Explicit level-set-based topology optimization using an exact Heaviside function and consistent sensitivity analysis

This paper presents a level-set-based topology optimization method based on numerically consistent sensitivity analysis. The proposed method uses a direct steepest-descent update of the design variables in a level-set method; the level-set nodal values. An exact Heaviside formulation is used to relate the level-set function to element densities. The level-set function is not required to be a signed-distance function, and reinitialization is not necessary. Using this approach, level-set-based topology optimization problems can be solved consistently and multiple constraints treated simultaneously. The proposed method leads to more insight in the nature of level-set-based topology optimization problems. The level-set-based design parametrization can describe gray areas and numerical hinges. Consistency causes results to contain these numerical artifacts. We demonstrate that alternative parameterizations, level-set-based or density-based regularization can be used to avoid artifacts in the final results. The effectiveness of the proposed method is demonstrated using several benchmark problems. The capability to treat multiple constraints shows the potential of the method. Furthermore, due to the consistency, the optimizer can run into local minima; a fundamental difficulty of level-set-based topology optimization. More advanced optimization strategies and more efficient optimizers may increase the performance in the future. Key Words: topology optimization; level-set method; consistency; sensitivity analysis, exact Heaviside; regularization