A uniqueness theorem for thermoelastic shells with generalized boundary conditions
Author:
M. B. Rubin
Journal:
Quart. Appl. Math. 44 (1986), 431-440
MSC:
Primary 73U05; Secondary 73L99
DOI:
https://doi.org/10.1090/qam/860896
MathSciNet review:
860896
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Abstract: The uniqueness of the solution of initial, mixed boundary value problems for linear thermoelastic shells is reconsidered within the context of recent developments in the thermomechanical theory of a Cosserat surface [4]. Fairly general boundary conditions are considered which allow mechanical contact with linear elastic media and thermal radiation on the boundary curve of the Cosserat surface and on the major surfaces of the shell.
P. M. Naghdi, The theory of shells and plates, in S. Flügge’s Handbuch der Physik, vol. VIa/2 (C. Truesdell, ed.), pp. 425–640, Springer-Verlag, Berlin (1972)
- A. E. Green and P. M. Naghdi, On thermodynamics and the nature of the second law, Proc. Roy. Soc. London Ser. A 357 (1977), no. 1690, 253–270. MR 462241, DOI https://doi.org/10.1098/rspa.1977.0166
A. E. Green and P. M. Naghdi, The second law of thermodynamics and cyclic processes, J. Appl. Mech. 45, 487–492 (1978)
- A. E. Green and P. M. Naghdi, On thermal effects in the theory of shells, Proc. Roy. Soc. London Ser. A 365 (1979), no. 1721, 161–190. MR 527033, DOI https://doi.org/10.1098/rspa.1979.0012
- P. M. Naghdi and J. A. Trapp, A uniqueness theorem in the theory of Cosserat surface, J. Elasticity 2 (1972), no. 1, 9–20 (English, with French summary). MR 475126, DOI https://doi.org/10.1007/BF00045690
- A. E. Green and P. M. Naghdi, On uniqueness in the linear theory of elastic shells and plates, J. Mécanique 10 (1971), 251–261 (English, with French summary). MR 278593
P. M. Naghdi, Finite deformation of elastic rods and shells, Proc. IUTAM Symp. Finite Elasticity, Bethlehem, Pa., 1980 (D. E. Carlson and R. T. Shield, eds.), pp. 47–103, Martinus Nijhoff, The Hague (1982)
- Bruno A. Boley and Jerome H. Weiner, Theory of thermal stresses, John Wiley & Sons, Inc., New York London, 1960. MR 0112414
A. E. Green and P. M. Naghdi, A theory of laminated composite plates, IMA J. Appl. Math. 29, 1–23 (1982)
P. M. Naghdi, The theory of shells and plates, in S. Flügge’s Handbuch der Physik, vol. VIa/2 (C. Truesdell, ed.), pp. 425–640, Springer-Verlag, Berlin (1972)
A. E. Green and P. M. Naghdi, On thermodynamics and the nature of the second law, Proc. Roy. Soc. London Ser. A 357, 253–270 (1977)
A. E. Green and P. M. Naghdi, The second law of thermodynamics and cyclic processes, J. Appl. Mech. 45, 487–492 (1978)
A. E. Green and P. M. Naghdi, On thermal effects in the theory of shells, Proc. Roy. Soc. London Ser. A 365, 161–190 (1979)
P. M. Naghdi and J. A. Trapp, A uniqueness theorem in the theory of Cosserat surfaces, J. Elast. 2, 9–20 (1972)
A. E. Green and P. M. Naghdi, On uniqueness in the linear theory of elastic shells and plates, J. Méc. 10, no. 2, 251–261 (1971)
P. M. Naghdi, Finite deformation of elastic rods and shells, Proc. IUTAM Symp. Finite Elasticity, Bethlehem, Pa., 1980 (D. E. Carlson and R. T. Shield, eds.), pp. 47–103, Martinus Nijhoff, The Hague (1982)
B. A. Boley and J. H. Weiner, Theory of thermal stresses, Wiley, New York (1960)
A. E. Green and P. M. Naghdi, A theory of laminated composite plates, IMA J. Appl. Math. 29, 1–23 (1982)
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Article copyright:
© Copyright 1986
American Mathematical Society
