The effect of cracks on the stability of the functionally graded plates with variable-thickness using HSDT and phase-field theory

In this paper, the stability in a rectangular functionally grade material (FGM) plate with central crack is studied. The plate thickness is changed exponentially following the length of the plate. The properties of the FGM plate are assumed to vary along the thickness direction according to a simple power law distribution. Based on the phase-field theory, the new third order shear deformation plate theory (TSDT) and the finite element method (FEM), the stability of cracked FGM plate is determined. The obtained numerical results are compared with the published articles to ensure credibility. The work also considered effects of changing of the plate thickness ratio, length, crack angle and volume fraction exponent of the functionally graded material on the stability of the plate. Lastly, some visual images of the mechanical instability forms of cracked FGM plates will be introduced.