Buckling analysis of restrained orthotropic plates under combined in-plane shear and axial loads and its application to web local buckling

Buckling analysis of orthotropic plates with two opposite edges simply supported and the other two opposite edges rotationally-restrained (RR) and under combined uniform in-plane shear and linearly varying axial loads is presented, and its application to web local buckling of composite structural shapes is illustrated. A new plate buckled displacement shape function is proposed, and the approximate solution is obtained by the Rayleigh-Ritz method. The accuracy of analytical solution is validated with the numerical finite element analysis, and excellent agreements are achieved. A parametric study is conducted to evaluate the influence of loading ratio and rotational restraint stiffness. By introducing generic non-dimensional parameters, the buckling formulas of long plates under uniform in-plane compression, pure in-plane bending and uniform in-plane shear are obtained using the curve fitting technique. Interaction curves between the uniform in-plane shear and pure in-plane bending for the simply supported (SS) and clamped-simply supported (CS) plates are established, and it is found that the interaction curve is only related to the material orthotropic parameter of β. Finally, the proposed discrete restrained plate solution is applied to predict the web local buckling of FRP shapes by adopting the proper rotational restraint stiffness.