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Abstract Composite materials have complex structural forms at the microscopic scale, and their structural analysis and design require refined finite element mesh discretization, resulting in a large computational scale. As a common structural form of composites, the in-plane periodic structure can withstand arbitrary directional loads on the macroscopic scale, but it is difficult to characterize its performance and difficult to design and analyze. In this paper, an efficient topology optimization method for in-plane periodic structures is established based on the thick plate assumption and multi-resolution mesh strategy. Firstly, the rough mesh is used to decouple the macro and micro structures, solve the micro edge-value conditions, and carry out the equivalent characterization of the mechanical properties of the non-homogeneous single cell; secondly, the macroscopic edge-value conditions are solved based on the homogenized equivalent properties, and the fine mesh is used to update the design variables and map the density variables. On the one hand, the assumption of thick plate considering out-of-plane shear deformation makes the two-scale topology optimization design more in line with the actual load-bearing scenarios; on the other hand, the multi-resolution modeling strategy is utilized to avoid the problem of limited solvable problem size due to excessive finite element computation without sacrificing the resolution of the optimized configuration.
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Received: 28 November 2023
Published: 02 July 2024
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2024, Vol. 45 
