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

Alaa A. El-Bary

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

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

Abstract

top
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.

How to cite

top

Alaa 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. [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. [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. [3] V.M. Aleksandrov and E.V. Kovalenko, Problems with mixed boundary conditions in continuous mechanics, Nauka Moscow 1986. 
  4. [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. [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. [6] A.A. El-Bary, Singular integrodifferential equation for infinite thermoelastic plate, Rep. Math. Phy. 55 (3) (2005), 397-403. Zbl1138.74360
  7. [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. [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. [9] A.H. England, Complex variable methods in elasticity, London, New York 1971. Zbl0222.73017
  10. [10] N.I. Muskhelishvili, Some basic problems of mathematical theory of elasticity, Moscow 1949. Zbl0041.22601
  11. [11] H. Parkus, Thermoelasticity, Springer Verlag, New York 1976. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.