Semi-analytical approach for nonlinear dynamic responses of complex curved functionally graded graphene metal matrix reinforced panels subjected to impulse loads

Abstract

This study develops a semi-analytical framework to investigate the nonlinear dynamic behavior of functionally graded graphene-reinforced metal matrix composite (FG-GRMMC) shallow panels with complex curvatures under thermal environments. Three panel geometries, cylindrical, parabolic, and sinusoid, are examined under impulsive loading conditions, including finite duration step and triangular blast loads. The analysis is formulated within the higher-order shear deformation theory (HSDT), incorporating von Kármán geometric nonlinearities. To address the geometric complexity, the stress function is approximated using an average-based like-Galerkin technique that satisfies the compatibility condition. The nonlinear governing equations of motion are derived via the Lagrange principle, with structural damping modeled through the Rayleigh dissipation function. Numerical simulations employing the fourth-order Runge-Kutta method are conducted to capture the time-dependent deflection responses. The results provide insights into the influence of panel geometry, graphene distribution, and impulse load characteristics on the nonlinear dynamic performance of FG-GRMMC panels.