Shape Design Sensitivity Analysis of Elliptic Problems in Boundary Integral Equation Formulation

Abstract

ABSTRACT Self-adjoint elliptic boundary-value problems are formulated in a standard direct boundary integral equation (BIE) form and a general method for shape design sensitivity analysis is developed, using the formulation. To describe the shape variation, the material derivative concept is utilized. Adjoint variables are employed to obtain an explicit formula for the variation of a performance functional due to boundary movement; i.e., shape change. The adjoint problem, although defined in the indirect BIE form, can also be solved using the same direct BIE of the primal problem, since the two BIE's are equivalent. The method developed is applied and formulas are obtained for potential, plate, and plane elasticity problems. Notes COMMUNICATED BY E. J. HAUG