An analytical model for the buckling of plates under mixed boundary conditions

An analytical approach for the buckling analysis of rectangular plates under mixed boundary conditions is presented. In order to solve the partial differential equation governing the problem at hand a method of separation of variables is here adopted, by introducing the displacement field as a result of the scalar product of two vectors which combine prescribed and unknown scalar functions. By following this strategy, exact buckling solutions for a wide class of problems, in which mixed boundary conditions can be assigned relaxing some usual constraints, are determined, and buckling load of plates, where biaxial tensile and compressive loads are applied in presence of piecewise clamped and partially supported sides, obtained analytically. Several cases of engineering interest are finally analyzed, and comparisons of the theoretical outcomes with literature data and Finite Element-based numerical results are also shown, in order to highlight the effectiveness of the proposed strategy.