Solution of Fredholm integrodifferential equation for an infinite elastic plate

Alaa A. El-Bary

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2004)

  • Volume: 24, Issue: 1, page 5-11
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Alaa A. El-Bary. "Solution of Fredholm integrodifferential equation for an infinite elastic plate." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 24.1 (2004): 5-11. <http://eudml.org/doc/271494>.

@article{AlaaA2004,
abstract = {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.},
author = {Alaa A. El-Bary},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {integrodifferential equation; Cauchy method; complex variable; infinite plate; curvilinear hole},
language = {eng},
number = {1},
pages = {5-11},
title = {Solution of Fredholm integrodifferential equation for an infinite elastic plate},
url = {http://eudml.org/doc/271494},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Alaa A. El-Bary
TI - Solution of Fredholm integrodifferential equation for an infinite elastic plate
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2004
VL - 24
IS - 1
SP - 5
EP - 11
AB - 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.
LA - eng
KW - integrodifferential equation; Cauchy method; complex variable; infinite plate; curvilinear hole
UR - http://eudml.org/doc/271494
ER -

References

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  2. [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. 
  3. [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. Zbl1068.74039
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  8. [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. Zbl1172.74307
  9. [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. 
  10. [10] I.H. El-Sirafy, Stretched plates weakened by inner curvilinear holes, J. of Appl. Math and Phys. (ZAMP) 28 (1977), 1153-1159. Zbl0371.73029
  11. [11] A.H. England, Complex variable method in elasticity, London, New York 1971. Zbl0222.73017
  12. [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. 
  13. [13] N.I. Muskhelishvili, Some basic problems of mathematical theory of elasticity, Moscow 1949. Zbl0041.22601
  14. [14] Parkus, Thermoelasticity, Springer Verlag, New York 1976. 
  15. [15] G.Ya. Popv, Contact problems for a linearly deformable function, Kiev, Odessa 1982. 

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