This contribution proposes a multiscale scheme for structural elements considering beam kinematics. The scheme is based on a first-order homogenization approach fulfilling the Hill–Mandel condition. Within this paper, special focus is given to the transverse shear stiffness. Using basic boundary conditions, the transverse shear stiffness drastically depends on the size of the representative volume element (RVE). The reason for this size dependency is identified. As a consequence, additional internal constraints are proposed. With these new constraints, the homogenization scheme leads to cross-sectional values independent of the size of the RVE. As they are based on the beam assumptions, a homogeneous material distribution in the length direction yields optimal results. Furthermore, outcomes of the scheme are verified with simple linear elastic benchmark tests as well as nonlinear computations involving plasticity and cross-sectional deformations.

中文翻译：

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结构元素耦合多​​尺度分析的均匀化假设：梁运动学

该贡献提出了考虑梁运动学的结构元素的多尺度方案。该方案基于满足 Hill-Mandel 条件的一阶均质化方法。在本文中，特别关注横向剪切刚度。使用基本边界条件，横向剪切刚度极大地取决于代表性体积单元 (RVE) 的大小。确定了这种大小依赖性的原因。因此，提出了额外的内部约束。有了这些新的约束，均质化方案导致横截面值与 RVE 的大小无关。由于它们基于梁假设，因此长度方向上的均匀材料分布会产生最佳结果。此外，