Finite plane deformations of highly anisotropic elastic-plastic plates and shells

Abstract

The theory of “ideal” fibre-reinforced materials is applied to the problem of a cantilevered fibre-reinforced plate of elastic-plastic material, subjected to increasing normal tractions. Simple analytical solutions are found for the finite deformation. These show that a plastic region forms at the built-in end and, in contrast with an isotropic plate, spreads along the plate towards the free end. It is also found that, however large the applied pressure, regions of purely elastic deformation exist at each end of the plate. The analysis is extended to incorporate deformation of plates with initial curvature (i.e. thick shells), and an analytical solution is obtained for the special case of a shell with uniform curvature. The associated problem of elastic unloading of a deformed initially flat plate is briefly discussed.