Shape optimization of a rubber bushing

Abstract

The present paper describes a solution to a non-parametric shape optimization problem of a rubber bushing in order to adjust a function of the reaction force with respect to static displacement to a desired function. The main problem is defined as a static hyperelastic problem considering a large deformation and a non-linear constitutive equation. The squared error norm of the work done by compulsory displacement and the volume are chosen as cost functions. The shape derivatives of the cost functions are derived theoretically. An iterative algorithm based on the $H^1$ gradient method is used to solve the shape optimization problem.