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

• Autorzy: Alaa A. El-Bary
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

infinite plate; Cauchy integral; first and second fundamental problems; integro-differential equation

Kategorie tematyczne

• 45J05: Integro-ordinary differential equations
• 74F05: Thermal effects
• 74B05: Classical linear elasticity
• 45E05: Integral equations with kernels of Cauchy type

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2006
• Tom: 26
• Numer: 1
• Strony: 77-86

Daty

wydano

2006

otrzymano

2005-03-01

Twórcy

autor

Alaa A. El-Bary

• Basic and Applied Science Department, Arab Academy for Science and Technology, P.O. Box 1029 Alexandria, Egypt

Bibliografia

• [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.
• [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).
• [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.
• [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.
• [8] I.H. El-Sirafy, Stretched plates weakened by inner curvilinear holes, J. Appl. Math and Phys. (ZAMP) 28 (1977), 1153-1159.
• [9] A.H. England, Complex variable methods in elasticity, London, New York 1971.
• [10] N.I. Muskhelishvili, Some basic problems of mathematical theory of elasticity, Moscow 1949.
• [11] H. Parkus, Thermoelasticity, Springer Verlag, New York 1976.

Identyfikatory

DOI

10.7151/dmdico.1065