Material derivative and control volume approaches to shape sensitivity analysis of nonlinear transient thermal problems

Abstract

The problem of the shape design sensitivity of nonlinear transient thermal systems is considered. The nonlinear shape design sensitivity is formulated by using a weighted residual method employing the continuum description. Both material derivative and control volume approaches for structural shape design sensitivity analysis are presented, analysed and compared. It is shown that the final design sensitivity expressions for the two approaches are theoretically equivalent.