abstract:Topology optimization of bi-material in coupled systems of structure and infinite acoustic field is investigated. The finite element method and boundary element method are used to simulate the structure and acoustic fields, respectively. The stiffness matrix, the mass matrix and the damping matrix are constructed based on the piecewise constant level set (PCLS)method. Minimization of the squared vibration amplitudes at specified points of the structure is chosen as the design objective, using the adjoint variable method to calculate the design sensitivities. Introducing the quadratic penalty method to satisfy the volume constraint, the optimization parameter is redefined to overcome its problem dependency by using the sensitivity information. Numerical results show that the vibration amplitudes can be reduced significantly, indicating the effectiveness of the optimization algorithm. The volume constraints are well satisfied under the same optimization parameters in different cases, showing the advantages of redefined optimization parameter.
苗晓飞,赵文畅,陈海波. 基于分段常数水平集方法的声振耦合系统拓扑优化[J]. 振动与冲击, 2022, 41(4): 192-199.
MIAO Xiaofei,ZHAO Wenchang,CHEN Haibo . Topology optimization in coupled structural-acoustic systems based on a piecewise constant level set method. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(4): 192-199.
[1] 杜建镔. 结构优化及其在振动和声学设计中的应用[M]. 北京:清华大学出版社, 2015.
[2] Bendsøe M P, Kikuchi N. Generating optimal topologies in structural design using a homogenization method[J]. Computer Methods in Applied Mechanics and Engineering,1988,71(2):197-224.
[3] Bendsøe M P, Optimal shape design as a material distribution problem[J]. Structural and Multidisciplinary Optimization, 1989,1(4):193-202.
[4] Xie Y M, Steven G P. A simple evolutionary procedure for structural optimization[J]. Computers and Structures, 1993, 49(5):885-896.
[5] Querin O M, Steven G P, Xie Y M. Evolutionary structural optimisation (ESO) using a bidirectional algorithm[J]. Engineering Computations Int J for Computer Aided Engineering, 1998, 15(8):1031-1048.
[6] Sui Y, Yang D. A new method for structural topological optimization based on the concept of independent continuous variables and smooth model[J]. Acta Mechanica Sinica, 1998, 14(2):179-185.
[7] Wang M Y, Wang X M, Guo D M. A level set method for structural topology optimization[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(1):227-246.
[8] 房占鹏,郑玲. 约束阻尼结构的双向渐进拓扑优化[J]. 振动与冲击, 2014, 33(8):165-170.
FANG Zhan-peng, ZHENG Ling. Topological optimization for constrained layer damping material in structures using BESO method[J]. Journal of vibration and shock,2014,33(8): 165-170.
[9] Zhang X P, Kang Z, Jiang S G, et al. On topology optimization of damping layer in shell structures under harmonic excitations[J]. Structural and Multidisciplinary Optimization, 2012, 46(1):51-67.
[10] Zheng H, Cai C, Pau G, et al. Minimizing vibration response of cylindrical shells through layout optimization of passive constrained layer damping treatments[J]. Journal of Sound and Vibration,2005,279(3):739-756.
[11] Xia Q, Shi T, Wang M Y. A level set based shape and topology optimization method for maximizing the simple or repeated first eigenvalue of structure vibration[J]. Structural and Multidisciplinary Optimization, 2011, 43(4):473-485.
[12] 商林源, 赵国忠, 陈刚. 声结构耦合系统双材料模型的拓扑优化设计[J]. 振动与冲击, 2016, 035(016):192-198.
Shang Lin-yuan, Zhao Guo-zhong, Chen Gang. Topology optimization of a bi-material model for acoustic-structural coupled systems[J]. Journal of vibration and shock,2016, 035(016):192-198.
[13] Shu L, Wang M Y, Ma Z. Level set based topology optimization of vibrating structures for coupled acoustic-structural dynamics[J]. Computers and Structures, 2014, 132(feb.):34-42.
[14] Akl W, El-Sabbagh A, Al-Mitani K, et al. Topology optimization of a plate coupled with acoustic cavity[J]. International Journal of Solids and Structures, 2009, 46(10):2060-2074.
[15] Zhao W, Zheng C, Liu C, et al. Minimization of sound radiation in fully coupled structural-acoustic systems using FEM-BEM based topology optimization[J]. Structural and Multidisciplinary Optimization, 2018, 58(1) :115-128.
[16] Zhao W, Chen L L, Chen H, et al. Topology optimization of exterior acoustic-structure interaction systems using the coupled FEM-BEM method[J]. International Journal for Numerical Methods in Engineering, 2019, 119(5):404-431.
[17] Christiansen O, Tai X C. Fast implementation of piecewise constant level set methods[J]. Berlin: Springer,2007, pp:289-308.
[18] Zhang Z, Chen W. An approach for maximizing the smallest eigenfrequency of structure vibration based on piecewise constant level set method[J]. Journal of Computational Physics, 2018, 361:377-390.
[19] Zhang Z, Chen W. An approach for topology optimization of damping layer under harmonic excitations based on piecewise constant level set method[J]. Journal of Computational Physics, 2019, 390:470-489.
[20] Dai X, Zhang C, Zhang Y, et al. Topology optimization of steady Navier-Stokes flow via a piecewise constant level set method[J]. Structural and Multidiplinary Optimization, 2018, 57:2193-2203.
[21] Burton A, Miller G. The Application of Integral Equation Methods to the Numerical Solution of Some Exterior Boundary-Value Problems[J]. Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, 1971, 323(1553):201-210.
[22] Marburg S. The Burton and Miller Method: Unlocking Another Mystery of Its Coupling Parameter[J]. Journal of Computational Acoustics, 2016, 24(01):1550016.