To establish a universal and convenient mathematical model for predicting static and dynamic performance of composite sandwich structures, a novel three-dimensional equivalent homogenized model (3D-EHM) is proposed based on variational asymptotic method. The multiscale mechanical analysis of composite hexagonal and re-entrant honeycomb sandwich structures is conducted by 3D-EHM, enabling reasonable transmission of mechanical information at different scales and facilitating accurate predictions of mechanical responses in sandwich structures. The comparison analysis with 3D printing experimental results and 3D finite element model results demonstrates that the 3D-EHM exhibits remarkable precision and computational efficiency in forecasting static displacement distributions and higher-order vibration modes, eliminating the need for time-consuming and expensive experiments. Moreover, the effects of the ply angle of the face sheet and core geometric parameters on the effective properties of composite hexagonal honeycomb sandwich structures are systematically investigated. In summary, 3D-EHM is an effective applied mathematical model for designing and analyzing composite sandwich structures, fully combining the systematicity of variational methods and the asymptotic convergence of asymptotic methods.

中文翻译：

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一种基于变分渐近法的新型多尺度建模策略，用于预测复合材料夹层结构的静态和动态性能


为了建立通用且方便的数学模型来预测复合材料夹层结构的静态和动态性能，提出了一种基于变分渐近法的三维等效均匀化模型（3D-EHM）。利用3D-EHM对复合材料六边形和凹角蜂窝夹层结构进行多尺度力学分析，能够合理传递不同尺度的力学信息，有利于准确预测夹层结构的力学响应。 3D打印实验结果与3D有限元模型结果的对比分析表明，3D-EHM在预测静态位移分布和高阶振动模式方面表现出卓越的精度和计算效率，无需进行耗时且昂贵的实验。此外，系统研究了面板铺层角度和芯材几何参数对复合材料六边形蜂窝夹层结构有效性能的影响。综上所述，3D-EHM是一种设计和分析复合材料夹层结构的有效应用数学模型，充分结合了变分方法的系统性和渐近方法的渐近收敛性。