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.

Thermal Stresses in a Generally Anisotropic Body With an Elliptic Inclusion Subject to Uniform Heat Flow

1998 ◽  
Vol 65 (1) ◽  
pp. 51-58 ◽  
Author(s):  
C. K. Chao ◽  
M. H. Shen
Keyword(s):  
Heat Flow ◽  
Thermal Stresses ◽  
Anisotropic Body ◽  
Analytical Continuation ◽  
Complex Matrix ◽  
Elliptic Inclusion ◽  
Uniform Heat ◽  
Special Cases ◽  
The Matrix ◽  
Stress Functions

A general analytical solution for the elliptical anisotropic inclusion embedded in an infinite anisotropic matrix subjected to uniform heat flow is provided in this paper. Based upon the method of Lekhnitskii formulation, the technique of conformal mapping, the method of analytical continuation, and the concept of superposition, both the solutions of the temperature and stress, functions either in the matrix or in the inclusion are expressed in complex matrix notation. Numerical results are carried out and provided in graphic form to elucidate the effect of material and geometric parameters on the interfacial stresses. Since the general solutions have not been found in the literature, comparison is made with some special cases of which the analytical solutions exist, which shows that our solutions presented here are exact and general.

Thermal Stresses Due to Disturbance of Uniform Heat Flow by an Insulated Ovaloid Hole

1960 ◽  
Vol 27 (4) ◽  
pp. 635-639 ◽  
Author(s):  
A. L. Florence ◽  
J. N. Goodier
Keyword(s):  
Heat Flow ◽  
Closed Form ◽  
Thermal Stresses ◽  
Thermoelastic Problem ◽  
Uniform Heat ◽  
Special Cases

The linear thermoelastic problem is solved for a uniform heat flow disturbed by a hole of ovaloid form, which includes the ellipse and circle as special cases. Results for stress and displacement are found in closed form, by reducing the problem to one of boundary loading solvable by a method of Muskhelishvili.

Green's Function for a Point Heat Source in an Anisotropic Body Containing an Elliptic Hole or a Rigid Inclusion

1999 ◽  
Vol 15 (3) ◽  
pp. 89-95
Author(s):  
Chung-Hao Wang ◽  
Ching-Kong Chao
Keyword(s):  
Heat Source ◽  
Rigid Inclusion ◽  
Elliptic Hole ◽  
Anisotropic Body ◽  
Point Heat Source ◽  
Intensity Factors ◽  
Rigid Line Inclusion ◽  
Rigid Line ◽  
Stress Functions ◽  
Line Inclusion

AbstractThe thermoelastic problem associated with a point heat source embedded in an anisotropic body containing an elliptic hole or a rigid inclusion is considered in this paper. By using the formalism of Stroh [1], the approach of analytic function continuation and the technique of conformal mapping, the expression for the temperature, displacements and stress functions is expressed in explicit matrix form. The present derived solutions are also valid for some special problems such as a crack or a rigid line inclusion if one lets the minor axis of the ellipse approach to zero. The stress intensity factors induced by a point heat source are also obtained.

scholarly journals Topological duals of some paranormed sequence spaces

2003 ◽  
Vol 2003 (30) ◽  
pp. 1883-1897
Author(s):  
Nandita Rath
Keyword(s):  
Sequence Spaces ◽  
Positive Sequence ◽  
Infinite Matrix ◽  
Linear Functionals ◽  
Normed Spaces ◽  
General Representation ◽  
Bounded Linear ◽  
Special Cases ◽  
The Matrix ◽  
Almost All

LetP=(pk)be a bounded positive sequence and letA=(ank)be an infinite matrix with allank≥0. For normed spacesEandEk, the matrixAgenerates the paranormed sequence spaces[A,P]∞((Ek)),[A,P]0((Ek)), and[A,P]((E)), which generalise almost all the well-known sequence spaces such asc0,c,lp,l∞, andwp. In this paper, topological duals of these paranormed sequence spaces are constructed and general representation formulae for their bounded linear functionals are obtained in some special cases of matrixA.

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 the General Solutions for Annular Problems With a Point Heat Source

1999 ◽  
Vol 67 (3) ◽  
pp. 511-518 ◽  
Author(s):  
C. K. Chao ◽  
C. J. Tan
Keyword(s):  
Fourier Series ◽  
Analytical Solution ◽  
Heat Source ◽  
Analytical Continuation ◽  
Series Expansions ◽  
Series Solutions ◽  
Point Heat Source ◽  
Free Boundary Conditions ◽  
Complex Functions ◽  
Stress Functions

A general analytical solution for the annular problem with a point heat source is provided in this paper. Based upon the method of analytical continuation and the technique of Fourier series expansions, the series solutions of the temperature and stress functions are expressed in complex explicit form. Single-valuedness of complex functions in the doubly connected region has been examined for both the stress-free and displacement-free boundary conditions. The dilatation stress in the annulus due to the application of a point heat source is discussed and shown in graphic form. [S0021-8936(00)02803-8]

Boundary layer flow of dusty fluid over a radiating stretching surface embedded in a thermally stratified porous medium in the presence of uniform heat source

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
B.J. Gireesha ◽  
P. Venkatesh ◽  
N.S. Shashikumar ◽  
B.C. Prasannakumara
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Thermal Stratification ◽  
Surface Shear Stress ◽  
Dusty Fluid ◽  
Uniform Heat ◽  
Special Cases

AbstractNumerical investigation for the effect of thermal stratification on MHD flow and heat transfer of dusty fluid over a vertical stretching sheet embedded in a thermally stratified porous medium in the presence of uniform heat source and thermal radiation. The governing equations for the problem were reduced in to dimensionless ordinary differential equations using suitable similarity transformations. The transformed nonlinear ordinary differential equations are numerically solved by applying efficient RungeKutta Fehlberg-45 Method with shooting technique. The effects of various flow controlling parameters such as Prandtl number, heat source/sink parameter, fluid particle interaction parameter, heat source parameter, radiation parameter on velocity and temperature distributions of both fluid and dust phases are depicted graphically. Finally, the numerical results are compared and found to be in good agreement with previously published results under special cases. The results indicate that the fluid phase velocity is always greater than that of the particle phase and thermal stratification significantly affects the surface shear stress as well as the surface heat transfer.

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