End effects in thermoelasticity

Mathematical Methods in the Applied Sciences

Volumn 24, Issue 2, 2001, Pages 93-102

  Quintanilla, R ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CYLINDERS (SHAPES); POLYNOMIALS; PROBLEM SOLVING;

END EFFECTS; SAINT-VENANT PRINCIPLE; SPATIAL ESTIMATES; THERMOELASTODYNAMICS;

THERMOELASTICITY;

EID: 0035114169     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/1099-1476(20010125)24:2<93::AID-MMA199>3.0.CO;2-N     Document Type: Article

References (29)

1. Galdi GP, Knops RJ, Rionero S. Asymptotic behaviour in the nonlinear elastic beam. Archives for Rational Mechanics and Analysis 1985; 87:305-318.
2. Knops RJ, Payne LE. A Saint-Venant Principle for nonlinear elasticity. Archives for Rational Mechanics and Analysis 1983; 81:1-12.
3. Kondratiev VA, Oleinick OA. Estimates for solutions of the Dirichlet problem for the biharmonic equation in a neighbourhood of an irregular boundary point and in a neighbourhood of infinity. Saint-Venant's principle. Proceedings of the Royal Society of Edinburgh 1983; 93A:327-343.
4. Oleinick OA, Yosifian GA. On the behavior at infinity of solutions of second order elliptic equations in domains with noncompact boundary. Mathematics of USSR Sbornik 1981; 40:527-548.
5. Oleinick OA, Yosifian GA. On the asymptotic behaviour at infinity of solutions in linear elasticity. Archives for Rational Mechanics and Analysis 1982; 78:29-53.
6. Toupin RA. Saint-Venant's principle. Archives for Rational Mechanics and Analysis 1965; 18:83-96.
7. Boley BA. Some observations on Saint-Venant's principle. Proceedings of the 3rd U.S. National Congress on Applied Mechanics ASME, New York, 1958; 259-264.
8. Morgan CO, Payne LE, Wheeler LT. Spatial decay estimates in transient heat conduction. Quarterly Applied Mathematics 1984; XLII:119-127.
9. Knowles JK. On the spatial decay of solutions of the heat equation. Journal of Applied Mathematics and Physics 1971; 22:1050-1056.
10. Flavin JN, Knops RJ, Payne LE. Energy bounds in dynamical problems for a semi-infinite elastic beam. Elasticity: Mathematical Methods and Applications. Ellis-Horwood: Chichester, 1989; 101-111.
11. Chirita S, Quintanilla R. Saint-Venant's principle in linear elastodynamics. Journal of Elasticity 1996; 42:201-215.
12. Chirita S, Quintanilla R. Spatial decay estimates of Saint-Venant type in generalized thermoelasticity. International Journal of Engineering and Science 1996; 34:299-311.
13. Chirita S, Quintanilla R. Spatial estimates in the dynamic theory of linear elastic materials with memory. European Journal of Mechanics A/Solids 1997; 16:723-736.
14. Borrelli A, Patria, MC. Energy bounds for a mixture of two linear elastic solids occupying a semi-infinite cylinder. Acta Mechanica 1995; 109:191-206.
15. Borrelli A, Patria, MC. Energy bounds in dynamic problems for a semi-infinite magnetoelastic beam. Journal of Applied Mathematics and Physics 1996; 47:880-893.
16. Bofill F, Quintanilla R. Spatial estimates for dynamical problems in several elasticity theories. Ricerche di Matematica 1997; XLVI:425-441.
17. Quintanilla R. A spatial decay estimate for the hyperbolic heat equation. SIAM Journal on Mathematical Analysis 1996; 27:423-435.
18. Quintanilla R. Phragmen-Lindelof alternative in nonlinear viscoelasticity. Nonlinear Analysis 1998; 34:7-16.
19. Horgan CO. Recent developments concerning Saint-Venant's Principle: an update. Applied Mechanics Reviews 1989; 42:295-303.
20. Horgan CO. Decay estimates for boundary-value problems in linear and nonlinear continuum mechanics. Mathematical Problems in Elasticity, Vol. 23, Russo R (ed.). World Scientific: Singapore, 1996; 48-89.
21. Horgan CO. Recent developments concerning Saint-Venant's Principle: a second update. Applied Mechanics Reviews 1996; 49:101-111.
22. Horgan CO, Knowles JK. Recent developments concerning Saint-Venant's Principle. Advances in Applied Mechanics, Hutchinson JW, Wu TY (eds). Academic Press: New York, 1983; 179-269.
23. Chirita S. Saint-Venant's principle in linear thermoelasticity. Journal of Thermal Stresses 1998; 18:485-496.
24. Chirita S. A Phragmen-Lindelof principle in dynamic linear thermoelasticity. Journal of Thermal Stresses 1997; 20:505-516.
25. Chirita S, Ciarletta M. Time-weighted surface power function method in linear thermoelasticity. In Thermal Stresses' 99, 3rd International Congress on Thermal Stresses. Skrzypek JJ, Hetnarski RB (eds). Krakow, 1999; 587-590.
26. Sokolnikoff IS, Redheffer RM. Mathematics of physics and modern engineering (2nd edn). McGraw-Hill: New York, 1966.
27. Horgan CO, Quintanilla R. Spatial decay of transient end effects in functionally graded heat conducting materials. Quarterly Applied Mathematics, accepted.
28. Payne LE, Schaefer PW, Song JC. Growth and decay results in heat conduction problems with nonlinear boundary conditions. Nonlinear Analysis 1999; 35:269-286.
29. Quintanilla R. Spatial behaviour for nonlinear heat equations. Mathematical Models and Methods in Applied Sciences 1997; 7:633-647.