Based on well-understood engineering models of an untwisted cylindrical structure, a suitable displacement field for a twisted cylinder is established. This allows for longitudinal, bending, and torsional deformations together with warping to occur and, in particular, local twisting to take place about a variable direction. The procedure requires a geometric framework that varies along the length, which is modelled using a vectorial approach. Direct and shear strains are derived for the continuous system.
DanielsonD. A.HodgesD. H.Nonlinear beam kinematics by decomposition of the rotation tensorTrans. ASME, J. Appl, Mechanics, 1987, 54, 258–262.
2.
GoodierJ. N.GriffinD. S.Elastic bending of pretwisted barsInt. J. Solids Structs, 1969, 5, 1231–1245.
3.
KrenkS.A linear theory for pretwisted elastic beamsTrans. ASME, J. Appl. Mechanics, 1983, 50, 137–142.
4.
KrenkS.The torsion-extension coupling in pretwisted elastic beamsInt. J. Solid Structs, 1983, 19, 67–72.
5.
StevensonA. C.Flexure with shear and associated torsion in prisms of uni-axial and asymmetric cross-sectionsPhil. Trans. R. Soc. Lond., 1939, 237, 161–229.
6.
SokolnikoffI. S.Mathematical Theory of Elasticity, 1983 (McGraw-Hill, New York).
7.
KosmatkaJ. B.On the behavior of pretwisted beams with irregular cross sectionsTrans. ASME, J. Appl. Mechanics, 1992, 59, 146–152.
8.
HodgesD. H.Nonlinear beam kinematics for small strains and finite rotationsVertica, 1987, 11 (3), 573–589.
9.
LoveA. E. H.A Treatise on the Mathematical Theory of Elasticity, 1944 (Dover Publications, New York).
10.
RosenA.Structural and dynamic behaviour of pretwisted rods and beamsAppl. Mechanics Rev., 1991, 44, 483–515.
11.
MorrisR. M.Some general solutions of St Venant's flexure and torsion problem IProc. Lond. Mathl Soc., 1940, 46, 81–98.
12.
WempnerG. A.Mechanics of Solids with Application to Thin Bodies, 1981 (Sijthoff and Noordhoff, Groningen).
