Transverse impact of ideal fibre-reinforced rigid—plastic plates

Abstract

A simple model of a plate of ductile material reinforced in two or more directions by strong fibres is constructed on the assumptions that the plate has rigid-plastic behaviour and is inextensible in the fibre directions. Such a plate deforms essentially by shear, and the yield function reduces to a function of the shear stress resultants. The flow rule is formulated for a work-hardening material and a quite general class of yield functions. A class of deformations is analysed in which, at any instant, the deflexion is constant on each of a family of curves which, in the plane of the plate, are similar curves to the yield curve in the shear stress resultant plane. This class of deformations is used to solve the problem of transverse impact of a large plate struck transversely at a point by a mass M travelling with speed V0; in this solution a region of the plate enclosing the point of impact moves as a rigid body, and a curve, across which the shear stress resultants and deflexion gradients are discontinuous, propagates outwards. This propagating curve is also similar to the yield curve. For a large plate, the solution is given for a general yield function. For circular and rectangular plates, and some special yield functions, some results are also given for the case in which the discontinuity is reflected at all or part of the fixed edge of the plate.