Topology Optimization of Structures with Contact Constraints by using a Smooth Formulation and a Nested Approach

1. Abstract In this paper a method for topology optimization of structures in unilateral contact is developed. A linear elastic structure that is unilateral constrained by rigid supports is considered. The supports are modeled by Signorini’s contact conditions which in turn are treated by a smooth approximation. This approximation must not be confused with the well-known penalty approach. The state of the system, which is defined by the equilibrium equations and the smooth approximation, is solved by a Newton method. The design parametrization is obtained by using the SIMP-model. The minimization of compliance for a limited value of volume is considered. The optimization problem is solved by a nested approach where the equilibrium equations are linearized and sensitivities are calculated by the adjoint method. The problem is then solved by SLP. The LP-problem is in turn solved by an interior point method that is available in Matlab. In order to avoid mesh-dependency the sensitivities are filtered by Sigmund’s filter. The method is implemented by using Matlab and Visual Fortran, where the Fortran code is linked to Matlab as mex-files. The implementation is done for a general design domain in 2D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust. 2.