基于等效静态载荷法的多相材料结构动态拓扑优化设计  

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

作　　者：占金青 王啸 蒲圣鑫 刘敏 ZHAN Jinqing;WANG Xiao;PU Shengxin;LIU Min(Key Laboratory of Conveyance Equipment,Ministry of Education,East China Jiaotong University,Nanchang 330013,China;Hefei Institutes of Physical Science,Chinese Academy of Sciences,Hefei 230031,China)

机构地区：[1]华东交通大学载运工具与装备教育部重点实验室,南昌330013 [2]中国科学院合肥物质科学研究院,合肥230031

出　　处：《振动与冲击》2024年第3期77-85,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(52065019,52165002,51665011);江西省自然科学基金(20202ACBL214013,20202BAB204015);中国博士后科学基金面上资助(2022M723189)。

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。Here,to meet dynamic performance requirements of multiphase material structure,a dynamic topology optimization design method for multiphase material structure based on the equivalent static load method was proposed.Using the sequential solid isotropic material with penalization(SIMP)interpolation model to penalize stiffness matrix and mass matrix,taking minimizing the total dynamic flexibility of multiphase material structure under multiple dynamic loads as the optimization goal,taking structural mass and cost as constraints,a dynamic topology optimization model for multiphase material structure was constructed.The equivalent static load method was used to convert dynamic topology optimization problem of multiphase material structure into a static topology optimization problem of multiphase material structure under multiple operating conditions,and reduce the complexity of sensitivity analysis.The moving asymptote algorithm was used to solve dynamic topology optimization problem of multiphase material structure.Numerical example results showed that the proposed method is effective;compared with traditional topology optimization methods,the dynamic topology optimization of multiphase material structure based on the equivalent static load method saves 75%of the solving time to greatly improve computational efficiency;compared with topology optimization results of single-phase material,the structure obtained with dynamic topology optimization design of multiphase material has better dynamic performance.

关 键 词：多相材料结构 动态拓扑优化 等效静态载荷法 序列固体各向同性料插值模型 

分 类 号：TB122[理学—工程力学]