Singularity at the apex of pyramidal notches with three equal angles
Authors:
L. M. Keer and K. S. Parihar
Journal:
Quart. Appl. Math. 35 (1977), 401-405
MSC:
Primary 31B25
DOI:
https://doi.org/10.1090/qam/460676
MathSciNet review:
460676
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Abstract: A Green’s function approach is employed to study the potential theory problem of determining the strength of singularity at the apex of a pyramid with three equal angles. The problem is reduced to finding the eigenvalue of a singular integral equation. Numerical results are obtained and compared with available literature.
Z. P. Bažant, Three-dimensional harmonic functions near termination or intersection of gradient singularity lines: a general numerical method, Int. J. Engng. Sci. 12, 221–243 (1974)
- L. M. Keer and K. S. Parihar, A note on the singularity at the corner of a wedge-shaped punch or crack, SIAM J. Appl. Math. 34 (1978), no. 2, 297–302. MR 489232, DOI https://doi.org/10.1137/0134024
A. Erdélyi, Tables of integral transforms. Vol. 1, McGraw-Hill, 1954
- J. A. Morrison and J. A. Lewis, Charge singularity at the corner of a flat plate, SIAM J. Appl. Math. 31 (1976), no. 2, 233–250. MR 416273, DOI https://doi.org/10.1137/0131019
A. Erdélyi, Higher transcendental functions, Vol. 1, McGraw-Hill, 1953
- F. Erdogan, G. D. Gupta, and T. S. Cook, Numerical solution of singular integral equations, Mechanics of fracture, Vol. 1, Noordhoff, Leiden, 1973, pp. 368–425. MR 0471394
Z. P. Bažant, Three-dimensional harmonic functions near termination or intersection of gradient singularity lines: a general numerical method, Int. J. Engng. Sci. 12, 221–243 (1974)
L. M. Keer and K. S. Parihar, A note on the singularity at the corner of a wedge-shaped punch or crack, SIAM J. Appl. Math., in press.
A. Erdélyi, Tables of integral transforms. Vol. 1, McGraw-Hill, 1954
J. A. Morrison and J. A. Lewis, Charge singularity at the corner of a flat plate, SIAM J. Appl. Math. 31, 233–250 (1976)
A. Erdélyi, Higher transcendental functions, Vol. 1, McGraw-Hill, 1953
F. Erdogan, G. D. Gupta and T. S. Cook, Numerical solution of singular integral equations, in Methods of analysis and solutions of crack problems, ed. G. C. Sih, Noordhoff, 1973, pp. 368–425
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Article copyright:
© Copyright 1977
American Mathematical Society
