基于RKPM梁固有频率及薄板柔度的拓扑优化  

RKPM-based topology optimization for natural frequency of beam and compliance of thin plate

作　　者：张建平[1] 蒋炎坤[1] 龚曙光[2] 刘欣[1] 

机构地区：[1]华中科技大学能源与动力工程学院,湖北武汉430074 [2]湘潭大学机械工程学院,湖南湘潭411105

出　　处：《华中科技大学学报（自然科学版）》2011年第6期101-105,共5页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(50875223)

摘　　要：以节点相对密度为设计变量,以固有频率最大为目标函数,通过修正低密度区质量矩阵建立了基于重构核粒子法(RKPM)的结构动力拓扑优化数学模型.采用罚函数法施加本质边界条件,利用直接微分法推导了结构固有频率灵敏度方程,同时研究了受横向载荷弯曲的基尔霍夫薄板柔度最小的拓扑优化问题.最后对比分析了节点依赖性以及设计变量对最优拓扑结构的影响,并结合以上算法和优化准则法编写程序完成了2个拓扑优化算例.优化结果表明:所建立的模型不仅能有效抑制局部模态和重特征频率的出现,而且因通过重构核近似提高了计算点密度场的连续性,棋盘格现象得以消除,可以得到清晰光滑的拓扑边界.Relative density of node was chosen as design variable, and maximizing the natural frequency was the objective function, and then a numerical model of structural dynamic topology optimization based on reproducing kernel particle method （RKPM） was established through modifying the mass matrix in low density domain. The penalty method was employed into imposing the essential boundary conditions, and the sensitivity equation of structural natural frequency was deduced by using direct differentiation method. Meanwhile, the topology optimization problem for the minimum compliance of Kirchhoff pla（e under a transverse load was studied. Finally, the node dependency and the effec（ of design variables on optimal topology were analyzed, and two numerical examples of topology optimiza- tion were performed by programming and integrating the above algorithms with optimality criteria method. The results show that the proposed model can not only suppress the appearance of localized eigenmodes and multiple eigenfrequencies effectively, but also the checkboards phenomenon is elimi- nated and a clear and smooth topological boundary can be obtained because the continuity of Gauss point＇s density field is improved through reproducing kernel approximation.

关 键 词：动力拓扑优化 无网格法 重构核粒子法 基尔霍夫薄板 灵敏度分析 

分 类 号：TH122[机械工程—机械设计及理论]