A MIXED VARIATIONAL FORMULATION FOR SHAPE OPTIMIZATION OF SOLIDS WITH CONTACT CONDITIONS

This paper is concerned with the development of a mixed variational formulation and computational procedure for the shape optimization problem of linear elastic solids in possible contact with a rigid foundation. The objective is to minimize the maximum value of the von Mises equivalent stress in a body (non-differentiable objective function), subject to a constraint on its volume and bound constraints on the design. For design purposes, the contact boundary is considered fixed. A finite element model that is appropriate for the mixed formulation is utilized in the discretization of the state and adjoint state equations. An elliptical mesh generator was used to generate the finite element mesh at each new design. The computational model is tested in several example problems.