Direct differentiation formulation for boundary element shape sensitivity analysis of axisymmetric elastic solids

An efficient direct differentiation method by continuum approach is presented for the shape design sensitivity analysis of axisymmetric elastic solids. The method is purely based on the axisymmetric boundary integral equation formulation. A new boundary integral equation for sensitivity analysis is derived by taking material derivative to the same integral identity that was used in the adjoint method. As sensitivities in terms of the shape design variables are directly calculated by solving the new BIE, the singular boundary condition which may arise in the adjoint method is avoided in the present direct method. To validate the theoretical formulation, numerical implementation is done for three examples. For a hollow disk and a thick-walled cylinder problem with analytic solution, the sensitivities by present method are compared with analytic sensitivities. For an example of a spherical vessel, being rather practical, the sensitivities are compared with those by finite differences. Copyright 0 1996 Elsevier Science Ltd