基于等效静态载荷法的多相材料结构动态拓扑优化设计

PDF(2077 KB)

振动与冲击 ›› 2024, Vol. 43 ›› Issue (3) : 77-85.

论文

占金青1，王啸1，蒲圣鑫1，刘敏1，2

作者信息 +

Dynamic topology optimization design of multiphase material structure based on equivalent static load method

ZHAN Jinqing1, WANG Xiao1, PU Shengxin1, LIU Min1,2

Author information +

文章历史 +

摘要

为了满足多相材料结构动态性能要求，提出一种基于等效静态载荷法的多相材料结构动态拓扑优化设计方法。采用序列固体各向同性料插值模型惩罚刚度矩阵和质量矩阵，以多个动载荷作用的多相材料结构总动态柔顺度最小化为优化目标，以结构质量和成本为约束条件，构建多相材料结构动态拓扑优化模型，利用等效静态载荷法将多相材料结构动态拓扑优化问题转化为多工况下的多相材料结构静态拓扑优化问题，以降低灵敏度分析的复杂程度；采用移动渐近线算法求解多相材料结构动态拓扑优化问题。数值算例结果表明所提方法是有效性的，与传统的拓扑优化方法相比，基于等效静态载荷法的多相材料结构动态拓扑优化求解时间节省了75%，大大地提高了计算效率；与单相材料拓扑优化结果相比，多相材料结构动态拓扑优化设计获得的结构具有更好的动态性能。

Abstract

A method for dynamic topology optimization of continuum structures with multiphase materials using the equivalent static load method is proposed to meet the dynamic performance requirements. The ordered solid isotropic material with penalization (SIMP) interpolation is used to penalize the stiffness matrix and mass matrix. The objective function is developed by minimizing the total dynamic compliance of a multi-material structure under multiple dynamic loads subject to a mass constraint and a cost constraint. The dynamic topology optimization model for multi-material continuum structures is developed. To reduce the complexity of sensitivity analysis, the equivalent static load method is used to transform the dynamic topology optimization problem into the problem for topology optimization under multiple static loads. The method of moving asymptotes algorithm is employed to solve the problem for dynamic topology optimization of multi-material continuum structures. The results of numerical examples demonstrate the effectiveness of the proposed method. In comparison to the traditional topology optimization method, the method for dynamic topology optimization of multi-material structures based on the equivalent static load method reduces solution time by 75% and significantly improves calculation efficiency. The structures obtained by dynamic topology optimization with multiple materials have better dynamic performance than those obtained by topology optimization with single phase material.

导出引用

占金青1，王啸1，蒲圣鑫1，刘敏1，2. 基于等效静态载荷法的多相材料结构动态拓扑优化设计[J]. 振动与冲击, 2024, 43(3): 77-85

ZHAN Jinqing1, WANG Xiao1, PU Shengxin1, LIU Min1,2. Dynamic topology optimization design of multiphase material structure based on equivalent static load method[J]. Journal of Vibration and Shock, 2024, 43(3): 77-85

参考文献

[1] SIGMUND O, MAUTE K. Topology optimization approaches[J]. Structural and Multidisciplinary Optimization, 2013, 48(6): 1031-1055. [2] WANG C, XU B, DUAN Z, et al. Structural topology optimization considering both manufacturability and manufacturing uncertainties[J]. Structural and Multidisciplinary Optimization, 2023, 66(1): 15. [3] 占金青, 王云涛, 刘敏等.考虑混合约束的柔顺机构拓扑优化设计[J]. 振动与冲击, 2022, 41(4): 159-166+222. ZHAN Jinging, WANG Yuntao, LIU Min, et al, Topological design of compliant mechanisms with hybrid constraints[J]. Journal of vibration and shock, 2022, 41(4): 159-166+222. [4] LUO Y, BAO J. A material-field series-expansion method for topology optimization of continuum structures[J]. Computers & Structures, 2019, 225:106122. [5] GAN N, WANG Q. Topology optimization of multiphase materials with dynamic and static characteristics by BESO method[J]. Advances in Engineering Software, 2021, 151: 102928. [6] 李雪平, 林猛峰, 魏鹏等.非平稳激励下薄板结构减振附加阻尼层的拓扑优化[J]. 振动与冲击, 2020, 39(8): 250-257. LI Xueping, LIN Mengfeng, WEl Peng, et al. Topology optimization of attached damping layers on thin plate structures forvibration attenuation under non stationary stochastic excitations[J]. Journal of Railway Science and Engineering, 2020, 39(8): 250-257. [7] MA Z D , KIKUCHI N, HAGIWARA I. Structural topology and shape optimization for a frequency response problem[J]. Computational Mechanics, 1993, 13(3):157-174. [8] YOON G H. Structural topology optimization for frequency response problem using model reduction schemes[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(25-28):1744-1763. [9] YANG X, LI Y. Topology optimization to minimize the dynamic compliance of a bi-material plate in a thermal environment[J]. Structural and Multidisciplinary Optimization, 2013, 47(3): 399-408. [10] GAO J, LUO Z, LI H, et al. Dynamic multiscale topology optimization for multi-regional micro-structured cellular composites. Composite structures. 2019. 211: 401-417. [11] 文桂林, 陈高锡, 王洪鑫, 等. 含自重载荷的功能梯度材料结构时域动力学拓扑优化设计[J].中国机械工程, 2022, 33(23): 2774-2782. WEN Guilin, CHEN Gaoxi, WANG Hongxin, et al. Time domain dynamic topology optimization of functionally gradient material structures with self-weight Load[J]. China Mechanical Engineering, 2022, 33(23): 2774-2782. [12] LONG K, WANG X, LIU H. Stress-constrained topology optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming[J]. Structural and Multidisciplinary Optimization，2019，59(5): 1747-1759. [13] JANG H H, LEE H A, LEE J Y, et al. Dynamic response topology optimization in the time domain using equivalent static loads[J]. AIAA journal, 2012, 50(1): 226-234. [14] 杨志军. 基于等效静态载荷原理的高速机构结构拓扑优化方法[J]. 机械工程学报, 2011, 47(17): 119-126. YANG Zhijun. Topological optimization approach for structure design of high speed mechanisms using equivalent static loads method[J]. Journal of Mechanical Engineering, 2011, 47(17): 119-126. [15] LU S, ZHANG Z, GUO H, et al. Nonlinear dynamic topology optimization with explicit and smooth geometric outline via moving morphable components method[J]. Structural and Multidisciplinary Optimization, 2021, 64(4): 2465-2487. [16] WANG L, LI Z, GU K. An interval-oriented dynamic robust topology optimization (DRTO) approach for continuum structures based on the parametric Level-Set method (PLSM) and the equivalent static loads method (ESLM)[J]. Structural and Multidisciplinary Optimization, 2022, 65(5): 150. [17] SIGMUND O, TORQUATO S. Design of materials with extreme thermal expansion using three-phase topology optimization method[J]. Journal of the Mechanics and Physics of Solids, 1997, 45( 6): 1037-1067. [18] YIN L, ANANTHASURESH, G. Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme. Structural and Multidisciplinary Optimization, 2001, 23: 49–62. [19] ALONSO C，ANSOLA R，QUERIN O M. Topology synthesis of multi-material compliant mechanisms with asequential element rejection and admission method[J].Finite Elements in Analysis & Design, 2014, 85(8): 11-19. [20] 张宪民，胡凯，王念峰，等. 基于并行策略的多材料柔顺机构多目标拓扑优化[J]. 机械工程学报, 2016, 52(19): 1-8. ZHANG Xianmin, HU Kai, WANG Nianfeng, et al. Multi-objective topology optimization of multiple materials compliant mechanisms based on parallel strategy[J]. Journal of Mechanical Engineering, 2016, 52(19): 1-8. [21] ZUO W, SAITOU K. Multi-material topology optimization using ordered SIMP interpolation[J]. Structural and Multidisciplinary Optimization, 2017, 55(2): 477-491. [22] 赵清海,张洪信,蒋荣超等.考虑载荷不确定性的多相材料结构稳健拓扑优化[J]. 振动与冲击, 2019, 38(19): 182-190. ZHAO Qinghai, ZHANG Hongxin, JIANG Rongchao, et al. Robust topology optimization design of a multi-material structure considering load uncertainty[J]. Journal of vibration and shock, 2019, 38(19): 182-190. [23] XU S, LIU J, ZOU B, et al. Stress constrained multi-material topology optimization with the ordered SIMP method[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113453. [24] 闫浩, 吴晓明. 基于ordered-EAMP模型的多相材料传热结构拓扑优化[J]. 航空动力学报, 2021, 36(5): 1007-1021. YAN Hao, WU Xiaoming. Multi-material topology optimization for heat transfer structurebased on ordered-EAMP model[J]. Journal of Aerospace Power, 2021, 36(5): 1007-1021. [25] GU X, HE S, DONG Y, et al. An improved ordered SIMP approach for multiscale concurrent topology optimization with multiple microstructures[J]. Composite Structures, 2022, 287:115363. [26] da Silveira, O A A, PALMA, L F. Some considerations on multi-material topology optimization using ordered SIMP[J]. Structural and Multidisciplinary Optimization, 2022, 65(9): 261. [27] CHOI W S, PARK G J. Structural optimization using equivalent static loads at all time intervals[J]. Computer Methods in Applied Mechanics & Engineering, 2002, 191(19-20): 2077-2094. [28] ANDREASSEN E, CLAUSEN A, SCHEVENELS M , et al. Efficient topology optimization in MATLAB using 88 lines of code[J]. Structural and Multidisciplinary Optimization, 2011, 43(1)：1-16. [29] MARTINELLI L B, ALVES E C. Optimization of geometrically nonlinear truss structures under dynamic loading[J]. REM-International Engineering Journal, 2020, 73: 293-301. [30] SVANBERG K. The method of moving asymptotes—a new method for structural optimization[J]. International journal for numerical methods in engineering, 1987, 24(2): 359-373.