Improved Strategy Based on the Variable Density Method for Continuum Structural Topology Optimization

ObjectiveTo address the numerical instability and insufficient optimization performance of the variable density method in continuum structural topology optimization, an improved strategy based on a modified interpolation model and a grayscale suppression operator was proposed to obtain ideal optimized structures with clear boundaries and fully discrete configurations.MethodsFirstly, an exponential improved interpolation model was constructed to overcome the limitations of the solid isotropic material with penalization model and the rational approximation material properties model in penalty efficiency and convergence speed, thereby enhancing the driving force for element densities to polarize toward 0 or 1 and providing support for subsequent optimization solving. Secondly, the Sigmund sensitivity filtering method was employed to eliminate checkerboard patterns and mesh dependency, ensuring the numerical stability of the optimized structures. Finally, a grayscale suppression operator was designed and integrated into the optimality criterion method to accelerate the transformation of grayscale elements toward solid or void states.ResultsThe results show that the proposed strategy achieves significant improvements in cantilever beam, double‑load cantilever beam, and L‑shaped beam examples under various load and constraint conditions. Compared with the control method, the iteration counts are reduced by 13, 5, and 82, respectively, while the structural compliances are decreased by 1.874, 2.943, and 16.948. Both the discreteness measure and the grayscale ratio are reduced to 0, yielding fully discrete, boundary‑clear optimized structures devoid of grayscale elements, which verifies the superiority of the proposed strategy in convergence speed and solution quality.