Nonlinear Buckling of Rectangular Plates

Abstract

The nonlinear deflections of a thin elastic simply-supported rectangular plate are studied. The plate is deformed by a compressive thrust applied along the short edges. For the boundary value problem considered we prove that the platecannot buckle for thrusts less than or equal to the lowest eigenvalue of the linearized buckling problem. For larger thrusts approximate solutions of the von Kármán equations are obtained by an accelerated iteration method. Each iterate is numerically evaluated by a finite difference procedure. Using this method approximate solutions are obtained for thrusts considerably larger than the lowest eigenvalue. These solutions bifurcate from the eigenvalues of the linearized problem. In addition, an asymmetric solution is found which appears to branch from a previously bifurcated solution. The extensive numerical results are used to study the formation of boundary layers and the related problem of the plate’s ultimate load. On the basis of the numerical results, an energy mechanism is proposed to explain a “mode-jumping” phenomenon which has been previously observed in experiments.