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Abstract In this paper, the filter function in ICM method and the penalty function in variable density method are both referred as the mapping function. The problem of how to select the mapping function is studied; and the influence of different mapping functions on the convergence efficiency of structural topology optimization is discussed. Therefore, an approach is proposed to construct a mapping function to achieve high-efficient convergence. Five common forms of mapping functions are given. An optimization model and optimization method matching MFHEC (Mapping function with highly efficient convergence) are proposed. Firstly, the convergence speed of the filter function and quasi-filter function of the same form of mapping functions is compared. Then the convergence speed of the fast filter function of different forms of mapping functions is compared. Taking the structural topology optimization problem minimizing structural volume under displacement constraints as an example, the ICM method is adopted to solve the problem. Through numerical comparison, the efficient convergence of MFHEC function is verified.The results show that the fast filter function has faster convergence rate than other functions in the same form functions. Compared with five different forms of mapping functions, the filter function of power function form converges fastest. Finally, it should be emphasized that the conclusions of the mapping function studied in this paper are equally applicable for the filter function of ICM method and the penalty function of variable density method.
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Received: 29 May 2023
Published: 11 April 2024
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2024, Vol. 45 
