| Title:
|
On an interaction of two elastic bodies: analysis and algorithms (English) |
| Author:
|
Svobodová, Ivona |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
333-357 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with existence and uniqueness results and with the numerical solution of the nonsmooth variational problem describing a deflection of a thin annular plate with Neumann boundary conditions. Various types of the subsoil and the obstacle which influence the plate deformation are considered. Numerical experiments compare two different algorithms. (English) |
| Keyword:
|
obstacle problem |
| Keyword:
|
variational formulation |
| Keyword:
|
semi-coercive problem |
| Keyword:
|
finite elements |
| Keyword:
|
semismooth Newton method |
| Keyword:
|
method of successive approximations |
| MSC:
|
65L10 |
| MSC:
|
74B99 |
| MSC:
|
74K10 |
| MSC:
|
74M20 |
| MSC:
|
74S05 |
| idZBL:
|
Zbl 1265.74053 |
| idMR:
|
MR2984607 |
| DOI:
|
10.1007/s10492-012-0020-0 |
| . |
| Date available:
|
2012-08-19T21:41:02Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142903 |
| . |
| Reference:
|
[1] Aubin, J.-P.: Applied functional analysis.Wiley-Interscience New York (2000). Zbl 0946.46001, MR 1782330 |
| 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] Drábek, P., Milota, J.: Lectures on Nonlinear Analysis.Vydavatelský Servis Plzeň (2004). Zbl 1078.47001 |
| Reference:
|
[4] Kufner, A.: Weighted Sobolev Spaces.Teubner Leipzig (1980). Zbl 0455.46034, MR 0664599 |
| Reference:
|
[5] Lagnese, J. E., Lions, J.-L.: Modelling Analysis and Control of Thin Plates.Mason Paris (1988). Zbl 0662.73039, MR 0953313 |
| Reference:
|
[6] Salač, P.: Optimal design of an elastic circular plate on a unilateral elastic foundation. II: Approximate poblems.ZAMM, Z. Angew. Math. Mech. 82 (2002), 33-42. MR 1878481, 10.1002/1521-4001(200201)82:1<33::AID-ZAMM33>3.0.CO;2-0 |
| Reference:
|
[7] Salač, P.: Shape optimization of elastic axisymmetric plate on an elastic foundation.Appl. Math. 40 (1995), 319-338. Zbl 0839.73036, MR 1331921 |
| Reference:
|
[8] 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 |
| . |
