Incompressibility in rod and shell theories

Stuart S. Antman; Friedemann Schuricht

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 2, page 289-304
  • ISSN: 0764-583X

How to cite

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Antman, Stuart S., and Schuricht, Friedemann. "Incompressibility in rod and shell theories." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.2 (1999): 289-304. <http://eudml.org/doc/193921>.

@article{Antman1999,
author = {Antman, Stuart S., Schuricht, Friedemann},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {planar deformation of rods; spatial deformation of rods; shells; thin incompressible bodies; constraints; exact theories},
language = {eng},
number = {2},
pages = {289-304},
publisher = {Dunod},
title = {Incompressibility in rod and shell theories},
url = {http://eudml.org/doc/193921},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Antman, Stuart S.
AU - Schuricht, Friedemann
TI - Incompressibility in rod and shell theories
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 2
SP - 289
EP - 304
LA - eng
KW - planar deformation of rods; spatial deformation of rods; shells; thin incompressible bodies; constraints; exact theories
UR - http://eudml.org/doc/193921
ER -

References

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  1. [1] S.S. Antman, Nonlinear Problems of Elasticity. Springer-Verlag (1995). Zbl0820.73002MR1323857
  2. [2] S.S. Antman, Convergence properties of hiérarchies of dynamical theories of rods and shells. Z. Angew. Math. Phys. 48 (1997) 874-884. Zbl0896.73029MR1488685
  3. [3] S.S. Antman and R.S. Marlow, Material constraints, Lagrange multipliers, and compatibility. Applications to rod and shell theories. Arch. Rational Mech. Anal. 116 (1991) 257-299. Zbl0769.73012MR1132762
  4. [4] P.G. Ciarlet, Mathematical Elasticity, Volume II: Theory of Plates. North-Holland (1997). Zbl0953.74004MR1477663
  5. [5] P.G. Ciarlet, Mathematical Elastictty, Volume III: Theory of Shells. North-Holland (1999). MR1757535
  6. [6] V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag (1986). Zbl0585.65077MR851383
  7. [7] P. Le Tallec, Numerical methods for solids in Handbook of Numerical Analysis, P.G. Ciarlet and J.-L. Lions Eds. North-Holland (1994) 465-622. Zbl0875.73234MR1307410
  8. [8] R. Saxton, Existence of solutions for a finite nonlinearly hyperelastic rod. J. Math Anal Appl. 105 (1985) 59-75. Zbl0561.73046MR773572
  9. [9] C. Schwab and S. Wright, Boundary layers of hierarchical beam and plate models. J. Elasticity 38 (1995) 1-40. Zbl0834.73040MR1323554
  10. [10] L. Trabucho and J. M. Viano, Mathematical Modelling of Rods, in Handbook of Numerical Analysis, P.G. Ciarlet and J.-L. Lions Eds. North-Holland 4 (1996) 487-974. Zbl0873.73041MR1422507
  11. [11] R. Temam, Navier-Stokes Equations. North-Holland (1977). Zbl0383.35057MR603444
  12. [12] T. Wright, Nonlinear waves in rods : results for incompressible elastic materials. Stud. Appl. Math. 72 (1984) 149-160. Zbl0558.73020MR782278

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