Analytical buckling loads for corner supported rectangular orthotropic and symmetrically laminated plates

In this research we present a new analytical solution for finding the buckling loads of thin isotropic and orthotropic rectangular plates in which all four corners are supported. This new solution is also capable of solving all cases where few or all the edges are supported. The methods that are currently known in the literature for finding the buckling loads of plates are mainly numerical. Although some plates with specific boundary conditions have analytical solutions, a comprehensive analytical method providing analytical solutions that fit all possible combinations of boundary conditions is lacking. The solution method in this study 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 series form, and the coefficients are solved to match the edge conditions. Using this new method, exact buckling loads and buckling modes of many new cases of classical boundary conditions are found. Results are given for several stiffness ratios in both directions of the plate, and for uni‐directional and bi‐directional loading. In this research we present a new analytical solution for finding the buckling loads of thin isotropic and orthotropic rectangular plates in which all four corners are supported. This new solution is also capable of solving all cases where few or all the edges are supported. The methods that are currently known in the literature for finding the buckling loads of plates are mainly numerical. Although some plates with specific boundary conditions have analytical solutions, a comprehensive analytical method providing analytical solutions that fit all possible combinations of boundary conditions is lacking….