# Mathematical treatment for thermoelastic plate with a curvilinear hole in S-plane

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2006)

- Volume: 26, Issue: 1, page 77-86
- ISSN: 1509-9407

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topAlaa A. El-Bary. "Mathematical treatment for thermoelastic plate with a curvilinear hole in S-plane." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 26.1 (2006): 77-86. <http://eudml.org/doc/271173>.

@article{AlaaA2006,

abstract = {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.},

author = {Alaa A. El-Bary},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {infinite plate; Cauchy integral; first and second fundamental problems; integro-differential equation; Goursat functions; Cauchy integral method; conformal map},

language = {eng},

number = {1},

pages = {77-86},

title = {Mathematical treatment for thermoelastic plate with a curvilinear hole in S-plane},

url = {http://eudml.org/doc/271173},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Alaa A. El-Bary

TI - Mathematical treatment for thermoelastic plate with a curvilinear hole in S-plane

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2006

VL - 26

IS - 1

SP - 77

EP - 86

AB - 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.

LA - eng

KW - infinite plate; Cauchy integral; first and second fundamental problems; integro-differential equation; Goursat functions; Cauchy integral method; conformal map

UR - http://eudml.org/doc/271173

ER -

## References

top- [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.
- [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. Zbl1068.74039
- [3] V.M. Aleksandrov and E.V. Kovalenko, Problems with mixed boundary conditions in continuous mechanics, Nauka Moscow 1986.
- [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). Zbl1052.74033
- [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.
- [6] A.A. El-Bary, Singular integrodifferential equation for infinite thermoelastic plate, Rep. Math. Phy. 55 (3) (2005), 397-403. Zbl1138.74360
- [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. Zbl1092.74546
- [8] I.H. El-Sirafy, Stretched plates weakened by inner curvilinear holes, J. Appl. Math and Phys. (ZAMP) 28 (1977), 1153-1159. Zbl0371.73029
- [9] A.H. England, Complex variable methods in elasticity, London, New York 1971. Zbl0222.73017
- [10] N.I. Muskhelishvili, Some basic problems of mathematical theory of elasticity, Moscow 1949. Zbl0041.22601
- [11] H. Parkus, Thermoelasticity, Springer Verlag, New York 1976.

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