Exact solutions for buckling of multispan rectangular plates

This paper presents exact solutions for buckling of multispan rectangular plates having two opposite edges simply supported and the other two edges being either free, simply supported, or clamped. The Levy solution procedure is employed to develop an analytical approach for buckling analysis of multispan plates. The Levy solution for each span is derived and the continuity along the interface of two spans is ensured through the implementation of the essential and natural boundary conditions at the interface. Extensive buckling factors, most of which are first-known exact solutions, are given in tabular and design chart forms for two- and three-unequal-span square plates subjected to uniaxial in-plane load in the x or y directions and biaxial in-plane load. The influence of the span ratios and plate boundary conditions on the buckling factors is discussed. Buckling factors are also obtained for two-, three-, and four-equal-span rectangular plates with various edge support conditions. The exact buckling solutions presented in this paper are of benchmark values for such plates.