The boundary integral equation method in plane elasticity
Author:
Christian Constanda
Journal:
Proc. Amer. Math. Soc. 123 (1995), 33853396
MSC:
Primary 73C02; Secondary 35J55, 73V99
MathSciNet review:
1301017
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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 farfield 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.
 [1]
N.I. Muskhelishvili, Some basic problems in the mathematical theory of elasticity, 3rd ed., Noordhoff, Groningen, 1949.
 [2]
V.
D. Kupradze, Potential methods in the theory of elasticity,
Translated from the Russian by H. Gutfreund. Translation edited by I.
Meroz, Israel Program for Scientific Translations, Jerusalem; Daniel Davey
&\ Co., Inc., New York, 1965. MR 0223128
(36 #6177)
 [3]
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
(95c:73021), http://dx.doi.org/10.1093/qjmam/47.2.261
 [4]
V.
D. Kupradze, T.
G. Gegelia, M.
O. Basheleĭshvili, and T.
V. Burchuladze, Threedimensional problems of the mathematical
theory of elasticity and thermoelasticity, Translated from the second
Russian edition, NorthHolland Series in Applied Mathematics and Mechanics,
vol. 25, NorthHolland Publishing Co., AmsterdamNew York, 1979.
Edited by V. D. Kupradze. MR 530377
(80h:73002)
 [5]
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 (91m:73016)
 [6]
M.
A. Jaswon and G.
T. Symm, Integral equation methods in potential theory and
elastostatics, Academic Press [Harcourt Brace Jovanovich, Publishers],
LondonNew York, 1977. Computational Mathematics and Applications. MR 0499236
(58 #17147)
 [7]
F.J. Rizzo, An integral equation approach to boundary value problems of classical elastostatics, Quart. Appl. Math. 25 (1967), 8395.
 [8]
Christian
Constanda, Integral equations of the first kind in plane
elasticity, Quart. Appl. Math. 53 (1995), no. 4,
783–793. MR 1359511
(96k:73025)
 [9]
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
(80h:73018), http://dx.doi.org/10.1007/BF01589295
 [10]
Carlo
Miranda, Partial differential equations of elliptic type,
Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 2, SpringerVerlag,
New YorkBerlin, 1970. Second revised edition. Translated from the Italian
by Zane C. Motteler. MR 0284700
(44 #1924)
 [11]
N.
I. Muskhelishvili, Singular integral equations,
WoltersNoordhoff 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
(50 #7968)
 [1]
 N.I. Muskhelishvili, Some basic problems in the mathematical theory of elasticity, 3rd ed., Noordhoff, Groningen, 1949.
 [2]
 V.D. Kupradze, Potential methods in the theory of elasticity, Israel Program for Scientific Translations, Jerusalem, 1965. MR 0223128 (36:6177)
 [3]
 C. Constanda, On nonunique solutions of weakly singular integral equations in plane elasticity, Quart. J. Mech. Appl. Math. 47 (1994), 261267. MR 1277149 (95c:73021)
 [4]
 V.D. Kupradze et al., Threedimensional problems of the mathematical theory of elasticity and thermoelasticity, NorthHolland, Amsterdam, 1979. MR 530377 (80h:73002)
 [5]
 C. Constanda, A mathematical analysis of bending of plates with transverse shear deformation, Longman, Harlow, 1990. MR 1072130 (91m:73016)
 [6]
 M.A. Jaswon and G.T. Symm, Integral equation methods in potential theory and elastostatics, Academic Press, London, New York, and San Francisco, 1977. MR 0499236 (58:17147)
 [7]
 F.J. Rizzo, An integral equation approach to boundary value problems of classical elastostatics, Quart. Appl. Math. 25 (1967), 8395.
 [8]
 C. Constanda, Integral equations of the first kind in plane elasticity, Quart. Appl. Math. (to appear). MR 1359511 (96k:73025)
 [9]
 , Some comments on the integration of certain systems of partial differential equations in continuum mechanics, J. Appl. Math. Phys. 29 (1978), 835839. MR 511916 (80h:73018)
 [10]
 C. Miranda, Partial differential equations of elliptic type, 2nd ed., SpringerVerlag, Berlin, 1970. MR 0284700 (44:1924)
 [11]
 N.I. Muskhelishvili, Singular integral equations, Noordhoff, Groningen, 1946. MR 0355494 (50:7968)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199513010173
PII:
S 00029939(1995)13010173
Keywords:
Boundary integral equation,
plane elasticity
Article copyright:
© Copyright 1995
American Mathematical Society
