Refined buckling analysis of plates under shear and uniaxial compression

In the classical buckling analysis of ship platings, Euler stresses are generally evaluated applying the classical thin plate theory and so neglecting the shear deformation, even if the plating thickness is not totally negligible as regards the panel’s mean dimensions. In the paper the two variable refined theory proposed by Shimpi (2006) is applied to the buckling analysis of simply supported rectangular plates under combined shear and uniaxial stresses, in order to take into account the transverse shear effects. The coupled bending-shear governing equations, derived by the Hamilton’s principle, are solved by the energy method, developing into appropriate double sine trigonometric series the displacement field. The convergence of solution, in terms of shear buckling coefficients, is fully investigated varying the number of harmonics. New relations, that permit to take into due consideration the plating thickness, are also obtained and compared with the classical design formulas and the relevant results, obtained by some FE eigenvalue buckling analyses of typical ship platings under the combined action of shear and uniaxial forces.