BUCKLING OF PLATES WITH ALLOWANCES FOR SHEAR AND PREBUCKLING INPLANE DEFORMATIONS

Abstract

Treated herein is the elastic buckling of plates with allowances for the effects of shear deformation, prebuckling inplace deformation and ‘curvature terms’. These ‘curvature terms’ are the nonlinear strain components pertaining to the inplane deformations. The effect of shear deformation is incorporated into the analysis by adopting the Reissner-Mindlin plate theory, which permits an additional rotation to the cross section. Analytical buckling solutions are obtained for simply supported and clamped circular plates under uniform radial inplane loading and simply supported rectangular plates under biaxial loading. Exact formula linking the Mindlin critical load to the corresponding Kirchhoff critical load is derived for simply supported, general polygonal plates and simply supported and clamped circular plates under isotropic inplane loading. Similar linking formula is also obtained for the case of simply supported rectangular plates under biaxial loading. It is found that with a slight modification to this formula, it can predict the critical load of biaxially loaded Mindlin plates with mixed edge conditions to within a few percent.