Effect of Cutout and Initial Geometrical Imperfection on Nonlinear Transient Response of Functionally Graded Material Folded Plate

This work presents the nonlinear transient response of imperfect functionally graded material (FGM) folded plates having square and circular cutouts. The top and the bottom layers of the imperfect FGM folded plate is made of pure ceramic and pure metal, respectively and the effective elastic property at any point along the thickness is estimated according to the rule of mixture. First-order shear deformation theory in conjunction with eight-noded isoparametric element and five degrees of freedom per node along with von Karman type nonlinearity is used in the development of the finite element method (FEM) based formulation. A global type imperfection (G1) is modelled using an imperfection function. The governing differential equation is obtained using total Lagrangian formulation. Further, the Newmark average acceleration method in conjunction with modified Newton–Raphson is used to obtain the nonlinear transient response of the functionally graded material folded plate. The results obtained from the present finite element formulation are first compared for a wide range of parameters to establish the correctness of the present finite element formulation. The parametric study is carried out to investigate the effect of cutout size, cutout shape, amplitude of geometric imperfection, crank angle and boundary condition on the nonlinear transient response of an imperfect functionally graded material folded plate having cutout.