Buckling of laminated anisotropic plates under cylindrical bending

We present an analysis, using three-dimensional linear elasticity theory for anisotropic inhomogeneous material, of buckling in the cylindrical bending mode of rectangular inhomogeneous or laminated plates under in-plane loading. The load may be mechanical, thermal or due to moisture absorption. The only material symmetry assumed is that of reflectional symmetry with respect to planes parallel to the plate surface. Arbitrary inhomogeneity is allowed in the through-thickness direction, with a laminate arising as a special case when the elastic moduli are piecewise constant functions of the through-thickness coordinate. A transfer matrix method is used which determines, in principle to any desired degree of accuracy, the stress and displacement in the plate in terms of the stress and displacement at the mid-surface. These mid-surface values are determined by the solution of, for the cylindrical bending case, an ordinary differential equation. Buckling is treated in the usual way as a bifurcation from the initially stressed state, so giving rise to an eigenvalue problem. It is shown that the buckling load as predicted by classical laminate theory arises naturally as a first approximation to the exact result, and that this first approximation also takes account of shear deformation.