| Title:
|
On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs (English) |
| Author:
|
Bock, Igor |
| Author:
|
Lovíšek, Ján |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
23 |
| Issue:
|
2 |
| Year:
|
1978 |
| Pages:
|
132-149 |
| Summary lang:
|
English |
| Summary lang:
|
Slovak |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The existence and the unicity of a weak solution of the boundary value problem for a shallow shell reinforced with stiffening ribs is proved by the direct variational method. The boundary value problem is solved in the space $W(\Omega)\subset H^1_0(\Omega)\times H^1_0(\Omega) \times H^2_0(\Omega)$, on which the corresponding bilinear form is coercive. A finite element method for numerical solution is introduced. The approximate solutions converge to a weak solution in the space $Q(\Omega)$. (English) |
| Keyword:
|
numerical analysis |
| Keyword:
|
weak solution |
| Keyword:
|
boundary value problem |
| Keyword:
|
shallow shell |
| Keyword:
|
variational problem |
| Keyword:
|
finite elements |
| MSC:
|
49L99 |
| MSC:
|
65N30 |
| MSC:
|
74K25 |
| MSC:
|
74S05 |
| idZBL:
|
Zbl 0397.73073 |
| idMR:
|
MR0495557 |
| DOI:
|
10.21136/AM.1978.103737 |
| . |
| Date available:
|
2008-05-20T18:09:08Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103737 |
| . |
| Reference:
|
[1] S. Agmon: Lectures on elliptic boundary value problems.New York, 1965. Zbl 0142.37401, MR 0178246 |
| Reference:
|
[2] I. Hlaváček J. Nečas: On inequalities of Korn's Type I. in boundary value problems for elliptic systems of partial differential equations.Arch. Rat. Mech. Annal. 36(1970), 305-311. MR 0252844 |
| Reference:
|
[3] J. Haslinger: Sur la solution d'un probleme de la plaque.Apl. mat. 19 (1974), No 5, 316-326. Zbl 0324.73049, MR 0369902 |
| Reference:
|
[4] J. L. Lions E. Magenes: Problems aux limites non homogenes et applications.Volume I. Paris 1968. |
| Reference:
|
[5] J. Lovíšek: A weak solution of statically nonlinear problem for shallow shells considering the wind action.Scientific research, SVŠT Bratislava, 1975 (in Slovak). |
| Reference:
|
[6] A. G. Nazarov: Some contact problems of the theory of shells.(in Russian), DAN Arm. SSR, Vol. 9, No. 2, 1948. |
| Reference:
|
[7] A. G. Nazarov: Foundations of the theory and the method of computing shallow shells.(in Russian), Moscow, 1966. |
| Reference:
|
[8] J. Nečas: Les méthodes directes en theorie des équations elliptiques.Academia, Praha, 1967. MR 0227584 |
| Reference:
|
[9] J. T. Oden J. N. Ready: Variational methods in theoretical mechanics.Springer Verlag, 1976. MR 0478957 |
| Reference:
|
[10] G. N. Sawin N. P. Fleischman: Plates and shells with stiffening ribs.(in Russian). Kiev, 1964. |
| Reference:
|
[11] P. Seide: Small elastic deformations of thin shells.Noordhoff International Publishing Leyden, 1975. Zbl 0313.73070, MR 0403382 |
| Reference:
|
[12] G. Strang Y. Fix: An analysis of the finite element method.Prentice Hall Inc., 1973. MR 0443377 |
| . |
