For the multi-material topology optimization problems which take structural minimum compliance as the object, based on the weight function and optimality criteria, an improvement to the original alternating active-phase algorithm is achieved in establishing and calculating the mathematical model of multi-material topology optimization problems. Simulations of numerical examples are implemented respectively by the improved alternating active-phase algorithm and the original algorithm. It can be found that the minimum compliance obtained by the improved algorithm is generally lower than that obtained by the original algorithm in each numerical example, whereupon the feasibility and efficiency of the improved algorithm are manifested.
We discover that the given initial structural density value has significant influence on the final result of multi-material topology optimization when adopting the SIMP interpolation scheme. The influence cannot be ignored if the grid is sparse, and there is a certain degree of periodic relationship between the structural minimum compliance and the given initial density value. By modifying the initial structural density value, a better topology optimization result with a smaller compliance can be obtained. The expression is proposed on how to modify the initial structural density value to get better results in multi-material topology optimization problems.
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