拓扑和形状集成优化设计  

Integration of topology and shape optimization

作　　者：傅晓锦[1] 卢炎麟[2] 

机构地区：[1]绍兴文理学院元培学院,浙江绍兴312000 [2]浙江工业大学机械制造及自动化教育部重点实验室,浙江杭州310014

出　　处：《计算机集成制造系统》2008年第6期1041-1048,共8页Computer Integrated Manufacturing Systems

基　　金：国家自然科学基金资助项目(50675206,50075083);浙江省自然科学基金资助项目(Y106847)。~~

摘　　要：将拓扑优化、形状优化、有限元分析和计算机辅助设计加以有机集成,构建了优化设计模型;利用几何重构技术,拟合拓扑优化后的边界;在形状优化中,将设计变量定义为B样条曲线或曲面的控制顶点的运动,建立了边界节点移动速度场计算方法,有效地控制节点的运动,给出了相应的算法和计算表达式,寻求较快的搜索方向,以合理速度分布使形状变为最佳。通过设计实例,证明了文中模型的合理性和方法的有效性。An integration approach was presented to support topology optimization, shape optimization, finite element analysis and Computer Aided Design （CAD）. Optimization design models were constructed. By using the geometric reconstruction technique mathematically, sound and error bounded for creating solid models of the topologically optimized structures with smooth geometric boundary. The control point movements of the B-spline curves or surfaces were defined as design variables in shape optimization. Method of velocity field computations was established for the boundary nodes. The design velocity field managed the movement of the structural material points due to design changes. Corresponding algorithm and the computation expression were also proposed. Seeking the quick search direction, the shape became the best by the reasonable velocity distribution. Rationality of the model and the effectiveness of the method were illustrated by an example.

关 键 词：拓扑优化 B样条 形状优化 几何引擎 有限元分析 

分 类 号：O241.82[理学—计算数学] TH122[理学—数学]