Analytic solution of rectangular plate buckling with rotationally restrained and free edges

In this research a new analytical solution is used for finding the buckling loads of rectangular plates with rotationally restrained edges. Until now, analytical solution were available only for a small number of specific combinations of boundary conditions. The solution method in this study is based on the development of a static solution for a plate. The solution is obtained in series form, and the coefficients are solved to match the edge conditions. The solution fits all the combinations of possible boundary conditions, of the deflection, slope, shear force and bending moment along the edges of the plate. The problem of buckling of part of an open cross section with a free edge is solved analytically. Any number of edges, from one to four, with rotational stiffening springs can be solved. Using this new method, the exact buckling loads and modes are found. The results are verified with published data, and many new cases are presented for uni-axially and bi-axially loaded plates.