Simultaneous Multicomponent Topology Optimization using Unilateral Contact-Constraints

In this paper, a framework for topology optimization of assemblies considering unilateral contact-constraints is introduced. Here, an assembly consists of two or more components that are connected via joints, and the topology of all components of the assembly are optimized simultaneously. Therefore, linear-elastic material is considered and the augmented Lagrangian approach imposing Signorini’s contact condition is used. In doing so, the unilateral characteristic of contact is taken into account. Furthermore, the influence of different contact modeling techniques, i.e. augmented Lagrangian approach, a standard penalty approach and a unilateral penalty approach, on the optimized designs are discussed. For topology optimization, the SIMP-approach is applied to all members of the assembly and sensitivity filtering is used. In consequence, the global design space of the optimization consists of the normalized densities of all members of the assembly. Using the proposed approach, one can optimize a topology for the whole assembly instead of optimizing all members of the assembly independently. This is of major importance, since changes in the topology of any member will lead to changes in the force transfer at the joints, which in consequence influences the optimization of all members of the assembly.