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The elastic sphere under nonsymmetric loading

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Abstract

Existing solutions to boundary value problems arising from an elastic sphere subjected to a body force have been primarily restricted to axisymmetric, conservative loading. In this paper, a method for solving the displacement equations governing the static equilibrium of an elastic sphere subjected to an arbitrary body force and surface displacement is presented. The solutions are obtained in terms of three vector spherical harmonics and expressions for the displacement and stress fields are presented. Additionally, a short discussion indicating extension of these solutions to dynamic problems is included.

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References

  1. S.H. Advani and H.B. McClung, Asymmetric Response of an Elastic Sphere—A Rotation Head Injury Model.Advances in Bioengineering, The American Society of Mechanical Engineers (1974) pp. 73–75.

  2. J.M. Blatt and V.F. Weisskopf,Theoretical Nuclear Physics. New York: Wiley (1952).

    Google Scholar 

  3. M.E. Gurtin and Eli Sternberg, On the completeness of certain stress functions in the linear theory of elasticity.4th U.S. Nat. Cong. App. Mech. Proc. (1962) pp. 793–797.

  4. M.E. Gurtin and Eli Sternberg, On the first boundary value problem of linear elastostatics.Arch. Rational Mech. Anal. 6(3) (1960) 177–187.

    Google Scholar 

  5. M.E. Gurtin and Eli Sternberg, Theorems in linear elastostatics for exterior domains.Arch. Rational Mech. Anal. 8(2) (1961) 99–119.

    Google Scholar 

  6. E.L. Hill, The theory of vector spherical harmonics.Am. J. of Physics 22 (1954) 211–214.

    Google Scholar 

  7. A.E.H. Love,A Treatise on the Mathematical Theory of Elasticity. 4th edition. New York: Dover (1944).

    Google Scholar 

  8. A.I. Lur'e,Three Dimensional Problems of the Theory of Elasticity. New York: Interscience (1964).

    Google Scholar 

  9. P.M. Morse and H. Feshbach,Methods of Theoretical Physics, Vol. II. New York: McGraw-Hill (1953).

    Google Scholar 

  10. W.T. Reid,Ordinary Differential Equations. New York: John Wiley and Sons (1971).

    Google Scholar 

  11. H. Reismann, On the forced motion of elastic solids.Appl. Sci. Res. 18 (1967) 156–165.

    Google Scholar 

  12. I.S. Sokolnikoff,Mathematical Theory of Elasticity. 2nd edition. New York: McGraw-Hill (1965).

    Google Scholar 

  13. Eli Sternberg, R.A. Eubanks and M.A. Sadowsky, On the axisymmetry problem of elasticity theory for a region bounded by two concentric spheres.1st U.S. Cong. Appl. Mech. Proc. (1951) p. 209.

  14. C. Truesdell, Invariant and complete stress functions for general continua.Arch. Rational Mech. Anal. 4(1) (1959/60) 1–29.

    Google Scholar 

  15. K.C. Valanis and C.T. Sun, Axisymmetric wave propagation in a solid viscoelastic sphere.Int. J. Engng. Sci. 5 (1967) 939–956.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Southwest Texas State University, 78666, San Marcos, Texas, U.S.A.

    H. B. McClung

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  1. H. B. McClung
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Additional information

This research was supported in part by an Organized Research Grant, Southwest Texas State University, 1979.

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McClung, H.B. The elastic sphere under nonsymmetric loading. J Elasticity 21, 1–26 (1989). https://doi.org/10.1007/BF00040931

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  • DOI: https://doi.org/10.1007/BF00040931

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