| Title:
|
Post-buckling range of plates in axial compression with uncertain initial geometric imperfections (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
25-44 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The method of reliable solutions alias the worst scenario method is applied to the problem of von Kármán equations with uncertain initial deflection. Assuming two-mode initial and total deflections and using Galerkin approximations, the analysis leads to a system of two nonlinear algebraic equations with one or two uncertain parameters-amplitudes of initial deflections. Numerical examples involve (i) minimization of lower buckling loads and (ii) maximization of the maximal mean reduced stress. (English) |
| Keyword:
|
elastic plates |
| Keyword:
|
Kármán equations |
| Keyword:
|
uncertain initial deflections |
| Keyword:
|
worst scenario |
| MSC:
|
35A35 |
| MSC:
|
35J65 |
| MSC:
|
65N30 |
| MSC:
|
74G15 |
| MSC:
|
74G60 |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 1090.74579 |
| idMR:
|
MR1876490 |
| DOI:
|
10.1023/A:1021702816894 |
| . |
| Date available:
|
2009-09-22T18:08:33Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134483 |
| . |
| Reference:
|
[1] Y. Ben-Haim, I. E. Elishakoff: Convex Models of Uncertainties in Applied Mechanics. Studies in Appl. Mech. 25.Elsevier, Amsterdam, 1990. |
| Reference:
|
[2] V. M. Broude: Limit States of Steel Beams.Nauka, Moskva, 1953. (Russian Russian) |
| Reference:
|
[3] I. E. Elishakoff, G. Q. Cai and J. H. Starnes, Jr.: Non-linear buckling of a column with initial imperfection via stochastic and non-stochastic convex models.Int. J. Non-Linear Mechanics 29 (1994), 71–82. 10.1016/0020-7462(94)90053-1 |
| Reference:
|
[4] I. Hlaváček: Einfluss der Form der Anfangskrümmung auf das Ausbeulen der gedrückten rechteckigen Platte.Acta Technica ČSAV (1962), 174–206. (German) |
| Reference:
|
[5] I. Hlaváček: Reliable solution of elliptic boundary value problems with respect to uncertain data.Proc. 2nd WCNA, Nonlin. Anal., Theory, Meth. & Appls. 30 (1997), 3879–3890. MR 1602891 |
| Reference:
|
[6] W. J. Supple: Changes of wave-form of plates in the post-buckling range.Int. J. Solids Structures 6 (1970), 1243–1258. 10.1016/0020-7683(70)90100-9 |
| Reference:
|
[7] S. P. Timoshenko, J. M. Gere: Theory of Elastic Stability.2nd edn., McGraw Hill, Burr Ridge, 1961. MR 0134026 |
| Reference:
|
[8] A. S. Volmir: Stability of Deformable Systems.Nauka, Moskva, 1967, 2nd edn. (Russian) |
| . |
