The Bending of the Cylindrically Aeolotropic Plate

Abstract

Abstract In this paper, the small-deflection theory, applicable to plates of cylindrically aeolotropic material, is presented, and expressions are obtained for the moments and deflections produced by the following combinations of loading and boundary conditions: The disk clamped along its circumference and loaded by a uniform lateral pressure; the clamped disk loaded by a central concentrated force; the simply supported disk loaded by uniform edge moment; the disk with a rigid core clamped along its circumference and loaded by a central concentrated force; the ring clamped along its outer edge and loaded by a uniform shear distribution along the inner edge; the simply supported disk with an elastic isotropic core loaded by a uniform edge moment; and the disk under the loading given by p = p0 r cos θ. The six symmetrical problems of this group were chosen for evaluation since they and their linear combinations comprise a large part of the total set of such problems. Curves are included showing, for three of the foregoing problems, the effect of the degree of anisotropy on the stresses. The practical application of solutions obtained by the following theory might lie, for example, in design problems involving circular plates which are built up of laminas of radial symmetry with different tangential and radial stiffnesses. The theory could also be applied to the design of circular concrete slabs with different amounts of reinforcing steel in the radial and tangential directions.