We present an adaptation of the multiscale finite element method to the analysis of sandwich beams and plates with complex lattice layers. The proposed modification significantly reduces the number of degrees of freedom (even by four orders) due to the anisotropic higher-order coarse-scale approximation and the novel shape functions that take into account the microscale boundary conditions. Moreover, the local iterative corrector scheme Nguyen and Schillinger (2019) adapted for the bending-dominated responses of sandwich structures provides converges of the coarse mesh approximation to the best possible fine-mesh solution. Several numerical examples are presented to demonstrate the capabilities of the method. We found that the proposed modifications of the shape functions and the higher-order coarse mesh approximation increase the convergence rate. Finally, we validated the proposed model by comparison of the numerical results with experimental ones for a sandwich panel with a dual corrugated high-density fiberboard core. Very good consistency of both results was observed.

中文翻译：

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夹层梁板的迭代多尺度有限元法

我们提出了多尺度有限元方法对具有复杂晶格层的夹层梁和板的分析的适应性。由于各向异性的高阶粗尺度近似和考虑到微尺度边界条件的新颖形状函数，所提出的修改显着减少了自由度的数量（甚至减少了四阶）。此外，适用于夹层结构的弯曲主导响应的局部迭代校正器方案 Nguyen 和 Schillinger (2019) 将粗网格近似收敛到可能的最佳细网格解。给出了几个数值例子来证明该方法的能力。我们发现对形状函数和高阶粗网格近似的建议修改提高了收敛速度。最后，我们通过比较具有双波纹高密度纤维板芯的夹芯板的数值结果与实验结果来验证所提出的模型。观察到两个结果的一致性非常好。