广义变分原理的结构形状优化伴随法灵敏度分析

ADJOINT SHAPE SENSITIVITY ANALYSIS BASED ON GENERALIZED VARIATIONAL PRINCIPLE

提出了一种利用伴随变量进行结构形状优化灵敏度分析的新方法.基于广义变分原理,考虑了形状优化中位移边界条件的变化对结构响应的影响.新方法弥补了Arora等人所提出的形状优化灵敏度分析变分原理中的缺陷,为采用伴随法进行灵敏度分析提供了新的框架.

Variational principle for adjoint design sensitivity analysis was first developed by Arora. The original form of the principle is stated in terms of an augmented functional that is denned by adding to the response functional whose sensitivity is required, the weak form equilibrium equation of the primary problem. In the present paper, a new adjoint shape sensitivity analysis method for shape optimization of continuum structures is proposed. Based on the generalized variational principle, the shape variation of the displacement prescribed boundary and the associated derivatives of the prescribed boundary conditions is considered in a consistent way. The proposed method eliminates the limitation of Arora's method for dealing with the variations of Dirichlet boundaries and provides a new framework for shape sensitivity analysis. An analytical example illustrates the effectiveness and validity of the proposed approach.