Integral equations formulation of classical elasticity
Author:
R. P. Kanwal
Journal:
Quart. Appl. Math. 27 (1969), 57-65
MSC:
Primary 73.45
DOI:
https://doi.org/10.1090/qam/245250
MathSciNet review:
245250
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E. Betti, Il Nuovo Cimento 6-10 (1872)
C. Somigliana, Il Nuovo Cimento 17-20 (1885); Annali di Matematica (2) 17 (1889)
I. Fredholm, Solution d’un problème fondamental de la théorie de l’élaslicilé, Arch. Mat. Astronom. Fysik, 2 (1905)
G. Lauricella, Sur l’integration de l’équation relative à l’equilibre des plaques élastiques encastrées, Acta Math. 32 (1909)
D. I. Sherman, Dokl. Akad. Nauk SSSR 27-28 (1940); 32 (1941)
- N. I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity. Fundamental equations, plane theory of elasticity, torsion and bending, P. Noordhoff, Ltd., Groningen, 1953. Translated by J. R. M. Radok. MR 0058417
- S. G. Mikhlin, Integral equations and their applications to certain problems in mechanics, mathematical physics and technology, Pergamon Press, New York-London-Paris-Los Angeles, 1957. Translated from the Russian by A. H. Armstrong. MR 0087877
- M. A. Jaswon and A. R. Ponter, An integral equation solution of the torsion problem, Proc. Roy. Soc. London Ser. A 273 (1963), 237–246. MR 149729, DOI https://doi.org/10.1098/rspa.1963.0085
F. J. Rizzo, An integral equation approach to boundary value problems of classical elaslostatics, Quart. Appl. Math. 25 (1967)
C. W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik, Leipzig, 1927
- W. E. Williams, Boundary effects in Stokes flow, J. Fluid Mech. 24 (1966), 285–291. MR 191216, DOI https://doi.org/10.1017/S0022112066000648
R. P. Kanwal, Dynamical displacements in an infinite elastic space and matched asymptotic expansions, J. Math. Phys. 44 (1965). Errata ibid. 47 (1965)
- J. B. Diaz and H. J. Greenberg, Upper and lower bounds for the solution of the first boundary value problem of elasticity, Quart. Appl. Math. 6 (1948), 326–331. MR 26529, DOI https://doi.org/10.1090/S0033-569X-1948-26529-X
- A. E. H. Love, A treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, 1944. Fourth Ed. MR 0010851
- G. N. Bycroft, Forced vibrations of a rigid circular plate on a semi-infinite elastic space and on an elastic stratum, Philos. Trans. Roy. Soc. London Ser. A 248 (1956), 327–368. MR 86506, DOI https://doi.org/10.1098/rsta.1956.0001
- I. N. Sneddon and R. Hill (eds.), Progress in Solid Mechanics. Vol.III, North-Holland Publishing Co., Amsterdam; Interscience Publishers John Wil ey & Sons, Inc. New York, 1963. Dynamical problems in elasticity by V. D. Kupradze. MR 0164488
E. Betti, Il Nuovo Cimento 6-10 (1872)
C. Somigliana, Il Nuovo Cimento 17-20 (1885); Annali di Matematica (2) 17 (1889)
I. Fredholm, Solution d’un problème fondamental de la théorie de l’élaslicilé, Arch. Mat. Astronom. Fysik, 2 (1905)
G. Lauricella, Sur l’integration de l’équation relative à l’equilibre des plaques élastiques encastrées, Acta Math. 32 (1909)
D. I. Sherman, Dokl. Akad. Nauk SSSR 27-28 (1940); 32 (1941)
N. I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, Noordhoff, Holland, 1953
S. G. Mikhlin, Integral equations, Pergamon Press, London, 1957
M. A. Jaswon and A. R. Ponter, An integral equation solution of the torsion problem, Proc. Roy Soc. Series A, 273 (1963)
F. J. Rizzo, An integral equation approach to boundary value problems of classical elaslostatics, Quart. Appl. Math. 25 (1967)
C. W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik, Leipzig, 1927
W. E. Williams, Boundary effects in Stokes flow, J. Fluid Mech. 24 (1966)
R. P. Kanwal, Dynamical displacements in an infinite elastic space and matched asymptotic expansions, J. Math. Phys. 44 (1965). Errata ibid. 47 (1965)
J. B. Diaz and H. J. Greenberg, Upper and lower bounds for the solution of the first boundary value problems of elasticity, Quart. Appl. Math. 6 (1948)
A. E. H. Love, Mathematical theory of elasticity, 4th ed., Dover, New York, 1944
G. N. Bycroft, Forced vibrations of a rigid circular plate on a semi-infinite elastic space on an elastic stratum, Trans. Royal Philos. Soc., 248 (1955-1956)
V. D. Kupradze, Dynamical problems in elasticity, North-Holland Publishing Company, Amsterdam, 1963
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Article copyright:
© Copyright 1969
American Mathematical Society