The Cauchy integral method has been applied to derive exact and closed expressions for Goursat's functions for the first and second fundamental problems for an infinite thermoelastic plate weakened by a hole having arbitrary shape. The plate considered is conformally mapped to the area of the right half-plane. Many previous discussions of various authors can be considered as special cases of this work. The shape of the hole being an ellipse, a crescent, a triangle, or a cut having the shape of a circular arc are included as special cases.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1065,
author = {Alaa A. El-Bary},
title = {Mathematical treatment for thermoelastic plate with a curvilinear hole in S-plane},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {26},
year = {2006},
pages = {77-86},
zbl = {1132.74025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1065}
}
Alaa A. El-Bary. Mathematical treatment for thermoelastic plate with a curvilinear hole in S-plane. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 26 (2006) pp. 77-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1065/
[000] [1] M.A. Abdou and E.A. Khar Eldin, A finite plate weakened by a hole having arbitrary shape, J. Comp. Appl. Math. 56 (1994), 341-351.
[001] [2] 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
[002] [3] V.M. Aleksandrov and E.V. Kovalenko, Problems with mixed boundary conditions in continuous mechanics, Nauka Moscow 1986.
[003] [4] A.A. El-Bary, et al, Solution of first and second fundamental problems of an elastic infinite plate with three poles, New Zeland J. Math. 32 (2) (2003). | Zbl 1052.74033
[004] [5] 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.
[005] [6] A.A. El-Bary, Singular integrodifferential equation for infinite thermoelastic plate, Rep. Math. Phy. 55 (3) (2005), 397-403. | Zbl 1138.74360
[006] [7] A.A. El-Bary, First and second fundamental problem of an elastic infinite plate with holes, Korean J. Comp. Appl. Math. 8 (3) (2001), 675-683. | Zbl 1092.74546
[007] [8] I.H. El-Sirafy, Stretched plates weakened by inner curvilinear holes, J. Appl. Math and Phys. (ZAMP) 28 (1977), 1153-1159. | Zbl 0371.73029
[008] [9] A.H. England, Complex variable methods in elasticity, London, New York 1971. | Zbl 0222.73017
[009] [10] N.I. Muskhelishvili, Some basic problems of mathematical theory of elasticity, Moscow 1949. | Zbl 0041.22601
[010] [11] H. Parkus, Thermoelasticity, Springer Verlag, New York 1976.