Boundary integral method for shape optimization of interface problems and its application to implant design in dentistry

Abstract

A boundary integral formulation for shape optimization is presented in linear elasticity problems with zoned-inhomogeneous bodies. Sensitivity formula for arbitrary functional with respect to the interface shape variation is derived based on a boundary integral identity. Analytic as well as numerical examples for the sensitivity analysis are presented to show the validity of the formulation. An optimum design problem to find interface shape of endosseous implant in dentistry is studied under the objective of uniform stress at the interface between the implant and the bone. Though the problem involves numerous simplifications that may lead to the lack of reality, it is worthwhile to mention that the optimum shapes look similar to those of tooth roots. This may reflect a kind of natural optimum.