<p>This paper is dedicated to the following objectives: with the precondition of circumventing sensitivity analysis, addressing the structural topology optimization problem that considers volume constraints and minimizes structural compliance, and obtaining a clear optimized structure with smooth boundaries. To achieve these objectives, this paper designs a novel floating projection filter and uses it to develop two enhanced proportional topology optimization (EPTO) methods, which are named EPTO_A and EPTO_B, respectively. Among these, the EPTO_A is proposed by modifying the proportional topology optimization (PTO) method using this novel floating projection filter, an improved material interpolation model, and a density filter. Although the EPTO_A can yield a clear optimized structure, this structure suffers from saw-tooth boundaries. To tackle this problem, a smooth operation is applied to modify density results from the EPTO_A, thereby proposing the EPTO_B. Subsequently, numerical examples and comparison methods are applied to evaluate these two new methods and the influence of the material interpolation model on the EPTO_A. The results show that the material interpolation model affects the EPTO_A’s convergence performance and ability to search for the optimal solution. Simultaneously, the EPTO_A exhibits a stronger searching ability for the optimal solution and possesses some other advantages, such as stable convergence performance, faster convergence speed, and a stronger ability to obtain a clear optimized structure. For the EPTO_B, its most outstanding advantage is that it can get a clear optimized structure with smooth boundaries. In addition, although the EPTO_B is not as good as the EPTO_A in the convergence speed and optimal solution searching ability, it can still showcase the characteristics of stable convergence performance and fast convergence speed.</p>

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Enhanced proportional topology optimization methods for the minimum compliance problem with volume constraints

  • Hui Wang,
  • Li Zhao,
  • Qihui Peng,
  • Yinqi Li,
  • Xiaojiang Shao,
  • Xiaodan Huo

摘要

This paper is dedicated to the following objectives: with the precondition of circumventing sensitivity analysis, addressing the structural topology optimization problem that considers volume constraints and minimizes structural compliance, and obtaining a clear optimized structure with smooth boundaries. To achieve these objectives, this paper designs a novel floating projection filter and uses it to develop two enhanced proportional topology optimization (EPTO) methods, which are named EPTO_A and EPTO_B, respectively. Among these, the EPTO_A is proposed by modifying the proportional topology optimization (PTO) method using this novel floating projection filter, an improved material interpolation model, and a density filter. Although the EPTO_A can yield a clear optimized structure, this structure suffers from saw-tooth boundaries. To tackle this problem, a smooth operation is applied to modify density results from the EPTO_A, thereby proposing the EPTO_B. Subsequently, numerical examples and comparison methods are applied to evaluate these two new methods and the influence of the material interpolation model on the EPTO_A. The results show that the material interpolation model affects the EPTO_A’s convergence performance and ability to search for the optimal solution. Simultaneously, the EPTO_A exhibits a stronger searching ability for the optimal solution and possesses some other advantages, such as stable convergence performance, faster convergence speed, and a stronger ability to obtain a clear optimized structure. For the EPTO_B, its most outstanding advantage is that it can get a clear optimized structure with smooth boundaries. In addition, although the EPTO_B is not as good as the EPTO_A in the convergence speed and optimal solution searching ability, it can still showcase the characteristics of stable convergence performance and fast convergence speed.