Application of finite element methods to the post-buckling behaviour of thin plates containing imperfections

Abstract

A finite element program, applicable to the pre- and post-buckling behaviour of plates with imperfections, is developed. Suitable incremental stiffness matrices are generated for a plate element with four nodes and twenty degrees of freedom. Preliminary work, together with a prototype pro- gram, is carried out on a simple strut in order to compare various nonlinear solution techniques, both incremental and iterative. Th6 plate program is veri- fied by large deflection calculations for a square plate under lateral pressure, and by comparison with theoretical buckling loads for a perfect plate, closely agreeing with previous theoretical work. Experimental results in compression, both with and without an artificially introduced imperfection, are used to demonstrate real plate behaviour, and they enable a comparison to be made with computed results. Measure- ments of deflection are made by the Moire fringe tech- nique, as well as by dial gauges. The program is used to investigate the effect of buckling on the compressive and shear stiffness of plates with various degrees of imperfection, including the compressive stiffness of a square plate after buckling in shear.