各向异性结构动态特性拓扑优化设计的敏度分析  

Sensitivity Analysis of Topology Optimization Design for Dynamic Characeristics of Anisotropic Materrial Structures

作　　者：梁森[1] 仪垂杰[1] 郭健翔[1] Michael Yu Wang 

机构地区：[1]青岛理工大学机械工程学院,青岛266033 [2]香港中文大学机械及自动化工程系

出　　处：《青岛理工大学学报》2008年第3期1-9,共9页Journal of Qingdao University of Technology

基　　金：山东省自然科学基金项目(Z2007F04)

摘　　要：利用水平集函数建立了各向异性连续结构动态特性拓扑优化设计的理论模型,使用一种全新方法证明了物质导数公式,得到了域积分和边界积分泛函的物质导数表达式.通过将物质导数法和不等式约束增广Lagrangian乘子法相结合推出了各向异性材料结构动态特性拓扑优化设计敏度分析的公式.设计边界的进化是通过人为的使目标函数下降的速度来控制,高维水平集曲面在不改变其拓扑结构的前提下上下运动,从而使嵌入在零水平集的结构形状通过其边界的合并与断裂在设计域内自动地改变其拓扑结构.广泛的2D正交各向异性悬臂梁研究验证了该方法的有效性,其结论为进一步发展复合材料结构的拓扑优化设计理论与算法奠定了基础.The new theoretic model of the topology optimization for the anisotropic material continuum structures with level set function is established. A new approach is employed here to prove the functional material derivative formulas of domain integral and boundary integral. The novel sensitivity analysis of the dynamic characteristics for topology optimization of an anisotropic material structure is presented by employing the material derivative method and augmented Lagrangian multipliers method. The evolution of the structural design boundary can be controlled by the artificial velocity which makes the objective function descend. The level set surface of a higher-dimensional function can be moved up and down without changing its topology structures, but the optimization boundaries embedded on level set function can automatically modify the topology structures by the boundaries merging and breaking. The extensively studied 2D examples are employed to demonstrate the validity of the presented methodologies. The conclusions indicate this investigation will provide an important foundation for the advanced development of the topological optimization theory and algorithm of the composite material structures.

关 键 词：物质导数 增广Lagrangian乘子 水平集方法 拓扑优化 正交各向异性 

分 类 号：TH123[机械工程—机械设计及理论]