基于虚荷载变量的形状优化和灵敏度分析  

Shape optimization and sensitivity analysis based on fictitious load variables

作　　者：龚曙光[1] 黄云清[2] 谢桂兰[1] 邱爱红[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]湘潭大学计算与应用数学研究所,湖南湘潭411105

出　　处：《计算力学学报》2005年第2期183-188,231,共7页Chinese Journal of Computational Mechanics

基　　金：国家重点基础研究专项经费(973);大规模科学计算研究项目;湖南省自然科学基金(03JJY3082)资助项目.

摘　　要：基于选择施加在结构"控制点"上的虚荷载作为优化设计变量,针对一种新的承受约束的形状优化数值方法进行了研究。借助于节点位移与虚荷载之间的线性关系,提出了一种新的计算灵敏度系数的解析方法。利用节点移动速度域概念构造了优化新形状产生的计算公式,以结构中节点的最大应力最小化作为优化目标,通过控制网格结点的最大位移量,较好地解决了单元网格在形状优化中的扭曲问题。对三个不同的实例成功地完成了形状优化。A novel numerical method for shape optimization was discussed in this paper, based on which the fictitious loads applying on control point of structure are chosen as the optimal design variable, and the analytic method for calculating sensitivity analysis coefficients was developed by means of a linear relationship between nodal displacement and fictitious loads. The shape optimized was formulated as presenting the concept of nodal moving velocity field matrix. The objective function is to minimize Von Mises stress of structure. By controlling grids nodal maximum deformation, the distortion of finite element meshes can be controlled better than that appear in the shape optimization. Three different kinds of examples are tested successfully.

关 键 词：形状优化 有限元法 灵敏度分析 虚载荷 

分 类 号：O241.82[理学—计算数学]