一种基于水平集函数的尺寸优化方法及应用  

A Level Set-based Size Optimization Method and Its Applications

作　　者：王书亭[1] 陈振兴[1] 杨勇[1] 张卫国[1] 

机构地区：[1]华中科技大学国家CAD支撑软件工程技术研究中心,武汉430074

出　　处：《中国机械工程》2011年第20期2437-2442,共6页China Mechanical Engineering

基　　金：国家自然科学基金资助项目(50975107);国家科技重大专项(2010ZX04001-032)

摘　　要：针对构建结构拓扑、形状、尺寸的统一优化模型的需求,采用水平集函数描述结构尺寸要素的方法,建立了基于水平集法的结构尺寸优化模型。该方法采用水平集函数描述规则孔洞的几何尺寸信息,并通过引入紧支径向基函数进行插值,将尺寸变量转化为基函数的扩展系数。将基于水平集法的尺寸优化方法与基于水平集法的拓扑形状优化方法融合,构建了结构统一优化模型,实现了结构尺寸、拓扑和形状的综合优化。In order to construct a synthetically structural optimization model with topology, shape and size, a level set-based method was presented to characterize the geometric shape and parameter, accordingly, a level set-based size optimization model can be achieved. The structural geometry boundary was described with a level set function, by applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate the level set function. The expansion coefficients of interplant were regarded as the design variables which reflected the structural perform- ance impacts of size. Furthermore, by combing the level set-based size optimization with the shape and topology optimization model, a unified optimization method was presented to carry out the struc- tural dynamic optimization for continuum structure,which can fulfill the structural topology, shape and size optimization at the same time.

关 键 词：几何尺寸表达 尺寸优化 拓扑形状优化 综合优化 水平集法 紧支径向基函数 

分 类 号：TB12[理学—工程力学]