Boundary element implicit differentiation equations for design sensitivities of axisymmetric structures

Design sensitivity analysis of axisymmetric elastic media is formulated using boundary elements. The kernels for sensitivity matrices are obtained through implicit differentiation of the corresponding boundary element elasticity kernels. The singular terms are obtained by applying the boundary displacements and tractions, and their respective sensitivities for the rigid body motion mode and the inflation mode. The equations for the recovery of sensitivities of axisymmetric boundary stresses are presented. As a check on accuracy, the approach is applied to a series of examples for which analytical elasticity solutions are available. The predictions for both displacement- and stress-sensitivities are accurate. Additional examples are provided to demonstrate the versatility of the present approach.