Bifurcation of a Circular Hollow Cylinder of Ideal Fiber-Reinforced Materials : For a Case of Axial Compression and Reinforcement

Abstract

The Bifurcation problem stated in the title is analyzed on the basis of the mechanics of incremental deformations. The cylinder is reinforced by ixextensible, completely flexible fibers in the direction of its axis. It is found that the smallest critical compression is equal to the shear modulus for infinitesimal deformations and does not depend on any dimensions of the cylinder. The associated bifurcation mode is that for n=1, n being the number of circumferential node. When it bifurcates, the singular stresses appear in the boundary fiber surfaces.