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An efficient self-filtering topology optimization method based on Free Element Method
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DOI：10.1016/j.enganabound.2025.106429.png)
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Abstract
En 中文
The Free Element Method (FrEM) combines the result stability of Finite Element Method (FEM) with the simplicity of system equation construction characteristic of meshless methods, demonstrating superior computational performance in solving solid mechanics and thermodynamic problems. This study proposes a highly efficient meshless topology optimization method by integrating FrEM with the Solid Isotropic Material with Penalization (SIMP) method. Owing to its foundation in the meshless collocation principle, the computational process eliminates the requirement for a background mesh. Within the proposed optimization method, nodal relative densities are taken as design variables, while a Shepard interpolation scheme facilitates the mapping from nodal density fields to integration point density fields. Through strategic arrangement of integration points, the algorithm achieves self-filtering functionality in topology optimization, effectively addressing the checkerboard patterns encountered in conventional methods and alleviates mesh dependency to some extent. Notably, the optimized results exhibit almost no gray-scale elements, enabling direct acquisition of clear structural boundaries without supplementary projection processing. The methodology's validity and applicability are confirmed through comparative analysis of FrEM-based and FEM-based optimization results of benchmark cases. Furthermore, the proposed algorithm's engineering practicality is demonstrated through its successful application to bicycle frame structural optimization, highlighting its potential for industrial implementation.
Keywords:
Free Element Method
meshless method
topology optimization
SIMP method
structural optimization
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5.8K
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