Shape optimization of hyperelastic structures subject to frictionless contact

This paper describes the shape optimization of hyperelastic structures exhibiting finite deformation and contact. The structure's shapes are parameterized with B-splines and the spline control point coordinates serve as the design variables. This design parametrization provides precise boundary representations and analytical sensitivity computations. To accommodate non-matching grids between the contacting bodies the mortar method is employed and, to hasten computations the accelerated Uzawa scheme is used to solve the displacement and contact pressure update equations. The formulation is used to optimize structures to achieve the desired mechanical response by exploiting both the non-linear hyperelastic material response and the contact phenomena.