Nonlinear dynamic responses of functionally graded graphene platelet reinforced composite spherical caps subjected to impulse loads

Abstract

This paper investigates the nonlinear dynamic behavior of functionally graded graphene platelet reinforced composite (FG-GPLRC) shallow axisymmetric spherical caps resting on a nonlinear viscoelastic Pasternak foundation and subjected to transient mechanical loading. The caps are exposed to a thermal environment, yet the mechanical properties of the material are considered temperature-independent. The theoretical framework is established based on higher-order shear deformation theory (HSDT) integrated with von Karman geometric nonlinearity. The governing equations of motion are derived using the Lagrangian approach, incorporating damping effects through the Rayleigh dissipation function. A semi-analytical solution is obtained by combining the Ritz method for spatial discretization and the Runge-Kutta method for time integration. Two forms of impulsive pressure, infinite duration step load and blast load, are examined to evaluate transient responses. Parametric studies are conducted to explore the effects of graphene distribution patterns, mass fraction, geometric parameters, thermal pre-deflection, foundation stiffness, and damping coefficients on the nonlinear response.