A semi-numerical approach to the buckling and post-buckling solution of plate

Abstract

In this semi-numerical approach to buckling of plates, a combination of polynomial and trigonometric functions are used as displacement functions in the Rayleigh-Ritz method. It is shown that a variety of loading and boundary conditions can be handled using simple variation of the trigonometric function proposed here. A two-dimensional plate buckling problem is therefore reduced to selecting one of the set of trigonometric function shown. The buckling coefficient values are then computed as eigenvalues of the stiffness and geometric matrix pair. These values compare well with available analytical and numerical approach solutions. The approach can also be extended to post buckling analysis using the eigenvectors found.