AI 中文总结
本文提出一种针对三维抗剪变形梁的FE2多尺度框架，通过约束方程消除RVE刚体位移并确保均匀化结果与RVE长度无关，引入局部修正系数减轻边界效应，数值验证表明其与参考模型高度一致。
AI 中文摘要
增材制造技术的进步促进了晶格状结构在承重构件中的日益广泛应用，这要求采用高效的多尺度方法进行结构分析。对于细长的晶格状结构，梁模型在宏观尺度上提供了计算高效的表示，同时通过均匀化方法保留了考虑底层晶格结构的能力。尽管已经建立了在宏观尺度上结合梁模型与微观尺度上连续介质模型的有限元平方（FE2）方法，但尚未有报道将基于梁的宏观模型与基于桁架的晶格结构微观模型相结合的FE2框架。为填补这一空白，本文开发了一种适用于具有周期性重复晶格状细观结构和周期性位移边界条件的三维抗剪变形梁的FE2框架。所提出的FE2框架引入了约束方程，这些方程（a）在不施加额外运动学限制的情况下防止代表性体积单元（RVE）的刚体平移和旋转，并且（b）确保均匀化的应力合力和材料矩阵与所选RVE长度无关。为减轻晶格状RVE边界处产生的人为边界效应，引入了局部修正系数。通过对具有不同几何形状的二维和三维晶格状结构进行数值研究，并考虑几何和材料的线性和非线性，对该框架进行了评估。结果表明，均匀化的应力合力和材料矩阵与所选RVE长度无关，并且在所有研究案例中与相应的参考模型表现出良好的一致性。
英文摘要
The increasing use of lattice-like architectures in load-bearing members, facilitated by advances in additive manufacturing, calls for efficient multiscale approaches to their structural analysis. For slender lattice-like structures, beam models provide a computationally efficient macroscopic representation while retaining the ability to account for the underlying lattice architecture through an homogenization approach. Although finite element squared (FE2) approaches combining beam models at the macroscopic scale with continuum models at the microscopic scale have been established, an FE2 framework combining a beam-based macroscopic model with a truss-based microscopic model of a lattice structure has not yet been reported. To address this gap, an FE2 framework is developed for three-dimensional shear-deformable beams with periodically repeated lattice-like microstructures and periodic displacement boundary conditions. The proposed FE2 framework introduces constraint equations that (a) prevent rigid-body translations and rotations of the representative volume element (RVE) without imposing additional kinematic restrictions and (b) ensure that the homogenized stress resultants and material matrix are independent of the selected RVE length. To mitigate artificial boundary effects arising at the boundaries of the lattice-like RVE, local correction factors are introduced. The framework is assessed through numerical studies of two- and three-dimensional lattice-like structures with different geometries, considering both geometric and material linearity and nonlinearity. The results demonstrate the independence of the homogenized stress resultants and material matrix from the selected RVE length and show good agreement with the corresponding reference models in all investigated cases.
Comments37 pages, 21 figures, 10 tables, 66 references
