Finite element methods for coupled thermoelasticity and coupled consolidation of clay

Alexander Ženíšek

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1984)

  • Volume: 18, Issue: 2, page 183-205
  • ISSN: 0764-583X

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Ženíšek, Alexander. "Finite element methods for coupled thermoelasticity and coupled consolidation of clay." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 18.2 (1984): 183-205. <http://eudml.org/doc/193432>.

@article{Ženíšek1984,
author = {Ženíšek, Alexander},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {hyperbolic; elliptic; linear and coupled two-dimensional problems; dynamical thermoelasticity; quasistatical thermoelasticity; consolidation of clay; dependent variables being the displacements and temperature; displacements and pore water pressure; finite element triangulation of the Hermitean type; spatial domain; time domain is approximated by means of the Newmark method; existence; maximum rate of convergence},
language = {eng},
number = {2},
pages = {183-205},
publisher = {Dunod},
title = {Finite element methods for coupled thermoelasticity and coupled consolidation of clay},
url = {http://eudml.org/doc/193432},
volume = {18},
year = {1984},
}

TY - JOUR
AU - Ženíšek, Alexander
TI - Finite element methods for coupled thermoelasticity and coupled consolidation of clay
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1984
PB - Dunod
VL - 18
IS - 2
SP - 183
EP - 205
LA - eng
KW - hyperbolic; elliptic; linear and coupled two-dimensional problems; dynamical thermoelasticity; quasistatical thermoelasticity; consolidation of clay; dependent variables being the displacements and temperature; displacements and pore water pressure; finite element triangulation of the Hermitean type; spatial domain; time domain is approximated by means of the Newmark method; existence; maximum rate of convergence
UR - http://eudml.org/doc/193432
ER -

References

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  1. [1] D. AUBRY, J. C. HUJEUX, Special algorithms for elastoplastic consolidation with finite elements, Third International Conference on Numerical Methods in Geomechanics (Aachem), 2-6 April 1979. 
  2. [2] B. A. BOLEY, J. H. WEINER, Theory of Thermal Stresses, John Wiley and Sons, New York-London-Sydney, 1960. Zbl0095.18407MR112414
  3. [3] J. R. BOOKER, A numerical method for the solution of Biot's consolidation theory, Quart. J. Mech. Appl. Math. 26, 1973, pp. 457-470. Zbl0267.65085
  4. [4] S.-I. CHOU, C.-C. WANG, Estimates of error in finite element approximate solutions to problems in linear thermoelasticity, Part I, Computationally coupled numerical schemes. Arch. Rational Mech. Anal. 76, 1981, pp. 263-299. Zbl0494.73071MR636964
  5. [5] P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. Zbl0383.65058MR520174
  6. [6] T. DUPONT, L2-estimates for Galerkin methods for second order hyperbolic equations, SIAM J. Numer. Anal. 10, 1973, pp. 880-889. Zbl0239.65087MR349045
  7. [7] G. FICHERA, Uniqueness, existence and estimate of the solution in the dynamical problem of thermodiffusion in an elastic solid, Arch. Mech. (Arch. Mech. Stos.) 26, 1974, pp. 903-920. Zbl0297.35015MR369959
  8. [8] C. JOHNSON, A finite element method for consolidation of clay, Research Report 77.05 R, Chalmers University of Technology, Göteborg, 1977. Zbl0392.73091
  9. [9] J. NEDOMA, F. LEITNER, Solution of problems of streess and strain of fully saturated porous media (In Czech.) Staveb, Cas. 27, 1979, pp. 23-27. 
  10. [10] J. NEDOMA, The finite element solution of parabolic equations, Apl. Mat. 23, 1978, pp. 408-438. Zbl0427.65075MR508545
  11. [11] J. NEDOMA, The finite element solution of elliptic and parabolic equations using simplical isoparametric elements, RAIRO Anal. Numér. 13, 1979, pp. 257-289. Zbl0413.65080MR543935
  12. [12] M. ZLAMAL, The finite element method in domains with curved boundaries, Internat. J. Numer. Methods Engrg. 5, 1973, pp. 367-373. Zbl0254.65073MR395262
  13. [13] M. ZLAMAL, Curved elements in the finite element method, II. SIAM J. Numer. Anal. 11, 1974, pp. 347-362. Zbl0277.65064MR343660
  14. [14] M. ZLAMAL, Finite element methods for nonlinear parabolic equations, RAIRO Anal. Numér. 11, 1977, No. 1, pp. 93-107. Zbl0385.65049MR502073
  15. [15] A. ZENISEK, Curved triangular finite Cm-elements, Apl. Mat. 23, 1978, pp. 346-377. Zbl0404.35041MR502072
  16. [16] A. ZENISEK, The existence and uniqueness theorem in Biot's consolidation theory. (To appear in Apl. Mat. 29, 1984.) Zbl0557.35005MR747212

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