Shape and topology optimization for contact applications

This paper combines density-based topology optimization (TO) with a “contact aware” shape optimization (SO) which combines the design freedom of TO with the precise boundary representation of SO. Using gradient based optimization, the objective is to design structures in frictionless contact, including the shape of the contacting surfaces. SO is performed on each contacting structure which defines its own TO domain and contact is modeled at the interface between the domains using a mortar formulation combined with the penalty method. The SO uses the finite element node coordinate parameterization, and to avoid undesired shape changes that can result in e.g. jagged boundaries or excessive interference between two contacting grids, a PDE-based filter is used. Two formulations are investigated, one that sequentially uses TO and then SO and one that uses them simultaneously.