Adjoint Shape Sensitivity Analysis Based On Generalized Variational

Variational principle for adjoint design sensitivity analysis wasfirst developed by Arora. The original form of the principle is stated interms of an augmented functional that is defined by adding to the responsefunctional whose sensitivity is required, the weak form equilibrium equationof the primary problem. In the present paper, a new adjoint shapesensitivity analysis method for shape optimization of continuum structuresis proposed. Based on the generalized variational principle, the shapevariation of the displacement prescribed boundary and the associatedderivatives of the prescribed boundary conditions is considered in aconsistent way. The proposed method eliminates the limitation of Arora'smethod for dealing with the variations of Dirichlet boundaries and providesa new framework for shape sensitivity analysis. An analytical exampleillustrates the effectiveness and validity of the proposed approach.