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Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element

机译：使用富集的三阶剪切变形梁元件自由振动和双向功能梯度夹层梁的振动和屈曲

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摘要

This paper formulates an efficient third-order shear deformation beam element for free vibration and buckling analysis of bidirectional functionally graded sandwich (BFGSW) beams. The beams consist of three layers, an axially functionally graded core and two face sheets with material properties varying in both the thickness and length directions by power-law distributions. The element is derived in this paper for the first time by using hierarchical functions to enrich the Lagrange and Hermite interpolations of a conventional beam element, and this enrichment results in a super convergent beam element. Using the formulated beam element, natural frequencies and buckling loads are evaluated for the beams with various boundary conditions. The effects of the material distribution and the layer thickness on the vibration and buckling characteristics are examined in detail and highlighted. The influence of the micromechanical models, namely the Voigt model and Mori-Tanaka scheme used in estimating the effective material properties, on the vibration frequencies and buckling loads of the beams is also examined and discussed.
机译：本文制定了一种有效的三阶剪切变形梁元件，用于双向振动和屈曲分析双向功能梯度夹层（BFGSW）梁。梁由三层，轴向功能梯度的芯和两个面板，其具有在厚度和长度方向上变化的材料特性，通过电力法分布。在本文中首次使用分层功能来推导本文中的元素，以丰富传统光束元件的拉格朗日和Hermite插值，并且该富集导致超级收敛梁元件。使用配制的光束元件，对具有各种边界条件的光束评估固有频率和屈曲负载。材料分布的效果和层厚度对振动和屈曲特性进行了详细，并突出显示。还研究了微机械模型的影响，即用于估计有效材料特性的voigt模型和森塔纳卡方案，对梁的振动频率和屈曲负荷进行讨论。

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