基于虚载荷变量的无网格法形状优化的研究  

A STUDY ON MESHLESS SHAPE OPTIMIZATION BASED ON FICTITIOUS VARIABLES

作　　者：邱爱红[1] 龚曙光[1] 黄云清 聂松辉[1] 

机构地区：[1]湘潭大学机械工程学院CAE研究所,湖南湘潭411105 [2]"科学工程计算与数值仿真"湖南省重点实验室,湖南湘潭411105

出　　处：《工程力学》2007年第9期26-30,36,共6页Engineering Mechanics

基　　金：国家自然科学基金资助项目(50475143);高等学校博士学科点专项科研基金资助课题(20040530001);国家重点基础研究专项经费资助(2005CB321701);湖南省教育厅资助科研项目(04C654);湖南省重点学科建设项目资助

摘　　要：将选择施加在"虚结构"控制点上的虚载荷作为形状优化的设计变量,并将它与无网格Galerkin法相结合来开展结构形状优化研究,采用罚函数法来施加边界条件,通过直接微分法建立了结构形状优化的离散型灵敏度分析算法,利用无网格法研究了节点坐标关于设计变量导数的计算。所提出的算法简单明了,它不仅解决了网格的畸变问题,而且简化了优化模型和迭代流程,并可使结构的受力特性得到进一步的改善。最后用2个工程实例验证了所建立的算法,并得到了形状优化结果。The fictitious loads applying at certain control nodes on an auxiliary structure are chosen as the design variables of shape optimization, and structural shape optimization is studied by integrating fictitious variables with the element-free Galerkin method in this paper. The essential boundary condition is imposed by employing a penalty method. Using the direct differential method, the discrete-based numerical method for sensitivity analysis is derived. The derivative of nodal coordinates with respect to the design variables is discussed by means of meshless method. The presented algorithms of shape optimization are easy to understand. The distortion of mesh is avoided, and the optimal model and the process of iteration are simplified, so that the loading characteristic of structures can be at best status. Finally two engineering examples are presented to testify the algorithm proposed, and the optimal shapes of structure are obtained.

关 键 词：形状优化 无网格GALERKIN法 灵敏度分析 虚载荷变量 罚函数法 

分 类 号：O241.82[理学—计算数学] TH122[理学—数学]