Abstract
We consider a problem of thermal stresses in cylindrical Cosserat elastic shells made from a material with voids. The cylindrical shells have arbitrary cross-sections. The problem consists in finding the equilibrium of the shell under the action of a given temperature distribution. We assume that the temperature field is independent of the axial coordinate and we determine a closed-form solution expressed in terms of the displacement vector and porosity field.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Naghdi P M (1972) The Theory of Shells and Plates. In: C. Truesdell (ed), Handbuch der Physik, Vol. VI a/2, pp. 425–640, Springer-Verlag, Berlin Heidelberg New York
Rubin M B (2000) Cosserat Theories: Shells, Rods, and Points. Kluwer Academic Publishers, Dordrecht
Green A E, Naghdi P M (1979) On thermal effects in the theory of shells. Proc. R. Soc. Lond. A365: 161–190
Bîrsan M (2006) On the theory of elastic shells made from a material with voids. Int. J. Solids Struct. 43: 3106–3123
Ciarlet P G (2000) Mathematical Elasticity, Vol. III: Theory of Shells. North-Holland, Amsterdam
Bîrsan M (2008) Inequalities of Korn’s type and existence results in the theory of Cosserat elastic shells. J. Elasticity 90: 227–239
Bîrsan M (2006) Several results in the dynamic theory of thermoelastic Cosserat shells with voids. Mech. Res. Comm. 33: 157–176
Rubin M B, Benveniste Y (2004) A Cosserat shell model for interphases in elastic media. J. Mech. Phys. Solids 52: 1023–1052
Bîrsan M (2006) On a thermodynamic theory of porous Cosserat elastic shells. J. Therm. Stresses 29: 879–900
Nunziato J W, Cowin S C (1979) A nonlinear theory of elastic materials with voids. Arch. Ration. Mech. An. 72: 175–201
Capriz G, Podio-Guidugli P (1981) Materials with spherical structure. Arch. Ration. Mech. An. 75: 269–279
Vekua I N, Rukhadze A K (1933) Torsion problem for a circular cylinder reinforced by a longitudinal circular rod (in Russian). Izv. Akad. Nauk SSSR 3: 1297–1308
Lomakin V A (1976) Theory of Nonhomogeneous Elastic Bodies (in Russian). MGU, Moscow
Hatiashvili G M (1983) Almansi-Michell Problems for Homogeneous and Composed Bodies (in Russian). Izd. Metzniereba, Tbilisi
Ieşan D (1987) Saint-Venant’s Problem. Lect. Notes Math., no. 1279, Springer-Verlag, Berlin
Bîrsan M (2004) The solution of Saint-Venant’s problem in the theory of Cosserat shells. J. Elasticity 74: 185–214
Bîrsan M (2006) Extension, bending and torsion of cylindrical Cosserat shells made from a porous elastic material. In: CD-ROM Proceedings of the 3rd European Conference on Computational Mechanics (Portugal, Lisbon, 5–8 June 2006), 18pp., ISBN 978-1-4020-4994-1, Springer, Dordrecht
Ieşan D (2007) Thermal stresses in inhomogeneous porous elastic cylinders. J. Therm. Stresses 30: 145–164
Vrabie I I (2004) Differential Equations: An Introduction to Basic Concepts, Results and Applications. World Scientific, New Jersey
Ieşan D (2004) Thermoelastic Models of Continua. Kluwer Academic Publishers, Dordrecht Boston London
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media B.V.
About this paper
Cite this paper
Bîrsan, M. (2008). On a Problem of Thermal Stresses in the Theory of Cosserat Elastic Shells with Voids. In: Jaiani, G., Podio-Guidugli, P. (eds) IUTAM Symposium on Relations of Shell Plate Beam and 3D Models. IUTAM Bookseries, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8774-5_6
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8774-5_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8773-8
Online ISBN: 978-1-4020-8774-5
eBook Packages: EngineeringEngineering (R0)