Stability of multi-cracked FG plate on elastic foundations

Abstract

Recently, the stability calculation of the functionally graded (FG) plate has attracted many scientists, especially when considering the FG plate with many cracks. In this work, the plate is made from a new generation composite material consisting of two components, ceramic and metal, with the law of continuous exponential material distribution. The plate is placed on a Winkler - Pasternak elastic foundation with two background parameters. Then, we used the third-order shear deformation plate theory to establish the dynamical equations. After applying Phase-Field theory to simulate the crack state, we applied the finite element method to solve the equations to find the critical force causing instability of the plate. Next, we investigated the influence of material index, number of cracks, crack length, crack shape as well as elastic foundation parameters on the plate stability. The results show that the crack length and elastic foundation parameter have the great influence on the stability of the FG plate. Especially, the elastic foundation with large shear coefficient, creating high stability for the plate. That is very meaningful in exploiting and using plate structure when the cracks appear.