Abstract
Special sets of linearly independent basis functions for biharmonic and Laplace’s equations are obtained in closed forms. These basis functions are suitable for the solutions of the problems in multiply connected circular and semicircular regions. They automatically satisfy the outer boundary condition(s), and contain singularities at the centers of the circular cutouts of the region. The basis functions are generated from the integrations of the Green’s functions representing the solutions for concentrated sources and satisfying the aforementioned outer boundary condition(s). Examples of plates, bending of prismatic bars, and two dimensional heat transfer are presented.
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References
Ling, C. B., Q. Appl. Math. 5, 168–181 (1947).
Kuo, Y. M.,and Conway, H.D., Int. J. Solids Structures 9, 1553–1566 (1973).
Rowley, J. C., and Payne, J. B., Bibliog. Diags ASME, Trans. Ser. C86 J. Heat Trans., 531-536 (1964).
Kraus, H., Trans. ASME 84E J. Appl. Mech. 3, 489–496 (1962).
Howland, R. C. J., Proc. Camb. Phil. Soc. 30, 315–326 (1935).
Conte, S. D., Q. Appl. Math. Vol. IX No. 4 435–440, (1951).
El-Saden, M. R., Bibliog. Diags ASME, Trans. Ser C83 J. Heat Trans., 510-512 (1961).
Naghdi, A. K., Int. J. Solids Structures, 16, 329–335 (1980).
Naghdi, A. K., J. Appl. Mech. 47, 677–679 (1980).
Naghdi, A. K., 10th Canadian Congress of Appl. Mech., C-1, C-2 (1985).
Hildebrand, F. B. Introduction to Numerical Analysis, McGraw-Hill (1956).
Dwight, H. B., Table of Integrals and Other Mathematical Data, Macmillan (1957).
Gradshteyn, I. S., and Ryzhik, I. M. Table of Integral Series and Products, New York and London (1965).
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© 1989 Springer-Verlag Berlin, Heidelberg
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Naghdi, A.K. (1989). Certain Basis Functions for Biharmonic and Laplace’s Equations and Applications. In: Koh, S.L., Speziale, C.G. (eds) Recent Advances in Engineering Science. Lecture Notes in Engineering, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83695-4_20
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DOI: https://doi.org/10.1007/978-3-642-83695-4_20
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