Analytic solution for buckling of rectangular isotropic plates with internal point supports

Abstract

In this paper, analytical solutions for the buckling loads of thin rectangular plates with internal supports and different boundary conditions are derived. The analytical method presented herein is based on the development of a static solution for a plate. The physical meaning of buckling is the loss of stiffness, and it is found as the value of the in-plane loading intensity at which a zero force on the plate surface will generate infinite displacement. The solution is obtained in a series form, and the coefficients are solved to match the edge conditions. For every internal support in the plate domain we add one equation enforcing zero deflection at that point. By using this new method, exact buckling loads and buckling modes of many new cases of plates with various boundary conditions and several internal supports are obtained. The optimal location for placing an additional support is shown for several cases of square plates. Results are given for several cases of uni-directional and bi-directional loading.