DIRECT DIFFERENTIATION METHOD FOR SHAPE DESIGN SENSITIVITY ANALYSIS USING BOUNDARY INTEGRAL FORMULATION

A direct differentiation method is proposed for shape design sensitivity analysis of elastic structures using the Boundary Integral Equation (BIE) formulation. A new BIE is derived, where unknowns are the design derivatives of the structural responses on the boundary, by applying the material derivative concept to the boundary integral identity. To remove the singularity problem arising in the new BIE, a regular BIE technique is employed by locating the collocation point outside the boundary. The accuracy of the results of the direct differentiation method is studied through the elliptic hole problem under tensile stress at infinity. A critical comparison is made for the sensitivity results of the direct differentiation and adjoint variable methods as well as for those of the finite difference method against the exact design sensitivity. Excellent accuracy is observed for the results of the direct differentiation method. © 1990.