Many authors discussed the problem of an elastic infinite plate with a curvilinear hole, some of them considered this problem in z-plane and the others in the s-plane. They obtained an exact expression for Goursat's functions for the first and second fundamental problem. In this paper, we use the Cauchy integral method to obtain a solution to the first and second fundamental problem by using a new transformation. Some applications are investigated and also some special cases are discussed.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1048,
author = {Alaa A. El-Bary},
title = {Solution of Fredholm integrodifferential equation for an infinite elastic plate},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {24},
year = {2004},
pages = {5-11},
zbl = {1208.74080},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1048}
}
Alaa A. El-Bary. Solution of Fredholm integrodifferential equation for an infinite elastic plate. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 24 (2004) pp. 5-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1048/
[000] [1] M.A. Abdou and E.A. Khar Eldin, An finite plate weakened by a hole having arbitrary shape, J. Comp. Appl. Math. 56 (1994), 341-351. | Zbl 0824.73025
[001] [2] M.A. Abdou and A.A. El-Bary, Fredholm-Volterra integral equation with potential kernel, Int. J. Math and Math. Sci. 26 (6) (2001), 321-330.
[002] [3] M.A. Abdou and A.A. El-Bary, Fundamental problems for infinite plate with a curvilinear hole having finite poles, Math. Prob. in Eng. 7 (6) (2001), 485-501. | Zbl 1068.74039
[003] [4] V.M. Aleksandrov and E.V. Kovalenko, Problems with mixed boundary conditions in continuous mechanics, Nauka Moscow (1986).
[004] [5] A.A. El-Bary, et al., Applications of integro-differential equations in the problems of infinite plate with a curvilinear hole, Proc. of 8th Int. Conf. Th. and Appl. Mech., Military Technical College, Cairo, Egypt 1998.
[005] [6] A.A. El-Bary and I.H. El-Sirafy, An infinite plate with a curvilinear hole in s-plane, Estratto da le Matematiche Vol. LIV - fasc II (1999), 261-274.
[006] [7] A.A. El-Bary, Chebyshev polynomial solution for Volterra-Fredholm integrodifferential equation with Cauchy kernel, Int. J. Appl. Math. 2 (12) (2000), 1399-1406. | Zbl 1051.45005
[007] [8] A.A. El-Bary and I.S. Ismail, Solution of first and second fundamental problems of an elastic infinite plate, Int. J. Appl. Math. 4 (3) (2000) 247-260. | Zbl 1172.74307
[008] [9] A.A. El-Bary, First and second fundamental problem of an elastic infinite plate with holes, Korean J. Comp. Appl. Math. 8 (3) (2001), 675-684.
[009] [10] I.H. El-Sirafy, Stretched plates weakened by inner curvilinear holes, J. of Appl. Math and Phys. (ZAMP) 28 (1977), 1153-1159. | Zbl 0371.73029
[010] [11] A.H. England, Complex variable method in elasticity, London, New York 1971. | Zbl 0222.73017
[011] [12] A.C. Koya and F. Erdogan, On the solution of integral equation with a generalized Cauchy Kernel, Quart. Appl. Math. Vol. XLV (3) (1997) 455-469.
[012] [13] N.I. Muskhelishvili, Some basic problems of mathematical theory of elasticity, Moscow 1949. | Zbl 0041.22601
[013] [14] Parkus, Thermoelasticity, Springer Verlag, New York 1976.
[014] [15] G.Ya. Popv, Contact problems for a linearly deformable function, Kiev, Odessa 1982.