标题： 基于单元尺寸和最小Jacobi的三重周期极小曲面结构改进的有限元建模方法 显示英文标题

标题： An Improved Finite Element Modeling Method for Triply Periodic Minimal Surface Structures Based on Element Size and Minimum Jacobian

摘要： 三重周期极小曲面（TPMS）结构是一种晶格结构，因其轻量化、可控性以及卓越的力学性能而备受关注。 基于体素的建模是通过有限元模拟研究此类晶格结构力学行为的常用方法。 本研究提出了一种双参数体素法，结合了单元尺寸和最小雅可比（MJ）的联合控制。 数值结果表明，当 MJ 达到 0.3 时，模拟结果趋于稳定。 基于理查森外推法的网格收敛指数（GCI）被引入，用于系统地评估体素模型和所提出的双参数体素模型的数值收敛行为。 这为评估 TPMS 建模中的离散化误差和网格收敛提供了系统的客观框架。 与传统体素法相比，所提出的方法表现出更好的网格收敛性、解的准确性和计算效率。 此外，双参数体素法在分析渐变 TPMS 结构时也显示出优异的适用性，其收敛行为甚至优于均匀结构。 显示英文摘要

摘要： Triply periodic minimal surface (TPMS) structures, a type of lattice structure, have garnered significant attention due to their lightweight nature, controllability, and excellent mechanical properties. Voxel-based modeling is a widely used method for investigating the mechanical behavior of such lattice structures through finite element simulations. This study proposes a two-parameter voxel method that incorporates joint control of element size and minimum Jacobian (MJ). Numerical results indicate that the simulation outcomes tend to stabilize when the MJ reaches 0.3. The grid convergence index (GCI), based on Richardson extrapolation, is introduced to systematically assess the numerical convergence behavior of both voxel models and the proposed two-parameter voxel models. This provides a systematic and objective framework for evaluating discretization errors and mesh convergence in TPMS modeling. Compared with traditional voxel method, the proposed method exhibits superior mesh convergence, solution accuracy, and computational efficiency. Furthermore, the two-parameter voxel method also shows excellent applicability in the analysis of graded TPMS structures, exhibiting even better convergence behavior than in uniform structures.