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Symmetry operators and general solutions of the equations of the linear theory of elasticity

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References

  1. P. F. Papkovich, “Expression of the general integral of the basic equations of the theory of elasticity in terms of harmonic functions,”Izv. Akad. Nauk SSSR, Ser. 7, Otd. Mat. Est. Nauk, No. 10, 1425–1435 (1932).

    Google Scholar 

  2. P. F. Papkovich, “A survey of several general solutions of the basic differential equations of a resting isotropic body,”Prikl. Mat. Mekh.,1, No. 1, 117–132 (1937).

    Google Scholar 

  3. P. F. Papkovich,Theory of Elasticity [in Russian], Oborongiz, Leningrad-Moscow (1939).

    Google Scholar 

  4. H. Neuber,Stress Concentration [Russian translation], OGIZ. Gostekhizdat, Leningrad-Moscow (1947).

    Google Scholar 

  5. Yu. A. Krutkov,Stress Function Tensor and General Solutions in the Static Theory of Elasticity [in Russian], Izd. Akad. Nauk SSSR, Moscow-Leningrad (1949).

    Google Scholar 

  6. B. G. Galerkin,Collection of Works [in Russian], Izd. Akad. Nauk SSSR, Moscow (1952), vol. 1.

    Google Scholar 

  7. E. N. Baida,General Solutions of the Theory of Elasticity and Problems on a Parallelepiped and a Cylinder [in Russian], Gosstroiizdat, Leningrad (1961).

    Google Scholar 

  8. A. S. Maliev, “On selection of functions in general solutions of the problem of equilibrium of an isotropic elastic body,” in:Proc. Leningrad Inst. of Railway Electric Eng., No. 4 (1952), pp. 180–244.

  9. N. I. Ostrosablin, “General representation of the solution of the equations of the linear theory of elasticity of an isotropic body,” in:Dynamics of Continuous Media [in Russian], Institute of Hydrodynamics, Novosibirsk,61 (1983), pp. 77–91.

    Google Scholar 

  10. N. I. Ostrosablin, “On a general solution of the equations of linear theory of elasticity,” in:Dynamics of Continuous Media [in Russian], Institute of Hydrodynamics, Novosibirsk,92 (1989), pp. 62–71.

    Google Scholar 

  11. K. Marguerre. “Ansätze zur Lösung der Grundgleichungen der Elastizitätstheorie,”Z. Angew. Math. Mech.,35, No. 6/7, 242–263 (1955).

    MATH  MathSciNet  Google Scholar 

  12. C. Truesdell, “Invariant and complete stress functions for general continua,”Arch. Ration. Mech. and Anal.,4, No. 1. 1–29 (1959).

    MathSciNet  Google Scholar 

  13. V. Novatskii.Theory of Elasticity [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  14. M. G. Slobodyanskii. “General forms of solutions of the elasticity equations for single- and multiple-connected regions expressed in terms of harmonic functions,”Prikl. Mat. Mekh.,18, No. 1, 55–74 (1954).

    MathSciNet  Google Scholar 

  15. M. G. Slobodyanskii, “On general and complete forms of solutions of the elasticity equations,”Prikl. Mat. Mekh.,23, No. 3, 468–482 (1959).

    MATH  Google Scholar 

  16. R. A. Eubanks and E. Sternberg, “On the completeness of the Boussinesq-Papkovich stress functions,”J. Ration. Mech. Anal.,5, No. 5, 735–746 (1956).

    MathSciNet  Google Scholar 

  17. P. M. Naghdi and C. S. Hsu, “On a representation of displacements in linear elasticity in terms of three stress functions,”J. Math. Mech.,10, No. 2, 233–245 (1961).

    MathSciNet  Google Scholar 

  18. M. E. Gurtin, “On Helmholtz's theorem and the completeness of the Papkovich-Neuber stress functions for infinite domains,”Arch. Ration. Mech. Anal.,9, No. 3, 225–233 (1962).

    MATH  MathSciNet  Google Scholar 

  19. M. Stippes. “Completeness of Papkovich potentials,”Quart. Appl. Math.,26, No. 4, 477–483 (1969).

    MATH  MathSciNet  Google Scholar 

  20. T. Tran-Cong and G. P. Steven, “On the representation of elastic displacement fields in terms of three harmonic functions,”J. Elast.,9, No. 3, 325–333 (1979).

    MathSciNet  Google Scholar 

  21. T. Tran-Cong, “On the completeness of the Papkovich-Neuber solution,”Quart. Appl. Math.,47, No. 4, 645–659 (1989).

    ADS  MATH  MathSciNet  Google Scholar 

  22. G. P. Yan and M. Z. Wang, “Somigliana formula and the completeness of Papkovich-Neuber and Boussinesq-Galerkin solutions in elasticity,”Mech. Res. Commun.,15, No. 2, 73–77 (1988).

    MathSciNet  Google Scholar 

  23. D. S. Chandrasekharaiah, “A complete solution in elastodynamics,”Acta Mech.,84, Nos. 1-4, 185–190 (1990).

    MATH  MathSciNet  Google Scholar 

  24. W. Wang and M. Z. Wang, “Constructivity and completeness of the general solutions in elastodynamics,”Acta Mech.,91, Nos. 3-4, 209–214 (1992).

    MathSciNet  Google Scholar 

  25. L. V. Ovsyannikov,Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  26. N. I. Ostrosablin and S. I. Senashov, “General solutions and symmetries of the equations of the linear theory of elasticity,”Dokl. Akad. Nauk SSSR,322, No. 3, 513–515 (1992).

    MathSciNet  Google Scholar 

  27. N. I. Ostrosablin, “General solutions and reduction of a system of equations of the linear theory of elasticity to diagonal form,”Prikl. Mekh. Tekh. Fiz.,34, No. 5, 112–122 (1993).

    MATH  MathSciNet  Google Scholar 

  28. Zhang Hong-qing and Yang Guang, “Constructions of the general solution for a system of partial differential equations with variable coefficients,”Appl. Math. Mech.,12, No. 2, 149–153 (1991).

    MathSciNet  Google Scholar 

  29. W. Miller, Jr.Symmetry and Separation of Variables [Russian translation], Mir, Moscow (1981).

    Google Scholar 

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  1. N. I. Ostrosablin
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Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 5, pp. 98–104, September–October, 1995.

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Ostrosablin, N.I. Symmetry operators and general solutions of the equations of the linear theory of elasticity. J Appl Mech Tech Phys 36, 724–729 (1995). https://doi.org/10.1007/BF02369286

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  • DOI: https://doi.org/10.1007/BF02369286

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