Buckling analysis of three-dimensional functionally graded sandwich plates using two-dimensional scaled boundary finite element method

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.

Keywords:

• Functionally graded material
• layerwise theory
• sandwich plate
• scaled boundary finite element method
• stability analysis

Acknowledgement

This research was supported by Grant 51779033 from the National Natural Science Foundation of China for which the authors are grateful.