| Title:
|
Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type (English) |
| Author:
|
Sysala, Stanislav |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
151-187 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
non-linear subsoil of Winkler's type |
| Keyword:
|
semi-coercive beam problem |
| Keyword:
|
approximation |
| Keyword:
|
iterative methods |
| Keyword:
|
convergence |
| Keyword:
|
projection |
| Keyword:
|
load stability |
| MSC:
|
65K10 |
| MSC:
|
74B20 |
| MSC:
|
74G65 |
| MSC:
|
74K10 |
| MSC:
|
90C20 |
| MSC:
|
90C31 |
| MSC:
|
90C90 |
| idZBL:
|
Zbl 1224.74011 |
| idMR:
|
MR2600940 |
| DOI:
|
10.1007/s10492-010-0006-8 |
| . |
| Date available:
|
2010-07-20T13:39:17Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140392 |
| . |
| Reference:
|
[1] Adams, R. A.: Sobolev Spaces.Academic Press New York (1975). Zbl 0314.46030, MR 0450957 |
| Reference:
|
[2] Chen, X., Nashed, Z., Qi, L.: Smoothing methods and semismooth methods for nondifferentiable operator equations.SIAM J. Numer. Anal. 38 (2000), 1200-1216. Zbl 0979.65046, MR 1786137, 10.1137/S0036142999356719 |
| Reference:
|
[3] Fučík, S., Kufner, A.: Nonlinear Differential Equations.Elsevier Amsterdam (1980). MR 0558764 |
| Reference:
|
[4] Kufner, A., John, O., Fučík, S.: Function Spaces.Academia Praha (1977). MR 0482102 |
| Reference:
|
[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. |
| Reference:
|
[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. |
| Reference:
|
[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. |
| Reference:
|
[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. |
| Reference:
|
[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. MR 2433726 |
| Reference:
|
[10] Sysala, S.: Unilateral elastic subsoil of Winkler's type: Semi-coercive beam problem.Appl. Math. 53 (2008), 347-379. Zbl 1199.49051, MR 2433726, 10.1007/s10492-008-0030-0 |
| Reference:
|
[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. MR 2433726 |
| Reference:
|
[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. MR 2433726 |
| . |
