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Construction of Exact Solutions to Three-Dimensional Elastic Problems in Stresses

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Abstract

A method is proposed to construct solutions to differential elastic equations in stresses (Beltrami compatibility equations and equilibrium equations). The method is based on potential theory and allows us to solve efficiently boundary-value problems of elastic theory. As an example, the second boundary-value problem for an elastic half-space is considered

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REFERENCES

  1. N. M. Borodachev, “One representation of the Beltrami compatibility equations,” Prikl. Mekh., 34, No. 2, 86–91 (1998).

    Google Scholar 

  2. Yu. A. Krutkov, The Tensor of a Stress Function and General Static Solutions in Elastic Theory [in Russian], Izd. AN SSSR, Moscow-Leningrad (1949).

    Google Scholar 

  3. A. I. Lurie, The Theory of Elasticity [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  4. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press (1959).

  5. W. Nowacki, The Theory of Elasticity [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  6. I. N. Sneddon and D. S. Berry, The Classical Theory of Elasticity, Vol. 6, Flugge Encyclopedia of Physics, Springer-Verlag, Berlin (1958).

    Google Scholar 

  7. L. N. Sretenskii, The Theory of Newtonian Potential [in Russian], Gostekhteorizdat, Moscow-Leningrad (1946).

    Google Scholar 

  8. H. G. Hahn, Elastizitätstheorie. Grundlagen der Linearen Theorie und Anwendungen auf Eindimensionale, Ebene und Räumliche Probleme, B. G. Teubner, Stuttgart (1985).

    Google Scholar 

  9. N. M. Borodachev, “Impression of a punch with a flat square base into an elastic half-space,” Int. Appl. Mech., 35, No. 10, 989–994 (1999).

    Google Scholar 

  10. A. P. Prusakov, “On displacement functions in problems of elasticity theory,” Int. Appl. Mech., 35, No. 5, 488–492 (1999).

    Google Scholar 

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Borodachev, N.M. Construction of Exact Solutions to Three-Dimensional Elastic Problems in Stresses. International Applied Mechanics 37, 762–768 (2001). https://doi.org/10.1023/A:1012459123490

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