A Generalized Analytical Approach for the Buckling Analysis of Thin Rectangular Plates With Arbitrary Boundary Conditions

An analytical approach for studying the elastic stability of thin rectangular plates under arbitrary boundary conditions is presented. Because the solution is given in closed-form, the approach can be regarded as "exact" under the Kirchhoff–Love assumption. The proposed procedure allows us to obtain the buckling load and modal displacements that do not depend on the number of elements adopted in the numerical discretization using, say, the finite element method. Due to the fact that the longitudinal variation of the displacements is taken into account, the two-dimensional model established for the plate is considered "complete." Such an approach overcomes the shortcomings of conventional modeling presented in the literature. In order to demonstrate the generality of the proposed approach, several examples are prepared and the results obtained are compared with finite element and analytical solutions existing elsewhere.