Nonlinear dynamic response of functionally graded half-cylinder sandwich shells with elastic boundary conditions subjected to explosive loading

Abstract

This study investigates the nonlinear dynamic of functionally graded half-cylinder sandwich (FGhCS) shells with elastic boundary conditions (EBCs) subjected to explosive loading (EL). The main goal is to establish an efficient finite element framework that can accurately capture the coupled mechanical responses arising from geometric and material nonlinearities. The sandwich shell consists of a ceramic core sandwiched between two functionally graded material (FGM) face sheets, whose effective properties vary continuously through the thickness according to a power-law distribution. Nonlinear geometric effects, including mid-plane stretching and large-amplitude deformation, are incorporated through the von Kármán-type nonlinear strain–displacement relations. The governing equations of motion are systematically derived from Hamilton’s principle within a novel first-order shear deformation theory (n-FSDT), which enhances both accuracy and computational efficiency compared with conventional FSDT formulations. The proposed finite element formulation is thoroughly validated against available benchmark results, demonstrating excellent agreement and significant reduction in computational cost. A detailed parametric study is then conducted to examine the influence of geometric parameters, power-law index, and boundary stiffness on the nonlinear dynamic response of FGhCS shells. The results reveal that material gradation and elastic boundary stiffness play critical roles in mitigating the adverse effects of explosive loads, offering practical insights for the optimal design and manufacturing of FGhCS shells under extreme dynamic environments.