On nonlinear dynamic analysis of hyperbolic tangent FG-GPL-reinforced shallow spherical cap under supersonic flow

Abstract

Shallow spherical caps are commonly encountered in the design of spacecraft components, such as fuel tanks or structural elements. Understanding the dynamic behavior can contribute to the identification of potential failure modes. The modulus of elasticity of the augmented composite upper layer is obtained using the model Halpin–Tsai, and this layer is augmented with graphene platelets (GPLs). Also, GPLs’ volume fraction from the top layer is considered for different cases of GPLs. The bottom layer is assumed functionally graded (FG) with two kinds, type A: FG layers and homogeneous core, and type B: FG core and homogeneous layers. To approximate the displacement field, the new hyperbolic tangent shear deformation theory (HTSDT) has been used which is no need for shear modification coefficients. By adopting Hamilton’s principle, the equations of motion are obtained and are solved by the discrete differential quadrature method (DQM) as well as Newmark's time marching scheme by implementing the famous Newton–Raphson iterative technique. When the FG index is infinite, it is observed that the point of maximum displacement decreases by 12.5%, and critical load increases by about 23% compared to the case where it is zero.