An explicit polynomial solution of the representative problem of the mechanics of fibrous composites

Abstract

The paper is focused on an important aspect of the central problem of the mechanics of the unidirectionally reinforced fibrous composites. This problem concerns the features of the matrix-fibre load transfer phenomenon which, actually, provides by itself the very reinforcing effect of the fibres. The paper illustrates that the successful analysis of this problem definitely needs, first, the exact solution of a certain typical or, say, representative axisymmetric boundary value problem of the elasticity theory and, second, a representation of this solution in a form, which is convenient enough for additional mathematical manipulations. Such an explicit with respect to the problem variables polynominal representation is derived in the paper.