The application of drilling degree of freedom to checkerboards in structural topology optimization

The subject of the paper is to investigate a new way for avoiding the development of checkerboard patterns in structural topology optimization, using an additional in-plane rotational freedom. The efficiency of a few, from the many existing formulations, with differing complexity are put into comparison, such as the standard 4 noded bilinear element, the Allman-type solution, the shell element from SAP2000 and finally an element constructed on the basis of micropolar theory. Since the emergence of checkerboarded regions is a general phenomenon, the optimization problem is as simple as possible, being a weight minimization with a compliance constraint, solved with the optimality criteria method and a FEM discretization of the design domain.