Nonconforming Finite Element for Checkerboard-Free Topology Optimization

摘要

Topology optimization using a 4-node nonconforming finite element is investigated in this paper. Because the L~2 -norm convergence of the nonconforming finite element is independent of the Lame parameters, numerical solutions are free from locking phenomena that cause the formation of checkerboards in topology design optimization. Numerical results for benchmark problems confirm the superior behavior of the non-conforming element; clear images free from checkerboard patterns are obtained without any filtering treatment. Since the present nonconforming element has nodes along its edges, this element appears very useful for the development of an efficient parallelized topology optimization strategy, and work is in progress towards this direction.