Inflation, Bending and Torsion of Reinforced Elastic Tubes

Analysis is given for elastic tubes containing a number of surfacesof balanced-angleply fibre reinforcement when subjected to internaland external pressures and to large displacements and rotationsof the cross-sections. The strain is small, so that the firstapproximation to the stress and strain distributions over eachcross-section is found to be a superposition of the types analysedby Green & Nicol (1978) and Nicol (1978). The equilibriumequations for a length of tube undergoing combined extension,inflation, bending and torsion are derived and an expressionfor the maximum tensions arising in the reinforcing fibres isobtained. Numerical calculations for tubes having the same compositionas those of Green & Nicol show that the only rigidity parameterwhich is significantly affected by the reinforcement is thetorsional rigidity, even though the tensions developed in theindividual reinforcement layers depend on the elastic propertiesof the fibres. The influence of a large torsional rigidity on configurationsadopted by a tube loaded only at its ends and subjected to internaland external pressures is illustrated by considering deformationsin which the tube becomes helical, with an additional materialtwist about the helical line of centres.