The Solid Isotropic Microstructure with Penalization (SIMP) model, a material interpolation model in the variable density method, has been widely applied in structural topology optimization. When combining the Sigmund sensitivity filtering method with the Optimality Criterion (OC) method for solving the SIMP model, numerical instabilities and relatively low optimization performance are often observed. To address these challenges, an improved scheme based on the variable density method is proposed. Firstly, an improved material interpolation model is proposed to overcome the deficiencies of the SIMP model in terms of penalty efficiency and convergence speed. Secondly, an improved sensitivity filtering method based on the Gaussian weight function is proposed, which not only successfully suppresses checkerboards and mesh-dependence but also contributes to a superior filtering effect. Furthermore, a new gray-scale suppression operator is designed to develop a function that suppresses gray-scale elements. This function is subsequently integrated into the iterative formula of the OC method, forming the improved OC method, which is capable of completely eliminating gray-scale elements. Finally, the feasibility and effectiveness of the improved scheme are verified through several typical numerical examples.
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