COMPARISON OF SHAPE DESIGN SENSITIVITY ANALYSIS FORMULATIONS VIA MATERIAL DERIVATIVE-ADJOINT VARIABLE AND IMPLICIT DIFFERENTIATION TECHNIQUES FOR 3-D AND 2-D CURVED BOUNDARY-ELEMENT

This paper reviews and compares two different approaches to continuum structural shape design sensitivity analysis: the material derivative- adjoint variable method and the implicit differentiation method using 3-D and 2-D BEM. Employing identical BEA models, curved element techno logy, numerical integration and equation solving techniques, the simil arities and differences of both methods are highlighted. Significant t heoretical and computational aspects associated with both methods are presented and accuracy and computational efficiency characteristics ar e demonstrated. Advantages and disadvantages of both techniques are id entified. The characterization provided can aid in the prudent selecti on between these sensitivity analysis techniques, based on the charact eristics of the proposed application.