Nonaxisymmetric punch and crack problems for initially stressed bodies
Author:
Leon M. Keer
Journal:
Quart. Appl. Math. 23 (1965), 97-107
DOI:
https://doi.org/10.1090/qam/99945
MathSciNet review:
QAM99945
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Abstract |
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Abstract: Using the theory developed by England and Green [1] for thermoelastic problems for initially stressed bodies and a certain class of potential functions, a group of punch and crack problems are solved. The requirement for solution is that the boundary data be expressible as a trignometric series with the coefficient of each term of the series a function of radial distance from the center of the punch or crack. The solutions are obtained by inversion of Abel’s integral equation.
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- A. E. Green, R. S. Rivlin, and R. T. Shield, General theory of small elastic deformations superposed on finite elastic deformations, Proc. Roy. Soc. London Ser. A 211 (1952), 128–154. MR 47486, DOI https://doi.org/10.1098/rspa.1952.0030
- A. E. Green and W. Zerna, Theoretical elasticity, Oxford, at the Clarendon Press, 1954. MR 0064598
A. Erdelyi, et. al., Table of integral transforms, vol. 2, McGraw-Hill, New York, 1954, p. 48
L. M. Kerr, A class of nonsymmetrical punch and crack problems, QJMAM, 17 (1964) 423
- B. Noble, Certain dual integral equations, J. Math. and Phys. 37 (1958), 128–136. MR 98293, DOI https://doi.org/10.1002/sapm1958371128
- E. T. Copson, On certain dual integral equations, Proc. Glasgow Math. Assoc. 5 (1961), 21–24 (1961). MR 199660
A. H. England and A. E. Green, Steady state thermoelasticity for initially stressed bodies, Proc. Roy. Soc. A253 (1961) 517
A. E. Green, R. S. Rivlin, and R. T. Shield, General theory of small elastic deformations superimposed on large deformations, Proc. Roy. Soc. A211 (1952) 128
A. E. Green and W. Zerna, Theoretical elasticity, Clarendon Press, Oxford, 1954, p. 114
A. Erdelyi, et. al., Table of integral transforms, vol. 2, McGraw-Hill, New York, 1954, p. 48
L. M. Kerr, A class of nonsymmetrical punch and crack problems, QJMAM, 17 (1964) 423
B. Noble, Certain dual integral equations, J. Math. Phys. 37 (1958) 128
E. T. Copson, On certain dual integral equations, Proc. Glasgow Math. Assoc. 5 (1961) 21
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Article copyright:
© Copyright 1965
American Mathematical Society
