Checkerboard-free topology optimization using non-conforming finite elements

The objective of the present study is to show that the numerical instability characterized by checkerboard patterns can be completely controlled when non-conforming four-node nite elements are employed. Since the convergence of the non-conforming nite element is independent of the Lam e parameters, the sti ness of the non-conforming element exhibits correct limiting behaviour, which is desirable in prohibiting the unwanted formation of checkerboards in topology optimization. We employ the homogenization method to show the checkerboard-free property of the non-conforming element in topology optimization problems and verify it with three typical optimization examples