scholarly journals Mathematical modeling of the thermoelastic state in a circular disk with a crack due to the action of the heat source

2019 ◽  
Vol 5 (1) ◽  
pp. 13-19
Author(s):  
Volodymyr Zelenyak ◽  
Liubov Kolyasa
Keyword(s):  
Mathematical Modeling ◽  
Heat Source ◽  
Circular Disk ◽  
Thermoelastic State

Transient Thermal Stresses on a Finite Disk Due to a Continuous Point Heat Source

1970 ◽  
Vol 92 (2) ◽  
pp. 357-365 ◽  
Author(s):  
T. R. Hsu
Keyword(s):  
Heat Source ◽  
Thermal Stresses ◽  
Circular Disk ◽  
Transient Temperature ◽  
Point Heat Source ◽  
Finite Radius ◽  
Transient Temperature Distribution ◽  
Instantaneous Point ◽  
Continuous Point ◽  
Transient Thermal

This paper contains exact solutions for the transient temperature distribution and the associated quasi-static thermal stresses and deformations which arise in a thin circular disk of finite radius subjected to a continuous point heat source acting on its periphery. It has been proven in this paper that the solutions of this type of problem may be obtained by integrating the time variable of the corresponding solutions in the case of an instantaneous point heat source. The solutions are given in the form of double infinite series and graphical representations of the solutions in dimensionless terms are included. Reference is made to methods of applying the solutions to shapes other than disks. The solutions are pertinent to problems which occur in welding engineering and modern nuclear technology.

On Bonded Circular Inclusions in Plane Thermoelasticity

1997 ◽  
Vol 64 (4) ◽  
pp. 1000-1004 ◽  
Author(s):  
C. K. Chao ◽  
M. H. Shen
Keyword(s):  
Heat Flow ◽  
Heat Source ◽  
Circular Disk ◽  
Infinite Matrix ◽  
Point Heat Source ◽  
Surrounding Matrix ◽  
Uniform Heat ◽  
Special Cases ◽  
The Matrix ◽  
Stress Functions

A general solution to the thermoelastic problem of a circular inhomogeneity in an infinite matrix is provided. The thermal loadings considered in this note include a point heat source located either in the matrix or in the inclusion and a uniform heat flow applied at infinity. The proposed analysis is based upon the use of Laurent series expansion of the corresponding complex potentials and the method of analytical continuation. The general expressions of the temperature and stress functions are derived explicitly in both the inclusion and the surrounding matrix. Comparison is made with some special cases such as a circular hole under remote uniform heat flow and a circular disk under a point heat source, which shows that the results presented here are exact and general.

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