Saint-Venant’s torsion of composite shafts reinforced with arbitrarily or periodically dispersed coated fibers

It is known that a circular shaft containing a number of composite cylinders, upon suitably designed material parameters, is an exactly solvable configuration under Saint-Venant’s torsion [Chen, T., Benveniste, Y., & Chuang, P. C. (2002). Exact solutions in torsion of composite bars: Thickly coated neutral inhomogeneities and composite cylinder assemblages. Proceedings of the Royal Society A, 458, 1719–1759]. Here we consider the boundary value problem of a circular shaft containing coated fibers under torsion without any restrictions on the material parameters. The formulation is based on a complex variable method together with simple mapping techniques, representing the warping fields in Laurent or Taylor series based on different origin points. Particularly when the coated fibers are periodically dispersed inside the host shaft, we show that the unknown coefficients for each coated fiber are correlated in specific manners, and thus rendering the governing framework much simplified. We verify analytically that our results conform with the exact results of partly neutrality and complete neutrality of the exact solvable configuration of a circular shaft containing neutral coated fibers. This work presents a feasible solution procedure that complements the exact configurations in which the material parameters must follow restrictive constraint, and also provides an estimate for the torsional rigidity in which the bounds are not sufficiently close.