Static and dynamic postbuckling analysis of imperfect SSFG cylindrical shells surrounded by nonlinear elastic foundation subjected to an axial compression

Abstract

In this article, the semianalytical method based on the Galerkin technique and fourth-order Runge-Kutta method is utilized to investigate the static and dynamic postbuckling analysis of internal/external spiral stiffened functionally graded (ISSFG/ESSFG) cylindrical shells, respectively. The simply supported SSFG shell subjected to an axial compression is resting on a nonlinear elastic foundation (EF) which is including the Pasternak and Winkler foundation parameters augmented by a softening/hardening cubic nonlinearity. The material constitutes of both the stiffeners and the shells that are continuously changed along the thickness. The discretized motion equation is extracted utilizing the Galerkin method regarding to the Donnel’s shells theory and nonlinear strain-displacement von Kármán. To obtain the responses of dynamic postbuckling (DPB) analysis, the fourth-order Runge-Kutta method is utilized. To validate the results, comparisons are made with the available solutions for both static postbuckling (SPB) and DPB analysis of stiffened homogeneous and functionally graded cylindrical shells. The influences of various material and geometrical parameters with the inclusion of the supporting nonlinear EF on the SPB and DPB behavior of imperfect ISSFG/ESSFG cylindrical shells are presented. As one of the most interesting results, for the ISSFG cylindrical shells with the stiffeners angle $\theta =\beta ={60}^{°}$ and ESSFG cylindrical shells with the stiffeners angle $\theta ={30}^{°},\mathrm{ }\beta ={60}^{°},$ the buckling load-bearing capacity is the most.

Keywords:

• Dynamic postbuckling
• functionally graded materials
• geometric imperfections
• nonlinear elastic foundation
• spiral stiffened cylindrical shells
• static postbuckling