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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The boundary integral equation method in plane elasticity
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by Christian Constanda PDF
Proc. Amer. Math. Soc. 123 (1995), 3385-3396 Request permission

Abstract:

The boundary integral equation method in terms of real variables is applied to solve the interior and exterior Dirichlet and Neumann problems of plane elasticity. In the exterior case, a special far-field pattern for the displacements is considered, without which the classical scheme fails to work. The connection between the results obtained by means of this technique and those of the direct method is indicated.
References
    N.I. Muskhelishvili, Some basic problems in the mathematical theory of elasticity, 3rd ed., Noordhoff, Groningen, 1949.
  • V. D. Kupradze, Potential methods in the theory of elasticity, Israel Program for Scientific Translations, Jerusalem; Daniel Davey & Co., Inc., New York, 1965. Translated from the Russian by H. Gutfreund; Translation edited by I. Meroz. MR 0223128
  • Christian Constanda, On nonunique solutions of weakly singular integral equations in plane elasticity, Quart. J. Mech. Appl. Math. 47 (1994), no. 2, 261–268. MR 1277149, DOI 10.1093/qjmam/47.2.261
  • V. D. Kupradze, T. G. Gegelia, M. O. Basheleĭshvili, and T. V. Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity, Translated from the second Russian edition, North-Holland Series in Applied Mathematics and Mechanics, vol. 25, North-Holland Publishing Co., Amsterdam-New York, 1979. Edited by V. D. Kupradze. MR 530377
  • C. Constanda, A mathematical analysis of bending of plates with transverse shear deformation, Pitman Research Notes in Mathematics Series, vol. 215, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1990. MR 1072130, DOI 10.1117/12.22907
  • M. A. Jaswon and G. T. Symm, Integral equation methods in potential theory and elastostatics, Computational Mathematics and Applications, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1977. MR 0499236
  • F.J. Rizzo, An integral equation approach to boundary value problems of classical elastostatics, Quart. Appl. Math. 25 (1967), 83-95.
  • Christian Constanda, Integral equations of the first kind in plane elasticity, Quart. Appl. Math. 53 (1995), no. 4, 783–793. MR 1359511, DOI 10.1090/qam/1359511
  • Christian Constanda, Some comments on the integration of certain systems of partial differential equations in continuum mechanics, Z. Angew. Math. Phys. 29 (1978), no. 5, 835–839 (English, with French summary). MR 511916, DOI 10.1007/BF01589295
  • Carlo Miranda, Partial differential equations of elliptic type, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 2, Springer-Verlag, New York-Berlin, 1970. Second revised edition. Translated from the Italian by Zane C. Motteler. MR 0284700
  • N. I. Muskhelishvili, Singular integral equations, Wolters-Noordhoff Publishing, Groningen, 1972. Boundary problems of functions theory and their applications to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted. MR 0355494
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 3385-3396
  • MSC: Primary 73C02; Secondary 35J55, 73V99
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1301017-3
  • MathSciNet review: 1301017