Correlation between hole insertion criteria in a boundary element and level set based topology optimisation method

The research work presented in this paper is based on the correlation between two hole insertion criteria in a boundary element method (BEM) and level set method (LSM) based structural topology optimisation scheme for 2D elastic problems. The hole insertion criteria used in this work are based on the von Mises stress and the topological derivative approaches. During the optimisation process holes are automatically inserted in the design domain using each of the two criteria. The LSM is used to provide an implicit description of the structural geometry, and is also capable of automatically handling topological changes, i.e. holes merging with each other or with the boundary. The evolving structural geometry (i.e. the zero level set contours) is represented by NURBS, providing a smooth geometry throughout the optimisation process and completely eliminate jagged edges. In addition the optimal NURBS geometry can be used directly in other design processes. Four different benchmark examples are considered in this study and each is tested against the two hole insertion criteria. The results obtained validate the proposed optimisation method and we demonstrate a clear correlation between the two hole insertion criteria.