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On a boundary value problem for an elastic dielectric half-plane

Über ein Randwertproblem für eine elastische, dielektrische Halbebene

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Summary

Using Papkovitchtype representations for the displacement and polarization vectors and Fourier transforms, a general solution to boundary value problems of a half plane subjected to an arbitrary charge distribution is constructed within Mindlin's theory of elastic dielectrics. Explicit expressions for various mechanical and electric potentials are obtained for a point charge located on the boundary of the elastic dielectric half-space.

Zusammenfassung

Auf der Basis von Mindlins Theorie des elastischen Dielektrikums und mit Benutzung der Papkovitch-Darstellungen für Verschiebungs- und Polarisationsvektoren wird mit Hilfe von Fourier-Transformationen eine allgemeine Lösung für Randwertprobleme einer Halbebene mit einer beliebigen Ladungsverteilung gefunden. Es werden explizite Ausdrücke für verschiedene mechanische und elektrische Potentiale für eine Punktladung an der Berandung des elastischen, dielektrischen Halbraums erhalten.

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References

  1. Toupin, R. A.: The elastic dielectric. J. Ration. Mech. Analysis5, 849–915 (1956).

    Google Scholar 

  2. Eringen, A. C.: On the foundations of electroelastostatics. Int. J. Engng. Sci.1, 127–153 (1963).

    Google Scholar 

  3. Mindlin, R. D.: Polarization gradient in elastic dielectrics. Int. J. Solids Struct.4, 637–642 (1968).

    Google Scholar 

  4. Suhubi, E. S.: Elastic dielectrics with polarization gradient. Int. J. Engng. Sci.7, 993–997 (1969).

    Google Scholar 

  5. Schwartz, J.: Solutions of equations of equilibrium of elastic dielectrics, stress functions, concentrated forces, surface energy. Int. J. Solids Struct.5, 1209–1220 (1969).

    Google Scholar 

  6. Chowdhury, K. L., Glockner, P. G.: Some problems in plane elastic dielectrics. J. Elasticity6, 295–311 (1976).

    Google Scholar 

  7. Gradshteyn, I. S., Ryzhik, I. M.: Tables of integrals, series and products. Academic Press. 1965.

  8. Achenbach, J. D.: Wave propagation in elastic solids. North-Holland. 1973.

  9. Gou, P. F.: Effects of gradient of polarization on stress concentration at a cylindrical hole in an elastic dielectric. Int. J. Solids Struct.7, 1467–1476 (1971).

    Google Scholar 

  10. Mindlin, R. D.: Elasticity, piezoelectricity and crystal lattice dynamics. J. Elasticity2, 217–282 (1972).

    Google Scholar 

  11. Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Tables of integral transforms, Vol. 1, p. 138. 1954.

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Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    K. L. Chowdhury (Research Associate)

  2. Department of Mechanical Engineering, The University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    P. G. Glockner (Professor and Head)

Authors
  1. K. L. Chowdhury
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  2. P. G. Glockner
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Chowdhury, K.L., Glockner, P.G. On a boundary value problem for an elastic dielectric half-plane. Acta Mechanica 37, 65–74 (1980). https://doi.org/10.1007/BF01441244

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  • DOI: https://doi.org/10.1007/BF01441244

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