Modelling torsion in an elastic cable in space

Applied Mathematical Modelling

Volumn 29, Issue 2, 2005, Pages 117-136

  Benecke, Stephen ^a   van Vuuren, Jan H ^a  

^a STELLENBOSCH UNIVERSITY   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; CABLES; DIFFERENTIAL EQUATIONS; ELASTICITY; MATHEMATICAL MODELS; PLASTIC DEFORMATION;

AXIAL TWIST; ELASTIC DEFORMATION;

TORSIONAL STRESS;

CABLE; MATHEMATICAL MODELING; TORSION;

EID: 10444275092     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2004.07.009     Document Type: Article

References (28)

1. S.S. Antman Kirchoff's problem for nonlinearly elastic rods Quart. Appl. Math. 32 1974 221-240
2. J.H. Argyris P.C. Dunne D.W. Scharpf On large displacement-small strain analysis of structures with rotational degrees of freedom Comput. Methods Appl. Mech. Engrg. 14 3 1978 401-451
3. A.-J.-C. Barré de St. Venant Mémoire sur le calcul de la résistance et del la flexion des pièces solides à simple ou àdouble courbure, en prenant simultanément en considèration les divers efforts auxquels elles peuvent être soumises dans tous les sens C.R. Acad. Sci. Paris 17 1843 942-954
4. J. Binet Mémoire sur l'intégration des équations de la courbe élastique à double courbare C.R. Acad. Sci. Paris 18 1844 1115-1119
5. A. Clebsch, Theorie der Elastizität fester Körper, Leipzig, 1862, §§48,49,55
6. H. Cohen A nonlinear theory of elastic directed curves Int. J. Engrg. Sci. 4 1966 511-524
7. J.J. Connor Analysis of Structural Member Systems 1976 Ronald Press New York
8. E. Cosserat F. Cosserat Sur la mècanique générale C.R. Acad. Sci. Paris 145 1907 1139-1142
9. E. Cosserat F. Cosserat Sur la théorie des corps minces C.R. Acad. Sci. Paris 146 1908 169-172
10. T.P. Dreyer J.H. van Vuuren A comparison between continuous and discrete modelling of cables with bending stiffness Appl. Math. Model. 23 1999 527-241
11. J.L. Ericksen C. Truesdell Exact theory of stress and strain in rods and shells Arch. Rational Mech. Anal. 1 1958 293-323
12. L. Euler Genuina principia doctrinae de statu aequilibrii et motu corporum tam perfecte flexibilium quam elasticorum Opera Omnia (2) 11 1771 37-61
13. G.E. Hay The finite displacement of thin rods Trans. Am. Math. Soc. 51 1942 65-102
14. G. Jeleni M. Saje A kinematically exact space finite strain beam model - finite element formulation by generalized virtual work principle Int. J. Numer. Methods Engrg. 33 3 1992 469-502
15. W. Jianga J.L. Henshall Torsion-extension coupling in initially twisted beams by finite elements Eur. J. Mech. A Solids 20 3 2001 501-508
16. G. Kirchhoff Über das Gleichgewicht and die Bewegung eines unendlich dünnen elastischen Stabes J. Reine Angew. Math 56 1859 285-313
17. G. Kirchhoff, Vorlesungen über mathematische Physik & Mechanik, Leipzig, 1876, §2
18. H.A. Koenig N.A. Bolle Non-linear formulation for elastic rods in three-space Int. J. Non-Linear Mech. 28 3 1993 329-335
19. A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, vol. 2, Cambridge, 1893, §233
20. A.K. Noor W.H. Greene S.J. Hartley Nonlinear finite element analysis of curved beams Comput. Methods Appl. Mech. Engrg. 12 3 1977 289-307
21. Mathworks: Ftp index fot /pub/contrib/v4/diffeq, [Online], [cited 2001, Aug 31], Available from http://www.mathworks.com/support/ftp/diffeqv4.shtml
22. S.W. Reagan W.D. Pilkey Constrained torsion of prismatic bars Finite Elem. Anal. Des. 38 10 2002 909-919
23. R.J. Roark Formulas for Stress and Strain fourth ed. 1965 McGraw-Hill Book Company New York
24. A. Rosen Structural and dynamic behavior of pretwisted rods and beams Appl. Mech. Rev. 44 12 1991 483-515
25. M. Saje A variational principle for finite planar deformation of straight slender elastic beams Int. J. Solids Struct. 26 8 1990 887-900
26. F.W. Sears M.W. Zemansky H.D. Young University Physics sixth ed. 1982 Addison-Wesley Publishing Company Reading, MA
27. J.C. Simo L. Vu-Quoc A geometrically-exact rod model incorporating shear and torsion-warping deformation Int. J. Solids Struct. 27 3 1991 371-393
28. C.E. Weatherburn Elementary Vector Analysis: With Applications to Geometry and Mechanics 1963 G. Bell & Sons, Ltd London pp. 97-100