Elastic buckling analysis of platings with torsionally and warping restrained supports by truncated series expansion applied to a hierarchical trigonometric function set

The paper provides a new framework for the elastic buckling analysis of platings under linearly varying uniaxial loads, with torsionally and warping restrained longitudinal supports. The new method, based on the employment of a hierarchical trigonometric function set, allows analysing any type of boundary conditions at the plate long edges, ranging from the simple support to the clamped ones. In order to make the calculations viable for practical design purposes, an analytical formulation, based on a 3rd order truncated series expansion of the vertical displacement field, is developed. The effectiveness of the new analytical solution is investigated, focusing on several values of the torsional stiffness of longitudinal supporting members, in order to cover various types of boundary conditions at the plate long edges. Particularly, the new analytical formulation is checked by a comparative analysis against the asymptotic values, the relevant results obtained by the eigenvalue buckling analysis, carried out by Ansys Mechanical APDL, as well as the Rule formulas. Based on current results, the new method not only provides a more rational approach for the elastic buckling analysis of ship platings, but it also allows improving the accuracy in determining the buckling capacity in the entire design range typical of ship platings.