Density and levelsets: A hybrid method for topology optimisation

Details

Supervisors

Remacle, Jean-François ; Beaufort, Pierre-Alexandre

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

Topology optimisation is a design methodology for reducing structural weight while preserving mechanical performance. However, high-resolution topology optimisation problems remain computationally demanding, and the resulting designs often require post-processing before they can be manufactured, because of grey regions and mesh dependencies. This thesis presents a novel framework combining density- and levelset-based topology optimisation with the eXtreme Mesh deformation method (X-Mesh) developed at UCLouvain. The proposed approach modifies the positions of the mesh nodes after the density-based optimisation to sharpen the material boundaries without remeshing the domain. The goal is to produce sharp and well-defined boundaries. The density approach is analysed in details to clearly define its limitations and which problems the new framework adresses. All experiments are conducted on the Messerschmitt-Bölkow-Blohm (MBB) beam, a classical benchmark problem in topology optimisation. The framework defined in this thesis shows great potential if further researched. It is also a very powerful tool in solving the problem of manufacturability, as it allows some complex constraints and flexible objective choices. Moreover, the framework creates a connection between the two main methods used in topology optimisation today. Future work on the subject should concentrate on the convergence of the method, as no clear criterion has been identified as relevant.