时域动载荷作用下多微结构多尺度并行动力学拓扑优化  

Multiscale concurrent topology optimization for cellular structures with multiple microstructures subjected to dynamic load

作　　者：江旭东[1] 吴昊 滕晓艳[2] 熊冶平[3] JIANG Xudong;WU Hao;TENG Xiaoyan;XIONG Yeping(Advanced Manufacturing Intelligent Technology of Key Laboratory of Ministry of Education,Harbin University of Science and Technology,Harbin 150080,China;Electromechanical Engineering College,Harbin Engineering University,Harbin 150080,China;Faculty of Engineering and Physical Sciences,University of Southampton,Southampton SO167QF,UK)

机构地区：[1]哈尔滨理工大学先进制造智能化技术教育部重点实验室,哈尔滨150080 [2]哈尔滨工程大学机电工程学院,哈尔滨150080 [3]南安普顿大学工程与物理科学系,英国南安普顿SO167QF

出　　处：《振动与冲击》2024年第12期53-64,共12页Journal of Vibration and Shock

基　　金：国家自然科学基金(52175502,51505096);黑龙江省自然科学基金(LH2020E064)。

摘　　要：采用拓扑优化方法对含多种多孔材料的结构进行结构与材料微结构构型一体化设计,可以获得具有优良力学性能的结构设计。该文面向多晶胞双尺度结构的时域动刚度最优设计问题,考虑不同晶胞间的可连接性,并行设计微结构的构型及其宏观布局。首先,引入双Helmholtz平滑-分块投影方案,识别不同多孔材料的宏观结构域。其次,通过均匀化方法计算多孔材料的宏观等效力学性能,利用有序SIMP(soid isotropic material with penalization)方法优化不同微观结构的宏观布局。同时,为了保证不同晶胞间的可连接性,在不同多孔材料微结构的边界区域设置为相同拓扑描述的可设计连接域。然后,基于先离散-后微分的伴随敏度分析方法,实现了时空离散动力系统的一致性敏度计算。最后,以双尺度结构动柔度最小化为目标,以材料用量为约束条件,提出了时域动载荷作用下多微结构多尺度并行动力学拓扑优化方法。数值算例结果表明,提出的优化方法能够实现多晶胞结构的构型与宏观布局设计,充分提高了多孔结构的承载性能,同时保证不同晶胞之间的几何连续性,研究结果可为高承载多孔材料结构设计提供理论参考。Topology optimization is an effective tool to perform the structure-material integrated design of a lattice structure with multiple microstructures for improving its mechanical performances.This paper aims to propose a concurrent design method for the lattice structure at both macro-and micro-scales considering the connectivity between neighboring microstructures for the dynamic stiffness maximization problem.Firstly,the double Helmholtz smoothing and piecewise projection scheme was introduced to identify the spatial distribution of multiple microstructure blocks at macroscale.Then,the spatial distribution of various microstructures was optimized by an ordered SIMP(soid isotropic material with penalization) method following the effective mechanical properties obtained by a homogenization method.Meanwhile,the different microstructural unit cells share the same topology description within their boundary regions to ensure the connectivity.Subsequently,the sensitivity analysis was implemented by an adjoint variable method based on the “discretize-then-differentiate” approach,such that the consistent sensitivities are obtained on the space-time discretized system.Finally,the dynamic compliance minimization problem was formulated under the constraint of material volume fractions,a multiscale concurrent topology optimization method was presented for structures periodically filled with multiple microstructures.Numerical examples demonstrate that the approach has the potential to perform the concurrent microscopic design of multiple unit-cells and their macroscopic layout for improving the load-carrying capacity and ensuring the geometrical connectivity between neighboring unit-cells.Themethod offers a theoretical reference for design of highly loading porous structures.

关 键 词：多尺度并行拓扑优化 多晶胞结构 瞬态动力学 微结构连接性 数值均匀化 

分 类 号：O346[理学—固体力学]