Topology optimization of structures in unilateral contact

Abstract In this paper a general framework for topologyoptimization of structures in unilateral contact isdeveloped. A linear elastic structure that is unilaterallyconstrained by rigid supports is considered. Thesupports are modeled by Signorini’s contact conditionswhich in turn are treated by the augmented Lagrangianapproach as well as by a smooth approximation. Thelatter approximation must not be confused with thewell-known penalty approach. The state of the system,which is defined by the equilibrium equation andthe two different contact formulations, is solved by aNewton method. The design parametrization is obtainedby using the SIMP-model. The minimization ofcompliance for a limited value of volume is considered.The optimization problems are solved by SLP. This isdone by using a nested approach where the state equationsare linearized and sensitivities are calculated bythe adjoint method. In order to avoid mesh-dependencythe sensitivities are filtered by Sigmund’s filter. Thefinal LP-problem is solved by an interior point methodthat is available inMatlab. The implementation is donefor a general design domain in 2D as well as in 3Dby using fully integrated isoparametric elements. Theimplementation seems to be very efficient and robust.The original publication is available at www.springerlink.com:Niclas Strömberg and Anders Klarbring, Topology optimization of structures in unilateral contact, 2010, Structural and multidisciplinary optimization, (41), 1, 57-64.http://dx.doi.org/10.1007/s00158-009-0407-zCopyright: Springer Science Business Mediahttp://www.springerlink.com