【摘要】 半解析法是计算状态变量对于形状设计变量灵敏度的一个有效的近似方法，但有 些情况下由该法求出的灵敏度的误差随单元数增加而迅速增加。本文先以端部受集中 弯矩的悬臂梁为例，分析了采用半解析法求自由端挠度对于梁长变化的灵敏度时产生 的误差，然后将该误差分析方法推广到梁发生任意变形的情形。最后，建议了随机差 分的方法，数值例子证明这一方法有效降低了误差。更多还原

【Abstract】 Semi-Analytic Method (SAM) is an efficient approximate method for computing the sensitivity of the structural response with respect to the shape design variables. However, under certain circumstance, the error of sensitivity obtained by the method increases rapidly as the number of elements increases. Taking the cantilever subject to a concentrated moment at its tip as an example, the present paper studies the sensitivity of the tip deflection with respect to its length and analyzes the source of the error from SAM. The error analysis is further extended to beams of arbitrarily deformation. Finally, a random difference method is proposed, and numerical example shows that the new method effectively suppresses the error.更多还原