Review and comparison of thin and thick FGM plate theories using a unified buckling formulation

Abstract

The main objective of this paper is to study and compare different kinematics during numerical modeling of FGM plates buckling. These kinematics, which are Classical Plate Theory (CPT), First Order Shear Deformation Theory (FSDT), Third-order shear deformation Theory (TSDT), have been presented in a unified formulation. Mathematical model of FGM plates stability was established without using either the homogenization technique or the mixture rule nor the assumption of laminated composite but it was obtained by a dimensionless form. Finite element method was used to build the system corresponding to the buckling problem thus obtained, then critical buckling load determination comes down to an eigenvalue problem. Numerical results on examples of uniaxial and biaxial loading validated our numerical modeling by comparing analytical and numerical solutions. They illustrated the effectiveness of our modeling in predicting the critical buckling load for FGM plates. These results allowed also to carry out a parametric and a comparative studies of three kinematics and to discuss their similarities and differences.