Topology optimization with optimal spatially varying length scale

Abstract: Density based topology optimization has become an efficient way to design optimal complex structures with different goals, constraints and boundary conditions. To regularize the solution, density filters are utilized and is controlled by the length scale. The length scale controls minimum feature sizes, as well as minimum curvatures in the structure. Usually a constant length scale is used throughout the design domain, but some recent articles have explored the possibility of varying the length scale spatially to control the peak stresses in a compliance minimization problem. The idea of a varying length scale and treating it as a design variable was then further explored in this thesis. The length scale was controlled by penalizing variations from the initial length scale. The idea of penalizing variations can be tied into the cost of producing the structure, where the penalty parameter for the length scale can be seen as a tradeoff between optimal structure and manufacturing cost. The concept of a varying length scale was then tested on a L-bracket with an objective function of minimizing the compliance of the structure with a volume constraint, and later on with a stress constraint as well. The optimization is solved using the Method of Moving Asymptotes. The final structures were quite similar to what was achieved with a constant length scale, but usually with 2-4\% increase in performance but at a cost at computation time. Finally a variation in the filtering scheme is proposed to achieve consistent feature sizes without the need of padding the structure.