A phased strategy for structural optimization: Enhanced proportional topology optimization and post-processing of results by level set method

In this study, we proposed an enhanced proportional topology optimization (EPTO) method by improving the traditional proportional topology optimization (PTO) algorithm. Specifically, a density filtering weight function based on an improved Heaviside threshold function, tanh weight function, is proposed to update variables and improve the density distribution formula in the inner loop. Moreover, uniformly distributed loads are used instead of concentrated loads to improve stress concentration and local grid dependence issues. These improvements have significantly improved the optimization efficiency and result of the EPTO method. The improved density distribution formula in the inner loop effectively eliminates holes and redundant branches, at the cost of only slightly sacrificing some mechanical properties. Furthermore, the results obtained by the EPTO method are post-processed using the Level Set Method (LSM). This method is an innovative post-processing technology for topology optimization based on level set boundary extraction and volume-preserving bisection, which can yield optimized structures that are clear, smooth, and directly applicable to engineering simulations. The numerical example results show that the post-processed topological configuration completely eliminates the gray transition zone while maintaining all original performance characteristics. This demonstrates that the phased strategy proposed in this article successfully integrates the high efficiency of the density method and the boundary accuracy of the level set method. This technology provides a powerful tool for the smooth transition of topology optimization results to engineering applications and has broad application prospects in fields such as aerospace and automotive light-weighting.