Topology optimization of structures in unilateral contact

• DOI: 10.1007/s00158-009-0407-z
• Publication Date: 2009-06-10T00:02:49Z
• Authors: Niclas Strömberg; Anders Klarbring
• Keywords: Topology optimization; Augmented Lagrangian method; Minification; Shape Optimization

In this paper a general framework for topology optimization of structures in unilateral contact is developed. A linear elastic structure that is unilaterally constrained by rigid supports is considered. The supports are modeled by Signorini’s contact conditions which in turn are treated by the augmented Lagrangian approach as well as by a smooth approximation. The latter approximation must not be confused with the well-known penalty approach. The state of the system, which is defined by the equilibrium equation and the two different contact formulations, 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 problems are solved by SLP. This is done by using a nested approach where the state equations are linearized and sensitivities are calculated by the adjoint method. In order to avoid mesh-dependency the sensitivities are filtered by Sigmund’s filter. The final LP-problem is solved by an interior point method that is available in Matlab. The implementation is done for a general design domain in 2D as well as in 3D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.