Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type

Stanislav Sysala

Applications of Mathematics (2010)

  • Volume: 55, Issue: 2, page 151-187
  • ISSN: 0862-7940

Abstract

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A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence properties is also investigated. The effectiveness of the algorithms is illustrated on numerical examples.

How to cite

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Sysala, Stanislav. "Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type." Applications of Mathematics 55.2 (2010): 151-187. <http://eudml.org/doc/37842>.

@article{Sysala2010,
abstract = {A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence properties is also investigated. The effectiveness of the algorithms is illustrated on numerical examples.},
author = {Sysala, Stanislav},
journal = {Applications of Mathematics},
keywords = {non-linear subsoil of Winkler's type; semi-coercive beam problem; approximation; iterative methods; convergence; projection; load stability; non-linear subsoil of Winkler's type; semi-coercive beam problem; approximation; iterative method; convergence; projection; load stability},
language = {eng},
number = {2},
pages = {151-187},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type},
url = {http://eudml.org/doc/37842},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Sysala, Stanislav
TI - Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 151
EP - 187
AB - A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence properties is also investigated. The effectiveness of the algorithms is illustrated on numerical examples.
LA - eng
KW - non-linear subsoil of Winkler's type; semi-coercive beam problem; approximation; iterative methods; convergence; projection; load stability; non-linear subsoil of Winkler's type; semi-coercive beam problem; approximation; iterative method; convergence; projection; load stability
UR - http://eudml.org/doc/37842
ER -

References

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  2. Chen, X., Nashed, Z., Qi, L., 10.1137/S0036142999356719, SIAM J. Numer. Anal. 38 (2000), 1200-1216. (2000) Zbl0979.65046MR1786137DOI10.1137/S0036142999356719
  3. Fučík, S., Kufner, A., Nonlinear Differential Equations, Elsevier Amsterdam (1980). (1980) MR0558764
  4. Kufner, A., John, O., Fučík, S., Function Spaces, Academia Praha (1977). (1977) MR0482102
  5. Horák, J. V., Netuka, H., Mathematical models of non-linear subsoils of Winkler's type, In: Proceedings of 21st Conference Computational Mechanics 2005 ZČU Plzeň (2005), 235-242, 431-438 Czech. (2005) 
  6. Netuka, H., A new approach to the problem of an elastic beam on a nonlinear foundation. Part 1: Formulations, Appl. Comput. Mech In print. 
  7. Netuka, H., Machalová, J., A new approach to the problem of an elastic beam on a nonlinear foundation. Part 2: Solution, Appl. Comput. Mech Submitted. 
  8. Sysala, S., Mathematical modelling of a beam on a unilateral elastic subsoil, In: Proceedings of the 14th International Seminar Modern Mathematical Methods in Engineering JČMF, VŠB-TU Ostrava (2005), 193-197 Czech. (2005) 
  9. Sysala, S., On a dual method to a beam problem with a unilateral elastic subsoil of Winkler's type, In: Proceedings of Seminar on Numerical Analysis---SNA'07 Institute of Geonics AS CR Ostrava (2007), 95-100. (2007) MR2433726
  10. Sysala, S., 10.1007/s10492-008-0030-0, Appl. Math. 53 (2008), 347-379. (2008) Zbl1199.49051MR2433726DOI10.1007/s10492-008-0030-0
  11. Sysala, S., Numerical illustration of theoretical results for non-linear semi-coercive beam problem, In: Proceedings of Seminar on Numerical Analysis---SNA'08 TU Liberec (2008), 110-114. (2008) MR2433726
  12. Sysala, S., Numerical illustration of theoretical results for non-linear semi-coercive beam problem, In: Proceedings of Seminar on Numerical Analysis---SNA'08 TU Liberec (2008), 110-114. (2008) MR2433726

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