Application of plate decomposition technique in nonlinear and post-buckling analysis of functionally graded plates containing crack

Abstract Nonlinear and post-buckling behaviors of internally cracked functionally graded plates subjected to uniaxial compressive loading have been presented in this paper. A general nonlinear mathematical model for cracked functionally graded plates has been developed based on the first order shear deformation theory within the framework of von-Karman nonlinearity. To approximate the primary variables, Legendre polynomials are used in the current research. The crack is modelled by decomposing the entire domain of the plate into several sub-plates and therefore, a plate decomposition technique is applied. In this study, the penalty technique is used to enforce interface continuity between the sub-plates. The integrals of the potential energy are numerically computed by Gauss-Lobatto quadrature formulas to get adequate accuracy. Finally, the obtained non-linear system of equations is solved by the well-known Newton-Raphson technique. Results are presented to show the influence of crack length, various locations of crack, crack direction, boundary conditions and volume fraction index in nonlinear behavior of functionally graded plates.