Buckling analysis of functionally graded materials by dynamic approach

Abstract

Laminated composites exhibit difference in the mechanical properties at the interface between two materials resulting in stress concentration. This may lead to damages in the form of delamination, matrix cracking and adhesive bond separation. Functionally Graded Materials (FGM) are formed by gradual variation of two or more material over a particular volume, thereby overcomes these issues. Buckling problems of FGM plates are usually solved by static approach. In some cases, particularly non-uniform loading and geometric discontinuity, the stress concentration usually occurs. In such cases, the solution to the buckling problem by dynamic approach is most suitable. In the dynamic approach, the natural frequencies are calculated by applying in-plane loads. As the intensity of the in-plane load increases, the frequency of the material decreases and finally becomes zero at the onset of buckling. The load at which the natural frequency becomes zero that load is called a buckling load. In this investigation, the vibration and buckling characteristics of FGM panels subjected to uniaxial and biaxial loading conditions have been studied by using the finite element method (F.E.M). In the Finite element (FE) formulation, the effective material properties of FGM plates are assumed to vary in the thickness direction according to the power-law distribution of volume fraction of the constituents. The plate is modelled by using 8-noded serendipity element by incorporating the effect of transverse shear deformation and rotary inertia. The effect of different parameters such as volume fraction index (n), the thickness of the panel (h) and boundary condition of the plate are considered to study the buckling behaviour of the FGM plate under uniaxial loading conditions.