A boundary element and level set based topology optimisation using sensitivity analysis

The structural topology optimisation method presented in this paper is based on the boundary element method, level set method and shape sensitivity analysis for two-dimensional linear elastic problems. The proposed method automatically nucleates holes within the design domain during the optimisation process using a topological derivative based hole insertion criterion. The level set method is used to provide an implicit description of the structural geometry, which is capable of automatically handling topological changes, i.e. holes merging with each other or with the boundary. During the optimisation process non-uniform rational b-splines are fitted through the zero level set contours, which links an implicit geometry representation to its structural model. In addition, this provides an optimal design in standard CAD format, and without intermediate material densities, which can be directly used in other design processes. The proposed optimisation method is tested against different benchmark examples and the optimal geometries generated are in close agreement those available in the literature of topology optimisation.