Topology Optimization of Two Linear Elastic Bodies in Unilateral Contact

Abstract The optimal solutions are most sensitive to the boundary conditions when performing topology optimization of components. In many applications the design domain of the components are subjected to unilateral contact conditions. In order to obtain relevant conceptual designs by topology optimization of such systems, the contact conditions should be included explicitly in the optimization. Recently, in a number of works by Strömberg and Klarbring, such a method has been developed for one elastic body unilateral constrained to rigid supports. Here, this approach is extended such that a system of two elastic bodies in unilateral contact is considered. For this systems the compliance is minimized by adopting the SIMP-model. A nested formulation of the problem is solved by SLP, where the sensitivities are obtained by solving an adjoint equation. In this latter equation, the Jacobian from the Newton method used to solve the state problem appears. The state problem is treated by an augmented Lagrangian formulation of the bodies in contact. Thus, the Jacobian is simply the gradient of the corresponding system of equations to this formulation. The method is implemented in the toolbox Topo4abq by using Matlab and Intel Fortran. The method is both efficient and robust. This is demonstrated by solving several 2D-problems. The results are also compared to the solutions obtained when the contact conditions are treated by joining the two bodies to one body. In a near future 3D-problems will also be solved by using the presented approach.