Nonlinear static and dynamic analyses of doubly curved sandwich shells with a porosity-dependent nanocomposite foam core

This research paper evaluates a nonlinear computation for the static and dynamic analyses of doubly curved sandwich shells made of a porosity-dependent nanocomposite foam core integrated with titanium layers. It is assumed that the geometry of sandwich shell is developed from a rectangular planform so that its main curvatures are set equal to constant. The core of the sandwich shell is also originated from six layers of a metal-based composite (aluminum) strengthened by graphene nanoplatelets (GNPs) considering porosity effects. Five different porosity orientation profiles as the uniform and random patterns are considered for the shell’s core. The modified Sanders shell theory, the first-order shear deformation model, and the von-Karman type of nonlinear assumptions are implemented to extract the kinematic equations of the doubly-curved sandwich shell. The time-dependent equations of motion are determined as a nonlinear system of partial differential equations using the principle of Hamilton. The static deflection and dynamic response of the shell are derived using a semi-analytical type of solution methods combined with a numerical technique. After validation of the presented formulation and computation, the impacts of geometrical parameters, material properties, and porosity value are explored in order to obtain the static/dynamic response of the doubly-curved sandwich shells.