Checkerboard-Free Topology Optimization Using Polygonal Finite Elements

Abstract

The checkerboard layout of material distribution is one of a number of serious numerical anomalies encountered in the solution of topology optimization problems. Regularization schemes such as filtering can be used to suppress the numerical instabilities, but these measures often involve heuristic parameters that can augment the optimization problem. Polygonal elements can be very useful in this aspect since they naturally exclude checkerboard layouts and provide flexibility in discretizing complex domains. Examples considering compliance minimization and compliant mechanism are presented that demonstrate the advantages of the proposed elements in achieving checkerboard-free solutions and avoiding one-node connections from the design optimization process. Potential extensions and impact of this work will also be discussed.