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  

Time Domain Dynamics Topology Optimization of Functionally Gradient Material Structures with Self-weight Load

作　　者：文桂林 陈高锡 王洪鑫 薛亮 魏鹏[4] 刘杰[1,2] WEN Guilin;CHEN Gaoxi;WANG Hongxin;XUE Liang;WEI Peng;LIU Jie(School of Mechanical Engineering,Yanshan University,Qinhuangdao,Hebei,066004;School of Mechanical and Electrical Engineering,Guangzhou University,Guangzhou,510006;School of Mechanical and Vehicle Engineering,Hunan University,Changsha,410082;School of Civil Engineering and Transportation,South China University of Technology,Guangzhou,510641)

机构地区：[1]燕山大学机械工程学院,秦皇岛066004 [2]广州大学机械与电气工程学院,广州510006 [3]湖南大学机械与运载工程学院,长沙410082 [4]华南理工大学土木与交通学院,广州510641

出　　处：《中国机械工程》2022年第23期2774-2782,共9页China Mechanical Engineering

基　　金：国家自然科学基金(11902085,11832009,12172095)。

摘　　要：提出了一种含自重载荷的功能梯度材料(FGM)结构时域动力学拓扑优化设计方法。在固体各向同性材料惩罚(SIMP)框架下,提出了一种针对FGM-SIMP的结构自重载荷分布策略。以FGM结构动柔度最小为优化目标、以结构体积为约束,建立了动力学结构优化列式。基于伴随法,在时域内进行了灵敏度推导,并用移动渐近线方法进行求解。通过二维和三维典型数值算例系统研究了含自重载荷下FGM结构的拓扑优化设计问题,并深入探讨了自重载荷和材料梯度分布方向对结构优化结果的影响,发现自重载荷和材料梯度分布方向对FGM结构的优化构型和动刚度具有很大影响。最后,以均一材料(FGM的特例)为例,通过数值仿真和实验测试方法验证了所提方法的有效性,并证实了所提方法可有效提高结构的固有频率和结构动刚度。A time domain dynamics topology optimization design method of FGM with self-weight load was developed.A structural self-weight distribution strategy of FGM-SIMP gradient materials was proposed under the framework of solid isotropic material with penalization(SIMP).The dynamics topology optimization formulations were established with minimum dynamic compliance as the optimization objective and structural volume as the constraints.The sensitivity was derived in the time domain based on the adjoint method and solved by the method of moving asymptotes(MMA).The topology optimization design of FGM structures with self-weight load was systematically analyzed through 2D and 3D typical numerical examples.Besides,the effects of the self-weight loads and the direction of material gradient distribution on the topology optimization results were deeply discussed.It is found that the self-weight loads and the direction of material gradient distributions have a significant influence on the optimal configuration and dynamic stiffness of the FGM structures.Finally,taking homogeneous materials(a special case of FGM)as an example,the validity of the proposed method was verified by numerical simulations and experiments,it is found that the proposed method may effectively improve the resonance frequency and dynamic stiffness.

关 键 词：结构拓扑优化 时域动力学分析 结构自重 功能梯度材料 

分 类 号：TB34[一般工业技术—材料科学与工程]