Shape Design Sensitivity Analysis Based on Boundary Integral Equation Method Considering General Shape Variations, Part I: For Self-Adjoint Elliptic Operator Problems

Abstract

A procedure for shape design sensitivity analysis is developed using a standard boundary integral equation (BIE) formulation for elliptic problems with static response. The performance functional to be considered involves both the domain and boundary integrals, and a complete consideration is given in describing the shape variation by including the tangential as well as the normal component of the velocity field. The material derivative concept and the adjoint variable method as applied to the BIE fomlUlation are basic tools for the derivation. This has opened a new un:fied approach using the BIE to the shape design sensitivity problems.