The state of stress of an elastically supported transversely isotropic beam

Abstract

The bending of a three-layer beam with stiff outer layers is studied. The middle layer (spacer) has small stiffness compared with the outer layers and can be regarded as an elastic Winkler-Zimmerman support. By assumption, the lower (stiffest) isotropic layer behaves as a Bernoulli-Euler beam if a load is applied. The boundary conditions at the ends of the beam can be arbitrary, in general. The case when the ends of the lower beam are fixed is considered. A uniformly distributed compressing load acts on the outer surface of the upper transversely isotropic layer. The ends of this layer are free of any loads. The plane state of stress of the transversely isotropic layer is determined by the equations of elasticity theory. The exact solution of the problem is obtained in terms of trigonometric series.