Shape design sensitivity analysis for interface problem in axisymmetric elasticity

A boundary integral equation method in the shape design sensitivity analysi s is developed for the elasticity problems with axisymmetric non-homogeneou s bodies. Functionals involving displacements and tractions at the zonal in terface are considered. Sensitivity formula in terms of the interface shape variation is then derived by taking derivative of the boundary integral id entity. Adjoint problem is defined such that displacement and traction disc ontinuity is imposed at the interface. Analytic example for a compound cyli nder is taken to show the validity of the derived sensitivity formula. In t he numerical implementation, solutions at the interface for the primal and adjoint system are used for the sensitivity. While the BEM is a natural too l for the solution, more generalization should be made since it should hand le the jump conditions at the interface. Accuracy of the sensitivity is eva luated numerically by the same compound cylinder problem. The endosseous im plant-bone interface problem is considered next as a practical application, in which the stress value is of great importance for successful osseointeg ration at the interface. As a preliminary step, a simple model with tapered cylinder is considered in this paper. Numerical accuracy is shown to be ex cellent which promises that the method can be used as an efficient and reli able tool in the optimization procedure for the implant design. Though only the axisymmetric problem is considered here, the method can be applied to general elasticity problems having interface.