Nonlinear transient response of doubly curved shallow shells reinforced with graphene nanoplatelets subjected to blast loads considering thermal effects

Abstract

The nonlinear transient dynamic response of graphene nanoplatelets (GPLs) reinforced composite doubly curved shallow shells with three GPL distribution patterns was investigated under time-dependent blast loads. The thermal effects were explicitly considered in the study, in which a modified Halpin–Tsai model was adopted to estimate the effective Young’s modulus. Rule of mixtures was employed to determine the mass density and Poisson's ratio. The equations of motion were derived from Hamilton's principle and the nonlinear von Karman strain–displacement relationship, based on a higher-order shear deformation theory. A set of second-order ordinary differential equations was obtained using Galerkin’s method. Numerical solutions were based on a fully implicit finite difference scheme in time. The derived nonlinear equations were then solved using the Newton–Raphson method. Further, parametric studies were conducted to consider the influence of the temperature difference between top and bottom surfaces, as well as the GPL weight fraction, distribution type, length-to-thickness ratio, total number of layers, parameters related to blast loading, and the aspect, shallowness, and curvature radius ratios of the doubly curved shallow shell on the nonlinear transient dynamic response of the structure.