Finite element computation of hyperelastic rods in large displacements
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 26 (1992) no. 5, p. 595-625
@article{M2AN_1992__26_5_595_0,
     author = {Le Tallec, P. and Mani, S. and Rochinha, F. A.},
     title = {Finite element computation of hyperelastic rods in large displacements},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {26},
     number = {5},
     year = {1992},
     pages = {595-625},
     zbl = {0758.73048},
     mrnumber = {1177389},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1992__26_5_595_0}
}
Le Tallec, P.; Mani, S.; Rochinha, F. A. Finite element computation of hyperelastic rods in large displacements. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 26 (1992) no. 5, pp. 595-625. http://www.numdam.org/item/M2AN_1992__26_5_595_0/

[1] S. S. Antman, Ordinary Differential Equations of One Dimensional Elasticity, Arch. Rat. Mech. Anal., 61, 1976, pp. 307-393. | MR 418580 | Zbl 0354.73046

[2] S. S. Antman, C. S. Kenney, Large Buckled States of Nonlinear Elastic Rods under Torsion, Thrust and Gravity, Arch. Rat. Mech. Anal., 76, 1981, pp. 289-338. | MR 628172 | Zbl 0472.73036

[3] J. Simo, A Finite Stram Beam Formulation The Three-dimensional Dynamic Problem, Part 1, Comp. Meth. Appl. Mech. Eng., 49, 1985, pp. 55-70. | Zbl 0583.73037

[4] J. F. Bourgat, P. Le Tallec, S. Mani, Modélisation et Calcul des Grands Déplacements de Tuyaux Elastiques en Flexion Torsion, J. Méc.Théor. Appl., 7, 1988, pp. 1-30. | MR 959482 | Zbl 0671.73060

[5] T. Dupont, R. Scott, Polynomial Approximation of Functions in Sobolev spaces, Math. Comp., 34, 1980, pp. 441-463. | MR 559195 | Zbl 0423.65009

[6] H. Keller, The bordering algorithm and path following near singular points of higher nullity, SIAM J. Sci. Stat. Comp., 4, 1983, pp. 573-582. | MR 725653 | Zbl 0536.65017

[7] T. J. R. Hughes, J. Winget, Finite Rotation Effects in Numerical Intégration of Rate Constitutive Equations Arising in Large Deformation Analysis, Int. J. Numer. Meth. Eng., 15, 1980, pp. 1413-1418. | MR 601532 | Zbl 0463.73081

[8] J. C. Simo, L. Vu Quoc, A Three-dimensional Finite Stram Rod Model Part II Computational Aspects, Comp. Meth. Appl. Mech. Engrg., 58, 1986, pp. 79-116. | Zbl 0608.73070

[9] K. E. Bisshop, D. E. Drucker, Large Deflections of Cantilever Beams, Quart. Appl. Math., 3, 1945, pp. 272-275. | MR 13360 | Zbl 0063.00418