3-DIMENSIONAL BOUNDARY ELEMENT IMPLICIT DIFFERENTIATION FORMULATION FOR DESIGN SENSITIVITY ANALYSIS

An analytical formulation based on implicit-differentiation of the boundary integral equations, for the determination of structural design sensitivities of three-dimensional continua, is presented here. A semi-analytical and a full-analytical numerical implementation of the sensitivity equations are described. The singular terms for these equations are evaluated using a rigid body motion sensitivity condition. The treatment of design sensitivities due to body forces is included using the particular integral approach. A reduced design sensitivity analysis is described which involves condensation of the equations for the unchanging portion of the design and subsequent expansion of results for the entire design. Numerical results are obtained to study the dependence of the semi-analytical approach on the perturbation step size and also to validate the present formulations through comparisons with alternative solutions.