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TECHNICAL PAPERS

Theory of Boundary Eigensolutions in Engineering Mechanics

[+] Author and Article Information
A. R. Hadjesfandiari, G. F. Dargush

Department of Civil Engineering, University at Buffalo, State University of New York, Buffalo, NY 14260

J. Appl. Mech 68(1), 101-108 (Jul 07, 2000) (8 pages) doi:10.1115/1.1331059 History: Received July 19, 1999; Revised July 07, 2000
Copyright © 2001 by ASME
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References

Carslaw, H. S., 1950, An Introduction to the Theory of Fourier’s Series and Integrals, Dover, New York.
Courant, R., and Hilbert, D., 1953, Methods of Mathematical Physics, John Wiley and Sons, New York.
Morse, P. M., and Feshbach, H., 1953, Methods of Theoretical Physics, McGraw-Hill, New York.
Tolstov, G. P., 1962, Fourier Series, Dover, New York.
Lanczos, C., 1966, Discourse on Fourier Series, Oliver & Boyd, Edinburgh.
Hadjesfandiari, A. R., 1998, “Theoretical and Computational Concepts in Engineering Mechanics,” Ph.D. dissertation, University at Buffalo, State University of New York, Buffalo, NY.
Hilbert, D., 1912, Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen, B. G. Teubner, Leipzig.
Shubin, M. A., 1987, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin.
Grubb, G., 1996, Functional Calculus of Pseudodifferential Boundary Problems, Birkhauser, Boston.
Banerjee, P. K., 1994, The Boundary Element Methods in Engineering, McGraw-Hill, London.
Hadjesfandiari, A. R., and Dargush, G. F., 2000, “Computational Mechanics Based on the Theory of Boundary Eigensolutions,” Int. J. Numer. Methods Eng., in press.
Bathe, K. J., 1996, Finite Element Procedures, Prentice-Hall, Englewood Cliffs, NJ.
Sneddon, I. N., 1966, Mixed Boundary Value Problems in Potential Theory, North Holland, Amsterdam.
Muskhelishvili, N. I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff, Groningen, Holland.
Noble, B., 1958, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations, Pergamon, New York.

Figures

Grahic Jump Location
Circle with notch—boundary eigenproblem definition
Grahic Jump Location
Circle with notch—boundary value problem definition
Grahic Jump Location
Circle with notch—weighted flux versus distance from crack tip
Grahic Jump Location
Square with a diamond-shaped cutout—problem definition
Grahic Jump Location
Square with a diamond-shaped cutout—convergence of weighted flux versus distance from singular point
Grahic Jump Location
Square with a diamond-shaped cutout—generalized flux intensity factor versus internal cutout angle

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