Combination of patch and wheel loads: Analytical approach to plate buckling

Abstract

Past studies on the stability of rectangular plates under the influence of variable loads were based on assumptions of simplified stress distributions, which put the question of the accuracy of results thus obtained. The procedure of applying the exact stress functions in the problem of elastic stability of the plate with different boundary conditions under effects of patch and wheel loading is presented in this paper. Mathieu (1890) obtained the exact solution for the plane-strain state for a rectangular element for certain types of variable stresses on the boundaries. Baker at al (1993), following Mathieu.s results, analyzed the general problem of a rectangular plate loaded by completely arbitrary distributions of (normal and/or shear) stresses along the edges of the plate. Analytical approach used for determination of the critical load is based on well known Ritz energy technique. The strain energy due to bending of the plate is defined in the traditional way. On the other hand, the exact stress distribution of Mathieu.s theory of elasticity is introduced through the potential energy of the plate associated with the work done by external loads. Results for the critical load obtained by presented analytical approach are reaffirmed by numerical finite-element (FE) runs.