AN EXPOSITION OF THE MATERIAL DERIVATIVE APPROACH FOR STRUCTURAL SHAPE SENSITIVITY ANALYSIS

The material derivative approach for structural shape design sensitivi ty analysis is described in a unified manner using the continuum formu lation. Both the direct differentiation and adjoint methods are derive d and computer implementation aspects are discussed. The basic purpose of the paper is to present the shape design sensitivity analysis as a n application of the material derivative concept of continuum mechanic s, and the calculus of variation procedures for taking variations of i ntegrals over the variable domains. It is also shown that the use of a recently developed variational principle for design sensitivity analy sis greatly simplifies derivation of the adjoint method. The indicial notation is used and expressions derived by different authors are rela ted to each other. A basic understanding of the material derivative ap proach of shape sensitivity analysis has been gained which can lead to insights for computer implementations of the method.