| Title:
|
Reliable solution of an elasto-plastic Reissner-Mindlin beam for Hencky's model with uncertain yield function (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
223-237 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We apply the method of reliable solutions to the bending problem for an elasto-plastic beam, considering the yield function of the von Mises type with uncertain coefficients. The compatibility method is used to find the moments and shear forces. Then we solve a maximization problem for these quantities with respect to the uncertain input data. (English) |
| Keyword:
|
elasto-plastic beams |
| Keyword:
|
Hencky’s model of plasticity |
| Keyword:
|
Mindlin-Timoshenko beam |
| Keyword:
|
uncertain data |
| MSC:
|
49A29 |
| MSC:
|
73E99 |
| MSC:
|
73K05 |
| MSC:
|
74C05 |
| MSC:
|
74K10 |
| MSC:
|
74P10 |
| idZBL:
|
Zbl 1042.74533 |
| idMR:
|
MR1620616 |
| DOI:
|
10.1023/A:1023228608356 |
| . |
| Date available:
|
2009-09-22T17:57:55Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134386 |
| . |
| Reference:
|
[1] Ekeland, I., Temam, R.: Convex Analysis and Variational Problems.North-Holland, Amsterdam, 1976. MR 0463994 |
| Reference:
|
[2] Hlaváček, I.: Reliable solutions of elliptic boundary problems with respect to uncertain data. Proceedings of the WCNA-96.Nonlinear Analysis, Theory, Methods & Applications 30 (1997), 3879–3890. MR 1602891 |
| Reference:
|
[3] Hlaváček, I.: Reliable solution of a quasilinear nonpotential elliptic problem of a nonmonotone type with respect to the uncertainty in coefficients.J. Math. Appl. 212 (1997), 452–466. MR 1464890 |
| Reference:
|
[4] Hlaváček, I.: Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function.Appl. Math. 41 (1996), 447–466. MR 1415251 |
| Reference:
|
[5] Hlaváček, I.: Reliable solution of an elasto-plastic torsion problem.(to appear). MR 1857675 |
| Reference:
|
[6] Hlaváček, I.: Reliable solution of a Signorini contact problem with friction, considering uncertain data.(to appear). MR 1731015 |
| Reference:
|
[7] Hlaváček, I., Lovíšek, J.: Optimal design of an elastic or elasto-plastic beam with unilateral elastic foundation and rigid supports.Z. Angew. Math. Mech. 72 (1992), 29–43. MR 1148885, 10.1002/zamm.19920720104 |
| Reference:
|
[8] Nečas, J., Hlaváček, I.: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier, Amsterdam, 1981. MR 0600655 |
| Reference:
|
[9] Lagnese, J. E., Lions, J.-L.: Modelling Analysis and Control of Thin Plates.Masson, Paris and Springer-Verlag, Berlin, 1989. MR 0953313 |
| Reference:
|
[10] Neal, B. G.: Structural Theorems and Their Applications.Pergamon Press, Oxford, 1964. Zbl 0142.23603 |
| Reference:
|
[11] Rakowski, J.: The interpretation of the shear locking in beam elements.Comput. & Structures 37 (1990), 769-776. 10.1016/0045-7949(90)90106-C |
| . |
