敏度分析与修正降维法

Sensitivity Analysis and Modified Reduced Basis

本文介绍了连续体结构形状优化设计中灵敏度分析的一种有效方法。根据设计变量和单元结点坐标之间的映射关系,推导出三结点常应变元敏度分析的显式,避免了用差分计算敏度时步长难以选定的困难,提高了精度及稳定性。本文还研究了修正降维法,并将该法应用于连续体结构的性态及敏度分析。示例表明,修正降维法具有很高的效率和满意的精度。

An efficient method for sensitivity analysis in shape optimization of continuum structures are presented in this paper. According to the mapping relations between design variables and element nodal coordinates, an explicit expression of sensitivity analysis is derived for 3-node elements. The difficulty of choosing step length of difference method is avioded. This enhances the accuracy and stability of result. This paper also studies the Modified Reduced Basis ( MRB ) and uses this method to calculate the structural responses and sensitivities. The example shows that MRB has high efficiency and satisfactory accuracy.