A contact aware regularization technique for shape optimization

A novel regularization method for shape optimization of contacting structures is proposed. The shape optimization avoids parameterizations via splines or the level set method by directly optimizing the nodes in the finite element mesh. In the past this approach was limited by numerical difficulties arising from mesh entanglement and serrated boundaries but recent advances in regularization techniques have proven successful in avoiding these issues. Traditionally, designing structures in contact presents a significant challenge since the structures are “unaware” of each other outside the contact region which can lead to design changes that cause the bodies to interfere. A straightforward solution to this problem is to restrict the design updates so that penetration is limited. The method presented in this paper allows relatively large design changes by utilizing a contact “aware” regularization that limits the interference caused by design changes. To enable larger shape changes the optimization sequentially resets the design. The features of the proposed method are showcased in several numerical examples that optimize the contact response.