An extended separation-of-variable method for eigenbuckling of orthotropic rectangular thin plates. (1st March 2021) - Yuan, Y.; Xing, Y.F.
Highlights: A closed-form solution method is proposed for eigenbuckling of thin plates. The proposed method is not an iterative method. Critical loads for plates with arbitrary boundary conditions are obtained. The obtained results agree well with existing results and FEM's results. Abstract: This paper develops an extended separation-of-variable (SOV) method for studying the eigenbuckling of orthotropic rectangular thin plates with simply supported, clamped, guided and free edges, and the closed-form eigensolutions are obtained for plates with non-Levy boundary conditions. In the extended SOV method based on the Rayleigh quotient variational principle, mode functions are in a separation-of-variable form, and critical loads pertaining to two-direction eigenbuckling mode functions are assumed to have different values in mathematical sense though they are the same physically. Besides, there are explicit and closed-form relationships between eigenvalues and the critical loads, and the eigenvalue equations and the coefficients of mode functions are achieved through two pairs of boundary conditions. Compared with the Kantorovich-Krylov method and the iterative SOV method, the extended separation-of-variable method solves eigenvalue equations simultaneously, not requiring iterations. The obtained results are in good agreement with the existing analytical and numerical results. Thus the validity of the present method and accuracy of the obtained solutions are verified. The obtained solutions can be used to measure the convergence and accuracy of numerical methods, and guide parametric design of structures.