The Influence of Sliding Friction on Optimal Topologies

In this paper the influence of sliding friction on optimal topologies is investigated and some preliminary results are presented. A design domain unilaterally constrained by a spinning support is considered. Most recently, Stromberg and Klarbring have developed methods for performing topology optimization of linear elastic structures with unilateral contact conditions. In this works sliding friction is also included in the contact model. In such manner it is possible to study how the spinning of the support will influence the optimal design. This was not possible before. The support is modeled by Signorini's contact conditions and Coulomb's law of friction. Signorini's contact conditions are regularized by a smooth approximation, which 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, where the LP-problem is solved by an interior point method that is available in the package of Mat lab. In order to avoid mesh-dependency and patterns of checker-boards the sensitivities are filtered by Sigmund's filter. The method is implemented by using Mat lab and Visual Fortran, where the Fortran code is linked to Mat lab 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.