| Summary: | The rapid development of material science is increasing the demand for the multiscale design of materials. The concurrent multiscale topology optimization based on the Direct FE<sup>2</sup> method can greatly improve computational efficiency, but it may lead to the checkerboard problem. In order to solve the checkerboard problem and reconstruct the results of the Direct FE<sup>2</sup> model, this paper proposes a filtering-based reconstruction method. This solution is of great significance for the practical application of multiscale topology optimization, as it not only solves the checkerboard problem but also provides the optimized full model based on interpolation. The filtering method effectively eliminates the checkerboard pattern in the results by smoothing the element densities. The reconstruction method restores the smoothness of the optimized structure by interpolating between the filtered densities. This method is highly effective in solving the checkerboard problem, as demonstrated in our numerical examples. The results show that the proposed algorithm produces feasible and stable results.
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