Elastic Buckling of Thin Flat Plates

Abstract

In the preceding chapters, elastic buckling of structures composed of one-dimensional members has been discussed wherein deflections and bending moments are assumed to be the functions of a single independent variable. On the other hand, buckling of plates involves bending in two planes, and thus deflections and bending moments at a point become function of two independent variables. Consequently, the structural behaviour of plates is described by partial differential equations, whereas ordinary differential equations were adequate to describe the behaviour of columns. Further, the number of boundary conditions was four in the columns whereas in plates there are two boundary condition on each of its edges. Another basic difference between a column and a plate lies in their buckling behaviour. Once a column has buckled, it cannot resist any additional axial load i.e. critical load of a column is also its failure load. On the other hand, the plates which are invariably supported at edges or are interconnected to other plate elements continue to resist additional axial loads even after the loads reach their buckling values. This additional load is sometimes as high as 10–15 times the initial elastic buckling load. Thus, for a plate element the post-buckling load is much higher than the initial buckling load. This fact is largely exploited in the minimum weight design of the structures. The components of open section columns with wide flanges behave more like plate elements. The plates making up a column may undergo a form of local failure, thus necessitating the consideration of instability of plate element. In order to enhance buckling load of a plate sometimes longitudinal and transverse stiffeners are provided. The inherent discontinuities in these stiffened structures make their analysis complex.