对CST单元采用半解析法计算灵敏度的误差分析

灵敏度分析是高效率结构优化方法的关键，半解析法是计算状态变量对于形状设 计变量灵敏度的一种有效方法，但对这一近似方法造成的误差还不完全清楚，因此受 到广泛的关注。本丈针对平面三角形常应变单元（ＣＳＴ）组成的结构，讨论了用半解 析法求得的灵敏度的误差，说明对这类单元误差并不随形状被修改的区域中采用的单 元数增长而增长。

0n Accuracy of Semi-Analytic Sensitivity Analysis for CST Elements

The sensitivity analysis is a key of efficient approaches of structural optimization.Semi-analytic method is efficient to compute sensitivities of state variables respect to shape related design variables.This method has attracted wide interests due to unsolved problem of error estimation. The accuracy of semi-analytic method has been studied in this paper considering structures composed of plane constant strain triangular (CST) elements. It is shown that the error of semi-analytic method for CST elements will not increase when the number of elements within those regions whose boundary shape have been changed increases.