Abstract
This study considered the effect of shear deformation in the bending model, which was important to assess of the plate buckling loads according to changes in the thickness. The buckling of square, skew, and perforated plates was studied with the rotation gradient (curvature) and the deflection gradient in the in the geometrical nonlinearity (GNL) effect using the BEM. The importance of the curvatures appeared when the thickness-to-span ratio reached 0.05 and increased for thicker plates in several cases. The present boundary elements formulation used the gradient of the displacements instead of second derivatives in the GNL, which disregarded the relation between the in-plane forces derivatives consequently. The singularities related to the differentiation process to obtain the BIEs for the gradient of displacements and for the stresses were reduced with using the tangent differential operator.
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