Topology optimization using non-conforming finite elements: three-dimensional case

As in the case of two-dimensional topology design optimization, numerical instability problems similar to the formation of two-dimensional checkerboard patterns occur if the standard eight-node conforming brick element is used. Motivated by the recent success of the two-dimensional non-conforming elements in completely eliminating checkerboard patterns, we aim at investigating the performance of threedimensional non-conforming elements in controlling the patterns that are estimated overly stiff by the brick elements. To this end, we will investigate how accurately the non-conforming elements estimate the stiffness of the patterns. The stiffness estimation is based on the homogenization method by assuming the periodicity of the patterns. To verify the superior performance of the elements, we consider three-dimensional compliance minimization and compliant mechanism design problems and compare the results by the non-conforming element and the standard 8-node conforming brick element