基于灵敏度分析的三维结构等几何形状优化方法

中国机械工程

基于灵敏度分析的三维结构等几何形状优化方法

陈龙;张高朋

上海理工大学机械工程学院，上海，200093

出版日期:2017-07-25 发布日期:2017-07-26
基金资助:
国家自然科学基金资助项目(51475309,61472111 )
National Natural Science Foundation of China （No. 51475309,61472111）

Three Dimensional Structural Shape Optimization Based on Sensitivity Analysis Using Isogeometric Analysis

CHEN Long;ZHANG Gaopeng

School of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai,200093

Online:2017-07-25 Published:2017-07-26
Supported by:
National Natural Science Foundation of China （No. 51475309,61472111）

摘要/Abstract

摘要： 以等几何分析为数值分析方法，针对三维结构的线弹性问题，以优化边界控制点坐标为设计变量，通过Coons体插值方法得到插值控制点对优化边界控制点的坐标导数，推导了单元刚度矩阵对控制点坐标变量的形状优化灵敏度方程，并对应力灵敏度和位移灵敏度方程进行了推导。数值算例证明该方法具有较高的优化效率，优化结果良好。

关键词: 等几何分析, 三维结构, 形状优化, 灵敏度

Abstract: An isogeometric analysis method was used as numerical analysis method. As for three-dimensional structures of linear elastic problem, boundary control points that needed to be optimized were regarded as design variables, derivatives of internal control points as to design variables might be obtained by using Coons interpolation method. In shape optimization, sensitivity equation of element stiffness matrix as to control points coordinates was derived, and sensitivity equations of stresses and displacements were deduced. Numerical examples show that the method has high efficiency and good results.

Key words: isogeometric analysis, three-dimensional structure, shape optimization, sensitivity

中图分类号:

TB121

陈龙;张高朋. 基于灵敏度分析的三维结构等几何形状优化方法[J]. 中国机械工程.

CHEN Long;ZHANG Gaopeng. Three Dimensional Structural Shape Optimization Based on Sensitivity Analysis Using Isogeometric Analysis[J]. China Mechanical Engineering.

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http://www.cmemo.org.cn/CN/Y2017/V28/I14/1723

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