THE PROBLEM OF LATERAL BUCKLING OF CANTILEVER PLATES

A two-dimensional formulation of the problem of lateral cantilever buc kling, within the frame work of the theory of sheardeformable thin ela stic anisotropic plates, is used as the basis of the derivation of a o ne-dimensional system of differential equations and boundary condition s for generalized versions of the lateral buckling problems associated with the names of Euler, Michell, Prandtl, and Timoshenko. It is show n that, in general, the one-dimensional formulation is governed by a t enth-older boundary value problem, which reduces to an eighth-order pr oblem upon assuming absent crosswise transverse shear deformability. T he remaining problem becomes one of the sixth-order, in the spirit of classical beam theory, upon an assumption of negligible negligible war ping stiffness effects. It is further shown that for the problem of a plate which is end loaded in shear only, the use of first integrals al lows the derivation of a fourth-aider problem and of a second order pr oblem, respectively, with the latter being consistent with the classic al Michell-Prandtl problem.