| Title:
|
On coupled thermoelastic vibration of geometrically nonlinear thin plates satisfying generalized mechanical and thermal conditions on the boundary and on the surface (English) |
| Author:
|
Wenk, Hans-Ullrich |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
27 |
| Issue:
|
6 |
| Year:
|
1982 |
| Pages:
|
393-416 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The vibration problem in two variables is derived from the spatial situation (a plate as a three-dimensional body) on the basis of geometrically nonlinear plate theory (using Kármán's hypothesis) and coupled linear thermoelasticity. That leads to coupled strongly nonlinear two-dimensional equilibrium and heat conducting equations (under classical mechanical and thermal boundary conditions).
For the generalized problem with subgradient conditions on the boundary and in the domain (including also classical conditions), existence and dependence of the weak variational solution on the given data is proved. (English) |
| Keyword:
|
nonlinear dynamical |
| Keyword:
|
kinematical |
| Keyword:
|
linear constitutive thermoelastic |
| Keyword:
|
coupled heat conduction equations |
| Keyword:
|
spatial problem |
| Keyword:
|
Kirchhoff’s and von Kármán’s hypothesis |
| Keyword:
|
twodimensional equations |
| Keyword:
|
generalized problem with subgradient conditions on boundary |
| Keyword:
|
existence of solution |
| Keyword:
|
continuous dependence on given data |
| MSC:
|
35K05 |
| MSC:
|
49J40 |
| MSC:
|
73K10 |
| MSC:
|
73U05 |
| MSC:
|
74A15 |
| MSC:
|
74F05 |
| MSC:
|
74H45 |
| MSC:
|
74K20 |
| MSC:
|
74S05 |
| MSC:
|
80A20 |
| idZBL:
|
Zbl 0506.73012 |
| idMR:
|
MR0678110 |
| DOI:
|
10.21136/AM.1982.103987 |
| . |
| Date available:
|
2008-05-20T18:20:21Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103987 |
| . |
| Reference:
|
[1] B. A. Boley J. H. Weiner: Theory of Thernal Stresses.Wiley & Sons, Inc., New York 1960. MR 0112414 |
| Reference:
|
[2] C. Dafermos: On the Existence and the Asymptotic Stability of Solutions to the Equations of Linear Thermoelasticity.Arch. Rat. Mech. Anal., 29 (1968), 241 - 271. Zbl 0183.37701, MR 0233539, 10.1007/BF00276727 |
| Reference:
|
[3] G. Duvaut J. L. Lions: Problèmes unilateraux dans la théorie de la flexion forte des plaques, I: Le cas stationaire.J. Méch., 13 (1974), 51 - 74. MR 0375885 |
| Reference:
|
[4] G. Duvaut J. L. Lions: Problèmes unilateraux dans la théorie de la flexion forte des plaques, II: Le cas d'évolution.J. Méch., 13 (1974), 245-266. MR 0375886 |
| Reference:
|
[5] G. Duvaut: Inéquations en thermoélasticité et magnétohydrodynamique.Arch. Rat. Mech. Anal., 46 (1972), 241-279. Zbl 0264.73027, MR 0346289, 10.1007/BF00250512 |
| Reference:
|
[6] G. Duvaut: Les inéquations en méchanique et en physique.Dunod, Paris 1972. MR 0464857 |
| Reference:
|
[7] S. A. Gribanov V. N. Ogibalov: Thermostability of Plates and Shells.(in Russian). Izd. Mosc. Univ. 1968. |
| Reference:
|
[8] I. Hlaváček J. Naumann: Inhomogeneous Boundary Value Problems for the von Kármán's Equations, I.Apl. Matem., 19 (1974), 253 - 269. MR 0377307 |
| Reference:
|
[9] I. Hlaváček J. Naumann: Inhomogeneous Boundary Value Problems for the von Kármán's Equations, II.Apl. Matem., 20 (1975), 280-297. MR 0377308 |
| Reference:
|
[10] I. Hlaváček J. Nečas: On Inequalities of Korn's Type, I: Boundary value problems for elliptic systems of partial differential equations, II: Applications to linear elasticity.Arch. Rat. Mech. Anal., 36 (1970), 305-334. MR 0252844 |
| Reference:
|
[11] R. Hünlich J. Naumann: On General Boundary Value Problems and Duality in Linear Elasticity, I.Apl. Matem., 23 (1978). MR 0489538 |
| Reference:
|
[12] J. L. Lions E. Magénès: Problèmes aux limites non homogènes et applications.vol. 1. Dunod, Paris 1968. MR 0247243 |
| Reference:
|
[13] J. Naumann: On Some Unilateral Boundary Value Problems for the von Kármán's Equations, part I: The coercive case.Apl. Matem., 20 (1975), 96-125. MR 0437916 |
| Reference:
|
[14] J. Naumann: On Some Unilateral Boundary Value Problems in Non-linear Plate Theory.Beiträge zur Analysis, 10 (1977), 119-134. MR 0489204 |
| Reference:
|
[15] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| Reference:
|
[16] W. Nowacki: Theory of Elasticity.(in Russian). Mir, Moscow 1975. Zbl 0385.73007, MR 0436704 |
| Reference:
|
[17] W. Nowacki: Thermoelasticity.Intern. Series of Monographs on Aeronautics and Astronautics, Div. I: Solid and Structural Mechanics, Pergamon Press 1962. |
| Reference:
|
[18] W. Nowacki: Dynamical Problems of Thermoelasticity.(in Russian). Mir, Moscow 1970. |
| Reference:
|
[19] K. Washizu: Variational Methods in Elasticity and Plasticity.Pergamon Press 1974. MR 0391680 |
| Reference:
|
[20] H.-U. Wenk: Functional-analytical Investigations on Unilateral Problems in Plate Theory.(in German). Thesis A, Humboldt-Univ., Berlin 1978. |
| . |
