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Abstract

I want to thank the organizers of this Congress for asking me to present the opening lecture. I thought it would be appropriate if I were to start with a rapid review of the field of thermal stresses and give some thoughts regarding an assessment (although necessarily a very personal one) of the present state of the field, and finally include guesses as to what the future might bring.

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References

  1. B.A. Boley, J.H. Weiner, and I.S. Tolins, “Thermal Stress Analysis for Aircraft Structures-Part II: Bibliography”, WACD Tech. Rep. pp. 56–102, Part I I, November 1955.

    Google Scholar 

  2. B.A. Boley, “Thermal Stresses Today”, Proc. 7th U.S. Nat. Congress of Applied Mechanics, Boulder, Colorado, June 3–7, 1974; publ. by ASME, New York (1974) pp. 99–107.

    Google Scholar 

  3. Duhamel, J.M.C., Second mémoire sur les phénomènes thermomécaniques, Journal de l’École Polytechnique, tome 15, cahier 25, 1837, pp. 1–57. This paper was read before the Academy of Sciences on February 23, 1835.

    Google Scholar 

  4. Fourier, J. Théorie analytique de la chaleur, Paris, 1822.

    Google Scholar 

  5. Navier, C.L.M.H., Mémoire sur les lois de l’équilibre et du movement des corps solides élastiques”, Mém. Inst. Nat. (1824). This paper was presented before the Academy of Sciences on May 14, 1921.

    Google Scholar 

  6. Almansi, E., “Use of the stress function in thermo-elasticity”, Mem. Reale Accad. Sci. Torino, Series 2, vol. 47, 1897,

    Google Scholar 

  7. Tedone, O. “The General Theroems of the Mathematical Theory of Elasticity”,Encyklopadie d. math. Wiss., Bd. IV, 4 Teilband, 1907, p. 68.

    Google Scholar 

  8. Muskhelishvili, N., “Relation between Thermal Stress in Steady Heat Flow and Dislocational Stress”, Bull. Elec. Tech. Inst., St. Petersburg, Vol. 13, 1916, p. 23.

    Google Scholar 

  9. Muskhelishvili, N., “Sur l’integr ation de l’equation biharmonique”, Bulletin de l’Academie des Sciences de Russie, VI Serie, Tome 13, 1919, pp. 663–686.

    Google Scholar 

  10. Goodier, J.N., Integration of thermoelastic equations, Phil. Mag. Vol. 23, 1937, p. 1017.

    Google Scholar 

  11. Hopkinson, J., Thermal Stresses in a Sphere, whose temperature is a function of r only, Messenger of Math., Vol. 8, 1879, p. 168.

    Google Scholar 

  12. Leon, A., On thermal stresses, Der Bautechniker, Bd. 26, 1904, p. 968.

    Google Scholar 

  13. _____, Stresses and deformations of a hollow cylinder under the assumption of a linear temperature distribution law, Zeit. f. Math u. Physik, Bd. 52, 1905, pp. 174–190.

    Google Scholar 

  14. Timoshenko, S., Bending and buckling of bi-metallic strips, J. Optical Society of America, vol. 11, 1925, p. 233.

    Article  Google Scholar 

  15. Signorini, A., Finite Thermo-elastic deformation, Proc. 3rd Int. Cong. Applied Mechanics, Stockholm, Vol. 2, 1930, pp. 80–89.

    Google Scholar 

  16. Biot, M.A., Propriété générale tensions thermiques en regime stationare dans corps cylindrique, Soc. Scientifiques de Bruxelles, serie B, Vol. 54, 1934, pp. 14–18.

    Google Scholar 

  17. Melan, E. and Parkus, H., Warmespannungen infolge stationà’rer Temperaturfelder, Springer, Vienne, 1953.

    Google Scholar 

  18. Alfrey, T., Mechanical Behavior of High Polymers, Interscience Publf, New York, 1948.

    Google Scholar 

  19. Tsien, H.S., “A Generalization of Alfrey1s Theorem for Viscoelastic Media”, Quart. Appl. Math., Vol. 8, 1950, pp. 104–106.

    MathSciNet  MATH  Google Scholar 

  20. Read, W.T., “Stress Analysis for Compressible ViscoelasticMaterials”, J. Appl. Physics, Vol. 21, 1950, ppc 671–674.

    Google Scholar 

  21. Freudenthal, A.M., On inelastic thermal stresses in flight structures, J. of the Aero. Sci., Vol. 21, 1954, pp. 772–778.

    MATH  Google Scholar 

  22. Prager, W., “Non-Isothermal Plastic Deformations”, Proc. Kon. Nederl, Adad van Wetenschappen, Series B, Vol. 61, no. 3, 1958, pp. 176–182.

    Google Scholar 

  23. Argyris, J.H., Thermal stress analysis and energy theorems, Great Britain Air Ministry, Aeronautical Research Council, Vol. 16, Dec. 1953, p. 489.

    Google Scholar 

  24. Hemp, W.S., Fundamental principles and methods of thermoelasticity Aircraft Engrng., Vol. 26, no. 302, Apr. 1954, pp. 126–127.

    Google Scholar 

  25. Danilovskaya, V.I., On a dynamical problem of thermoelasticity Prikl. Mat. Mekh., Vol. 16, no. 3, May/June 1952, pp. 341–344.

    Google Scholar 

  26. Boley, B., Thermally induced vibrations of beams, Journ. of the Aero. Sci., Vol. 23, No. 2, Feb. 1956, pp. 179–181.

    MathSciNet  MATH  Google Scholar 

  27. Goodier, J.N., “Thermal Stresses and Deformations”, J. Appl. Mech. Vol. 24, No. 3, 1957, pp. 467–474.

    MATH  Google Scholar 

  28. Boley, B.A., “The Calculation of Thermoelastic Beam Deflections by the Principle of Virtual Work”, J. Aero. Sci., Vol. 24, no. 2, 1957, pp. 139–141.

    MathSciNet  MATH  Google Scholar 

  29. _____, The determination of temperature, stresses and deflections in two-dimensional thermoelastic problems, Journ. of the Aero. Sci., Vol. 23, No. 1, January 1956, pp. 67–75. (Originally published as WADC Tech. Rept. 54 - 424, March 1954.

    Google Scholar 

  30. Boley, B.A. and Tolins, I.S., Thermoelastic stresses and deflections in thin-walled beams, WADC TR 54 - 426, December 1954.

    Google Scholar 

  31. Boley, B.A. and Weiner, J.H., Theory of Thermal Stresses, Wiley, New York, 1960.

    MATH  Google Scholar 

  32. Weiner, J.H., “A Uniqueness Theorem for Coupled Thermoelastic Problems”, Quart. Appl. Math., Vol. 15, no. 1, 1957, pp. 102–105.

    MathSciNet  MATH  Google Scholar 

  33. Mura, T., “Thermal Strains and Stresses in Transient State”, Prof. Second Jap. Congress Appl. Mech., 1952.

    Google Scholar 

  34. Ignaczak, J., “Thermal Displacements in an Elastic Semispace Due to Sudden Heating of the Boundary Plane”, Nedb. Arch. Mech. Stos., Vol. 9, 1957, p. 395.

    MathSciNet  Google Scholar 

  35. Deresiewicz, H., “Plane Waves in a Thermoelastic Solid”, J. Acoust. Soc. Am., Vol. 29, no. 2, 1957, pp. 204–209.

    Article  MathSciNet  Google Scholar 

  36. Boley, B.A. and Tolins, I.S., “Transient Coupled Thermoelastic Boundary-Value Problems in the Half-Space”, J. Appl. Mech., Vol. 29, no. 4, 1962, pp. 637–646.

    Google Scholar 

  37. Mindlin, R.D., “Investigations in the Mathematical Theory of Vibrations of Anisotropic Bodies”, U„S. Army Signal Corps Eng. Labs., Fort Monmouth, N.J., 1956, pp. 84ff.

    Google Scholar 

  38. Nowacki, W.,Dynamiczne zagadniena termosprezystości, Państ. Wydawn. Nauk., Warsaw, 1966. (English translation as Dynamic Problems of Thermoelasticity, Nordhoff, 1975.

    Google Scholar 

  39. Lord, H.W. and Shulman, U., “A generalized Dynamical Theory of Thermoelasticity”, J. Mech. Phys. Solids, Vol. 15, no. 5, 1967, pp. 299–309.

    Article  MATH  Google Scholar 

  40. Weiner, J.H. and Boley, B.A., “Elasto-Plastic Thermal Stresses in a Solidifying Slab”, J. Mech. Phys. Solids, Vol. 11, 1963, pp. 145–154.

    Article  MATH  Google Scholar 

  41. Friedman, E. and Boley, B.A., “Stresses and Deformations in Melting Plates”, J. Spacecraft and Rockets, Vol. 7, no. 3, 1970, pp. 324–333.

    Article  Google Scholar 

  42. Boley, B.A. “Temperature and Deformations in Rods and Plates Melting under Internal Heat Generation”, Prof. First Int. Cong. Struct. Mech. in Reactor Tech. (SMiRT-1), Berlin, 1971, vol. 5, Part 1, Paper L2/3.

    Google Scholar 

  43. Tadjbakhsh, I., “Thermal Stresses in an Elastic Half-Space with a Moving Boundary”AIAA Journ., Vol. 1, no. 1, 1963, pp. 214–215.

    Article  Google Scholar 

  44. Testa, R.B. and Boley, B.A., “Basic Thermoelastic Problems in Fiber-Reinforced Materials”, paper in Mechanics of Composite Materials, Pergamon Press, 1970. (Prof, of Fifth Symp. of Naval Struct. Mech., Philadelphia, Pennsylvania, 1967 ).

    Google Scholar 

  45. Biot, M.A., “Thermoelasticity and Irreve rsible Thermodynamics”, J. Appl. Phys., Vol. 27, no. 3, 1956, pp. 240–253.

    Article  MathSciNet  MATH  Google Scholar 

  46. Boley, B.A., “Bounds on the Maximum Thermoelastic Stress and Deflection in a Beam or Plate”, J. Appl. Mech., Vol. 23, no. 4, 1966, pp. 881–887.

    MathSciNet  Google Scholar 

  47. _____, “Estimate of Errors in Approximate Temperature and Thermal Stress Calculations”. Proc. Eleventh Int. Congress Appl. Mech., Springer, 1964.

    Google Scholar 

  48. Takeuti, Y., “Approximate Formulae for Temperature Distribution in a Heat-Generating Polygonal Cylinder with Central Circular Hole”, Nucl. Eng. Des., Vol. 8, 1968, pp. 241–246.

    Google Scholar 

  49. Boley, B.A., “Thermal Stresses” in Structural Mechanics, Edited by J.N. Goodier and J.J. Hoff, Pergamon Press, 1960, pp. 378–406 (Proc. fo First Symp. on Naval Struct. Mech., Stanford Univ., August 11–14, 1958 ).

    Google Scholar 

  50. _____, “On Thermal Stresses in Beams”, Int. J. Solids and Struct., Vol. 8, no. 4, 1972, pp. 571–579.

    Article  MATH  Google Scholar 

  51. _____, “On Thermal Stresses and Deflections in Thin Rings”, Int. J. Mech. Sci., Vol. 11, 1969, pp. 781–789.

    Article  Google Scholar 

  52. Ockendon, J.R. and Hodgkins, W.R., Moving Boundary Problems in Heat Flow and Diffusion, Clarendon Press, Oxford, 1975.

    MATH  Google Scholar 

  53. Wilson, D.G., Solomon, A.D. and Boggs, P.T., Moving Boundary Problems, Acad. Press, 1978.

    Google Scholar 

  54. Boley, B.A. and Hetnarski, R.B., “Propagation of Discontinuities in Coupled Thermoelastic Problems”, J. Appl. Mech., Vol. 35, no. 3, 1968, pp. 489–494.

    MATH  Google Scholar 

  55. Dundurs, J., “Distorsion of a Body Caused by Free Thermal Expansion”, Mech. Res. Communications, Vol. 1, no. 3, 1974, pp. 121–124.

    Article  Google Scholar 

  56. Tabakman, H.D. and Lin, Y.J., “Stresses and Displacements in Simply Supported Curved Plates Subjected to an Arbitrary Temperature Distribution”, J. of Thermal Str., Vol. 1, no. 2, 1978, pp. 183–191.

    Article  Google Scholar 

  57. Nowacki, W., “Some General Theorems of Thermopiezoelectricity”, J. Th. Str., Vol. 1, no. 2, 1978, pp. 171–182.

    Article  Google Scholar 

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© 1980 Plenum Press, New York

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Boley, B.A. (1980). Thermal Stresses: A Survey. In: Hasselman, D.P.H., Heller, R.A. (eds) Thermal Stresses in Severe Environments. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3156-8_1

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  • DOI: https://doi.org/10.1007/978-1-4613-3156-8_1

  • Publisher Name: Springer, Boston, MA

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