An exposition of the material derivative approach for structural shape sensitivity analysis

Abstract

The material derivative approach for structural shape design sensitivity analysis is described in a unified manner using the continuum formulation. Both the direct differentiation and adjoint methods are derived and computer implementation aspects are discussed. The basic purpose of the paper is to present the shape design sensitivity analysis as an application of the material derivative concept of continuum mechanics, and the calculus of variation procedures for taking variations of integrals over the variable domains. It is also shown that the use of a recently developed variational principle for design sensitivity analysis greatly simplifies derivation of the adjoint method. The indicial notation is used and expressions derived by different authors are related to each other. A basic understanding of the material derivative approach of shape sensitivity analysis has been gained which can lead to insights for computer implementations of the method.