Abstract

For the stability analysis of functionally graded material (FGM) sandwich plates, a semi-analytical scaled boundary finite element method (SBFEM) is established within the frame work of layerwise theory in this paper. Two different configurations of FGM sandwich plates are studied, one of which consists of ceramic-rich core and FGM face sheets, and another involves metal-rich and ceramic-rich material face sheets as well as a FGM core, and the modulus of elasticity for each FGM layer is assumed to be changed continuously along thickness according to a power-law distribution. The layerwise theory performed in present work is based on the three-dimensional theory of elasticity for each individual layer satisfying the displacement continuity boundary conditions at layer interfaces, and the two-dimensional high order spectral element with three degrees of freedom per node is employed to discrete the reference surface of each individual layer. And then, based on the principle of virtual work, the SBFEM governing equation for each individual layer of FGM sandwich plates is derived, and a dual variable including the displacement and internal nodal force is used to reduce the governing equations to a system of first-order ordinary differential equation, which is solved analytically by a general approach. Finally, the critical buckling load can be obtained by solving the eigenvalue equation once the bending stiffness matrix and geometric stiffness matrix of FGM sandwich plates are determined. Fast rate of convergence of the proposed formulations is confirmed and comparison studies are presented to construct its high accuracy and excellent predictive capability. Furthermore, effects of gradient index, side-to-thickness ratio, layer configuration, and boundary conditions on dimensionless critical buckling loads of FGM sandwich plates are also studied. The proposed semi-analytical approach is simple in program implementation, accurate and computationally efficient.

摘要

针对功能梯度材料（FGM）夹层板的稳定性分析，本文在分层理论框架下建立了半解析尺度边界有限元法（SBFEM）。研究了两种不同的 FGM 夹层板配置，其中一种由富含陶瓷的芯和 FGM 面板组成，另一种涉及富含金属和富含陶瓷的材料面板以及 FGM 芯，弹性模量为假设每个 FGM 层根据幂律分布沿厚度连续变化。目前工作中执行的分层理论基于满足层界面处位移连续性边界条件的每个单独层的弹性三维理论，并且采用每个节点具有三个自由度的二维高阶谱元来离散每个单独层的参考表面。然后，基于虚功原理，推导出FGM夹层板各层的SBFEM控制方程，并利用位移和节点内力的对偶变量将控制方程简化为一阶-阶常微分方程，通过一般方法解析求解。最后，一旦确定了 FGM 夹层板的弯曲刚度矩阵和几何刚度矩阵，就可以通过求解特征值方程获得临界屈曲载荷。所提出的公式的快速收敛速度得到证实，并提出了比较研究以构建其高精度和出色的预测能力。此外，还研究了梯度指数、侧厚比、层配置和边界条件对 FGM 夹层板无量纲临界屈曲载荷的影响。所提出的半解析方法在程序实现中简单、准确且计算效率高。