Chapter 10 - Buckling of General Shell Elements

Abstract

Shell theories are based on the assumption that the strains in the shell are small enough to be discarded in comparison with unity. It is also assumed that the shell is thin enough that quantities, such as the thickness/radius ratio may be discarded in comparison with unity. This chapter explains the buckling of general shell elements with non linear equilibrium equations. In shell theory, a special type of curvilinear coordinate system is usually employed. The middle surface of the shell is defined by X = X(x,y),Y = Y (x,y), and Z = Z(x,y), where X,Y,Z are rectangular coordinates and x, y are surface coordinates. The normal distance from the middle surface in the thickness direction is denoted by ± z. In addition, structural shells often take the shapes of shells of revolution. The middle surface of a shell of revolution is formed by rotating a plane curve with respect to an axis in the plane of the curve.