Adjoint Shape Sensitivity Analysis Based On Generalized Variational
广义变分原理的结构形状优化伴随法灵敏度分析

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.