Mathematical modelling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems

Josef Malík

Applications of Mathematics (2004)

  • Volume: 49, Issue: 1, page 1-38
  • ISSN: 0862-7940

Abstract

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A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected with the homogenizing procedure is proposed and the existence and uniqueness of a solution are proved.

How to cite

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Malík, Josef. "Mathematical modelling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems." Applications of Mathematics 49.1 (2004): 1-38. <http://eudml.org/doc/33172>.

@article{Malík2004,
abstract = {A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected with the homogenizing procedure is proposed and the existence and uniqueness of a solution are proved.},
author = {Malík, Josef},
journal = {Applications of Mathematics},
keywords = {cable stayed bridges; existence; uniqueness; continuous dependence on data; homogenization of cable systems; cable stayed bridges; existence; uniqueness; continuous dependence on data; homogenization of cable systems},
language = {eng},
number = {1},
pages = {1-38},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Mathematical modelling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems},
url = {http://eudml.org/doc/33172},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Malík, Josef
TI - Mathematical modelling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems
JO - Applications of Mathematics
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 1
SP - 1
EP - 38
AB - A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected with the homogenizing procedure is proposed and the existence and uniqueness of a solution are proved.
LA - eng
KW - cable stayed bridges; existence; uniqueness; continuous dependence on data; homogenization of cable systems; cable stayed bridges; existence; uniqueness; continuous dependence on data; homogenization of cable systems
UR - http://eudml.org/doc/33172
ER -

References

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  1. 10.1137/S0036139996308698, SIAM J.  Appl. Math. 58 (1998), 853–874. (1998) MR1616611DOI10.1137/S0036139996308698
  2. Time-periodic oscillations in suspension bridges: existence of unique solution, Nonlinear Anal., Real World Appl. 1 (2000), 345–362. (2000) MR1791531
  3. 10.1023/A:1022257304738, Appl. Math. 44 (1999), 97–142. (1999) MR1667633DOI10.1023/A:1022257304738
  4. 10.1016/0377-0427(94)90352-2, J.  Comput. Appl. Math. 52 (1994), 113–140. (1994) MR1310126DOI10.1016/0377-0427(94)90352-2
  5. Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974. (1974) MR0636412
  6. 10.1007/BF00944997, Z. Angew. Math. Phys. 40 (1989), 171–200. (1989) MR0990626DOI10.1007/BF00944997
  7. Function Spaces, Academia, Prague, 1977. (1977) MR0482102
  8. 10.1016/S0294-1449(16)30368-7, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 4 (1987), 244–274. (1987) MR0898049DOI10.1016/S0294-1449(16)30368-7
  9. 10.1137/1032120, SIAM Review 32 (1989), 537–578. (1989) MR1084570DOI10.1137/1032120
  10. 10.1007/BF00251232, Arch. Rational Mech. Anal. 98 (1987), 167–177. (1987) MR0866720DOI10.1007/BF00251232
  11. Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1969. (French) (1969) Zbl0189.40603MR0259693
  12. Variational formulations of some models of suspension and cable stayed bridges, European J. Mech.—Solids/A, Submitted. 
  13. Applications of Functional Analysis in Mathematical Physics, American Mathematical Society, Providence, 1963. (1963) Zbl0123.09003MR0165337
  14. 10.1023/A:1022255113612, Appl. Math. 42 (1997), 451–480. (1997) MR1475052DOI10.1023/A:1022255113612
  15. Cable Stayed Bridges, Thomas Telford, , 1999. (1999) 
  16. Functional analysis, Springer-Verlag, Berlin-Götingen-Heidelberg, 1965. (1965) Zbl0126.11504

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