An intrinsic formulation for nonlinear elastic rods

International Journal of Solids and Structures

Volumn 34, Issue 31-32, 1997, Pages 4191-4212

  Rubin, M B ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTICITY; FUNCTIONS; INTEGRAL EQUATIONS; LOADS (FORCES); STRAIN; TORSIONAL STRESS;

COSSERAT RODS;

SHEAR DEFORMATION;

EID: 0031274310     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(96)00158-8     Document Type: Article

References (14)

1. Antman, S. S. (1972). The theory of rods. In Handbuch der Physik vol. VIa/2, Springer-Verlag, Berlin.
2. Antman, S. S. (1974). Kirchhoff's problem for nonlinearly elastic rods. Quart. Appl. Math. 32, 221-240.
3. Antman, S. S. (1995). Nonlinear Problems of Elasticity, Springer-Verlag, New York.
4. Antman, S. S. and Jordan, K. B. (1975). Qualitative aspects of the spatial deformation of non-linearly elastic rods. Proc. Roy. Soc. Edinburgh 73A, 85-105.
5. Dill, E. H. (1992). Kirchhoff's theory of rods. Archive for History of Exact Sciences 44, 1-23.
6. Ericksen, J. L. (1970). Simpler static problems in nonlinear theories of rods. Int. J. Solids Structures 6, 371-377.
7. Green, A. E., Naghdi, P. M. and Wenner, M. L. (1974a). On the theory of rods I: derivations from the three-dimensional equations. Proc. Royal Soc. London A337, 451-483.
8. Green, A. E., Naghdi, P. M. and Wenner, M. L. (1974b). On the theory of rods II: developments by direct approach. Proc. Royal Soc. London A337, 485-507.
9. Love, A. E. H. (1944). A Treatise On the Mathematical Theory of Elasticity, fourth edition, Dover, New York.
10. Lu, C.-L. and Perkins, N. C. (1994). Nonlinear spatial equilibria and stability of cables under uni-axial torque and thrust. ASME J. Appl. Mech. 61, 879-886.
11. Naghdi, P. M. and Rubin, M. B. (1984). Constrained theories of rods. J. Elasticity 14, 343-361.
12. Naghdi, P. M. (1982). Finite deformation of elastic rods and shells. In Proc. IUTAM Symp. on Finite Elasticity (eds Carlson, D. E. and Shield, R. T.), Martinus Nijhoff Publishers, The Hague, Netherlands pp. 47-103.
13. Nayfeh, A. H. and Mook, D. T. (1979). Nonlinear Oscillations, John Wiley, New York.
14. Whitman, A. B. and DeSilva, C. N. (1974). An exact solution in a nonlinear theory of rods. J. Elasticity 4, 265-280.