Shape sensitivity analysis using low- and high-order finite elements

Abstract

A general procedure to perform the sensitivity analysis for the shape optimal design of elastic structures is proposed. The method is based on the implicit differentiation of the discretized equilibrium equations used in the finite element method (FEM). The so-called semianalytical approach is followed, that is, finite differences are used to differentiate the finite element matrices. The technique takes advantage of the geometric modeling concepts typical of the computer-aided design (CAD) technology used in the creation of a compact design model. This procedure is largely independent of the types of finite elements used in the analysis and has been implemented in ah-version andp-version finite element program. Very accurate and stable shape sensitivity derivatives were obtained from both programs over a wide range of finite difference step sizes. It is shown that the method is computationally efficient, general, and relatively easy to implement. Some classical shape optimal design problems have been solved using the CONLIN optimizer supplied with these gradients.