A three-dimensional implementation of the boundary element and level set based structural optimisation

Abstract

This paper presents a three-dimensional structural optimisation approach based on the boundary element and level set methods. The structural geometry is implicitly represented with the level set method, which evolves an initial structural model towards an optimal configuration using an evolutionary structural optimisation approach. The boundary movements in the three-dimensional level set based optimisation method allow automatic hole nucleation through the intersection of two surfaces moving towards each other. This suggests that perturbing only the boundary can give rise to changes not only in shape, but also in topology. At each optimisation iteration, the Marching Cubes algorithm is used to extract the modified geometry (i.e. the zero level set contours) in the form of a triangular mesh. As the boundary element method is based on a boundary discretisation approach, the extracted geometry (in the form of a triangular mesh) can be directly analysed within it. However, some mesh smoothing is required; HC-Laplacian smoothing is a useful algorithm that overcomes the volumetric loss associated with simpler algorithms. This eliminates the need for an additional discretisation tool and provides a natural link between the implicitly represented geometry and its structural model throughout the optimisation process. A complete algorithm is proposed and tested for the boundary element and level set methods based topology optimisation in three-dimensions. Optimal geometries compare well against those in the literature for a range of benchmark examples.