Estimation of stresses and displacements of a rectangular plate after compression buckling based on effective width theory by Karman

In this paper, the equations of in-plane and out-of-plane displacements, in-plane stress distributions, and Mises stress of the rectangular plate after buckling are composed using the well-known buckling deflection shape, based on the plane stress state and the effective width theory by Karman. Equations of in-plane displacement and stress distributions are obtained from the large deflection theory, and the maximum value of out-of- plane displacement is derived by use of Karman’s theory. The composed equations are compared with results of the finite element method (FEM) with shell elements. The boundary condition used in FEM is that the in-plane displacement of both long side edges is unconstrained. As a result, the following conclusions were obtained. Among the composed equations, the out-of-plane displacement amplitude and the in-plane compressive displacement are close enough to FEM computation results. Three in-plane stresses near the both long sides show slightly different distributions between composed equations and FEM results. The normal stress distribution of the FEM result fluctuates near the both long side edges, although that distribution by the composed equation indicates the intermediate value of the FEM result, and it was found that the maximum compressive stress appearing at both sides is lower than the one by the FEM result. On the other hand, the Mises stress distribution and its maximum value were close to the FEM results. As factors of these differences, it is considered that the in-plane deflection of the both sides and the out-of-plane displacement shape at larger load are different from the shape used in this paper.