力学建模在变密度法中密度与刚度关系中的应用  

An Application to Mechanical Modeling to the Relation Between Density Variable and Stiffness in Variable Density Approach

作　　者：邓扬晨[1] 张卫红[1] 邱克鹏[1] 刘晓欧[1] 章怡宁[2] 

机构地区：[1]西北工业大学中法并行工程联合实验室,西安710072 [2]沈阳飞机设计研究所,沈阳110035

出　　处：《机械科学与技术》2003年第S2期95-98,共4页Mechanical Science and Technology for Aerospace Engineering

基　　金：中国博士后基金项目(2002032222);航空科学基金项目(03853003);国家自然科学基金项目(10172072);西北工业大学研究生创业种子基金(20030057);2004年度西北工业大学本科毕业设计重点扶持项目资助

摘　　要：将结构拓扑优化中的变密度人为过程视作材料纵横方向收缩的物理过程,并把此收缩量转化为密度与刚度关系的中间变量。利用一种有限元数值模型将三者建立离散的数据关系,再使用幂指近似函数建立密度与收缩量的解析关系,最后利用力学关系建立密度与刚度的解析关系。数值计算表明:本文方法概念明确、操作简捷、数据拟合效果好。The artificial process of variable density on structural topology optimization is regarded as a physical process of material shrinkage along two dimensions in this paper. The shrinkage is transferred into intermediate-variable about the relation between density and stiffness. Utilizing a stiffness-density numerical model constructed by FEM, the authors form their discrete data relation. With exponential approximate function, we construct the analytical relation between density and middle-variable. Finally, the analytical relation between density and stiffness is also formed by the principle of mechanics. Results reveal that the method here is simple and effective.

关 键 词：结构拓扑优化 密度变量 材料收缩 刚度—密度数值模型 幂指近似函数 

分 类 号：O39[理学—工程力学]