The Influence of Variable Thickness in Two Directions on the Stability of Cracked FG Plate on Pasternak Foundation

In this study, the effects of cracks and elastic foundation of functionally grade plate (FGP) with bidirectional thickness changes are studied. The crack is assumed to appear at the center or at the edge of the plate with its length and angle of inclination being variable. The plates are made of functionally grade material, whose properties change along the thickness of the plate. The plate with thickness varying linearly along two axes is placed on a two-parameter elastic foundation. High-order shear deformation theory and phase-field method are used to calculate the critical force of plate instability. To ensure the reliability of the calculation method, part of the article's results are compared with the results of some other reputable articles. The calculated plate instability coefficient depends on the following parameters: crack length and inclination angle; parameter of plate thickness change; ratio of component materials; two elastic foundation parameters; and the ratio of two sides of the plate. The results showed that crack length, linear thickness variation index along the axes, volume fraction index of material and elastic foundation stiffness have great influence on the stability of FGP.