| Title:
|
Unilateral elastic subsoil of Winkler's type: Semi-coercive beam problem (English) |
| Author:
|
Sysala, Stanislav |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
347-379 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The mathematical model of a beam on a unilateral elastic subsoil of Winkler's type and with free ends is considered. Such a problem is non-linear and semi-coercive. The additional assumptions on the beam load ensuring the problem solvability are formulated and the existence, the uniqueness of the solution and the continuous dependence on the data are proved. The cases for which the solutions need not be stable with respect to the small changes of the load are described. The problem is approximated by the finite element method and the relation between the original problem and the family of approximated problems is analyzed. The error estimates are derived in dependence on the smoothness of the solution, the load and the discretization parameter of the partition. (English) |
| Keyword:
|
non-linear subsoil of Winkler's type |
| Keyword:
|
semi-coercive beam problem |
| Keyword:
|
existence |
| Keyword:
|
uniqueness |
| Keyword:
|
continuous dependence on data |
| Keyword:
|
finite element method |
| Keyword:
|
numerical quadrature |
| MSC:
|
49K05 |
| MSC:
|
49K15 |
| MSC:
|
49K27 |
| MSC:
|
49M25 |
| MSC:
|
65D30 |
| MSC:
|
74B20 |
| MSC:
|
74K10 |
| MSC:
|
74M15 |
| MSC:
|
74S05 |
| idZBL:
|
Zbl 1199.49051 |
| idMR:
|
MR2433726 |
| DOI:
|
10.1007/s10492-008-0030-0 |
| . |
| Date available:
|
2010-07-20T12:28:06Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140326 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
[12] Svobodová, I.: Cone decomposition of Hilbert space: Existence of weak solution for 1D problem.http://home1.vsb.cz/ svo19 (2005). |
| Reference:
|
[13] Sysala, S.: Problem with unilateral elastic subsoil of Winkler's type: Numerical methods.In: Proc 8th International Scientific Conference Applied Mechanics 2006, FAV ZČU Plzeň, Srní (2006), 85-86 Czech. MR 2433726 |
| Reference:
|
[14] Sysala, S.: On a dual method to a beam problem with a unilateral elastic subsoil of Winkler's type.In: Proc. Seminar on Numerical Analysis---SNA'07 Institute of Geonics AS CR Ostrava (2007), 95-100. MR 2433726 |
| . |
