Nonlinear axisymmetric dynamic buckling of functionally graded graphene reinforced porous nanocomposite spherical caps

Here, the axisymmetric dynamic snap-through buckling of graphene platelets (GPLs) reinforced porous nanocomposite spherical caps subjected to a suddenly applied external pressure load is focused using finite element approach and adopting shear deformation theory. Different types of porosity distributions and dispersion patterns of GPLs in the matrix of nanocomposite shell are treated in the thickness direction of shell. The effective material properties of porous nanocomposite with graphene reinforcement are determined introducing Halpin-Tsai micromechanics model and the rule of mixture. A three-noded axisymmetric field consistent shell element is proposed to solve the governing equations developed from Lagrange’s equation of motion. The geometric nonlinearity is accounted for following von-Karman’s strain displacement relationship. The critical buckling pressure is evaluated based on dynamic response analysis obtained using Newmark’s integration technique coupled with the modified Newton-Raphson iteration scheme. For validating the formulation and solution technique, the results are compared with the available solutions in literature for the cases of isotropic and nanocomposite shells wherever possible. A comprehensive parametric study is performed to understand the effect of weight fraction of GPLs, distribution pattern of porosity and GPL, GPL geometry, shell geometry parameter and boundary conditions on the dynamic buckling of spherical caps.