Stability of Plates and Shells

The stability problems of shell structures are covered in this chapter. The attention is focused on two different forms of stability loss, which are buckling and snap-through phenomena. The analytical and numerical results of the linear buckling analysis are presented for rectangular membranes under unidirectional compression, uniform shear or in-plane bending, circular plate under radial compression, and cylindrical, barrel and hyperboloidal shells under axial compression or external pressure. For each considered case, the values of critical load parameters and buckling modes are determined as a solution of the eigenvalue problem. A detailed discussion of the numerical simulation of the loading process associated with an instability of a shallow cylindrical shell and a rectangular membrane, both under unidirectional compression, is given. Shell sensitivity to imperfections is also discussed. The chapter ends with the presentation of a nonlinear finite element method (FEM) analysis of a shallow cylindrical shell loaded with a normal concentrated force. The calculation methodology involving an incremental-iterative (step-by-step) algorithm for tracing a nonlinear equilibrium path in the load-displacement space is summarized. The diagrams obtained under load, displacement and arc-length control are shown.