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The solid isotropic microstructure with penalization (SIMP) model is widely used in structural topology optimization. When the optimality criterion (OC) method is used for solving the SIMP model, the optimization solution process not only has relatively low computational efficiency, but also causes a large number of grey-scale elements in the obtained structure. To enhance the computational efficiency, an advance and retreat golden searching scheme is proposed to update the Lagrange multiplier, thereby improving the OC method for solving the SIMP model. To eliminate the grey-scale elements and also to enhance the computational efficiency, the improved OC method combined with the tanh-based density filtering is proposed for solving the SIMP model of structural topology optimization. Furthermore, the improved OC method combined with the sigmoid-based Heaviside density filtering is proposed for solving the SIMP model of multi-material structural topology optimization to eliminate the grey-scale elements and to enhance the computational efficiency.

An improved optimality criterion combined with density filtering method for structural topology optimization