A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method

TL;DR

This study investigates how internal defects like cracks and cutouts affect the buckling behavior of functionally graded material plates under mechanical and thermal loads, using an extended finite element method.

Contribution

It introduces a numerical approach combining the extended finite element method with the Mori-Tanaka scheme to analyze buckling of FG plates with internal discontinuities.

Findings

Critical buckling load decreases with larger cracks and cutouts.

Material gradient index reduction weakens buckling resistance.

Boundary conditions influence buckling behavior.

Abstract

In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction and the effective properties are estimated using the Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation theory. The influence of various parameters, viz., the crack length and its location, the cutout radius and its position, the plate aspect ratio and the plate thickness on the critical buckling load is studied. The effect of various boundary conditions is also studied. The numerical results obtained reveal that the critical buckling load decreases with increase in the crack length, the cutout radius and the material gradient index. This is attributed to the degradation in the stiffness either due to the presence of local defects or due to the change in the material composition.