Static Buckling of a Pre-loaded Complex Nano-composite Shell

This paper describes a technique for analyzing the phenomenon of static buckling of a pre-loaded complex nano-composite shell. Most of the works devoted to the analysis of complex structures consider vibration processes, while the phenomenon of buckling can be an important factor that limits the use of new materials in space-rocket hardware. A nano-composite constant-thickness shell consisting of two spherical covers and a cylindrical body is considered. It is acted upon by internal pressure and an axial compressive force. This shell simulates the fuel tank of a launch vehicle. Conditions under which the shell is deformed non-axisymmetrically, buckling statically, are investigated. A technique is proposed that allows the problem to be divided into the analysis of the pre-loaded state of the shell and the analysis of buckling. Further analysis is performed using a technique based on the high-order shear deformation theory and the Ritz method. The problem is discretized by representing the variables that determine the state of the shell in the form of expansions in basis functions with unknown coefficients. Thus, it is the expansion coefficients that become unknown in the problem. Th