Closed-Form Solutions of the Homogeneous Isotropic Elastic Half Space Subjected to a Circular Plane Heat Source

2010 ◽  
Author(s):  
John C. -C. Lu ◽  
Wei-Chih Lin ◽  
Feng-Tsai Lin
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Half Space ◽  
Elastic Half Space ◽  
Closed Form Solutions ◽  
Circular Plane

Closed-Form Solutions of the Elastic Half Space due to a Line Heat Source

2014 ◽  
Vol 638-640 ◽  
pp. 2082-2091
Author(s):  
John C.C. Lu ◽  
Feng Tsai Lin
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Half Space ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Line Heat Source ◽  
Closed Form Solutions ◽  
Line Sink ◽  
Vertical Displacements ◽  
Thermoelastic Response

Thermoelastic response due to a line heat source is analog to poroelastic reaction caused by a fluid line sink. In this study, the strata are modeled as a thermoelastic or poroelastic half space bounded by horizontal surface in the mathematical model. Thermomechanics and poromechanics are applied on the formulation of basic governing equations, and an analogy is drawn to show the similarity. Using Hankel transform technique and approaching symbolic integral through Mathematica, the closed-form solutions of the horizontal and vertical displacements due to a fluid line sink are obtained. The displacements produced by the line heat source are described through analog quantities between thermoelasticity and poroelasticity. The solutions can be applied to dewater operations and build waste repository.

Elastic Solutions for a Saturated Isotropic Half Space Subjected to a Fluid Line Sink

2013 ◽  
Vol 405-408 ◽  
pp. 275-284 ◽  
Author(s):  
John C.C. Lu
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Mass Conservation ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Governing Equations ◽  
Closed Form Solutions ◽  
Cylindrical Coordinate ◽  
Line Sink ◽  
The Mathematical Model

The study derives the closed-form solutions of the long-term elastic consolidation subjected to the fluid line sink in a homogeneous isotropic elastic half space aquifer. The Hankel transform in a cylindrical coordinate system is employed to develop the analytical elastic solutions. Derivations of governing equations are based on the mathematical model of Biots theory of poro-mechanics, and the half space aquifer is modelled as a saturated porous stratum which is bounded by a horizontal surface. The total stresses of the aquifer obey Newtons second law and Hookes law. Besides, the mass conservation and Darcys law are introduced to formulate the governing equations of pore fluid flow. The software Mathematica is used to complete the symbolic integrations and obtain the closed-form solutions. The solutions can be applied in dewatering operations of compressible aquifer.

Closed-Form Expression for Temperature in a Semi-Infinite Solid Due to a Fast Moving Surface Heat Source

1991 ◽  
Vol 113 (4) ◽  
pp. 828-831 ◽  
Author(s):  
J. A. Tichy
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Frictional Contact ◽  
Closed Form Expression ◽  
Moving Heat Source ◽  
Convolution Integral ◽  
Form Expression ◽  
Exponential Integral ◽  
Surface Conditions ◽  
Closed Form Solutions

In the thermal analysis of an asperity on a sliding surface in frictional contact with an opposing surface, conditions are often idealized as a moving heat source. The solution to this problem at arbitrary Pe´cle´t number in terms of a singular integral is well known. In this study, closed-form solutions are found in terms of the exponential integral for high Pe´cle´t number. Fortunately, the closed-form solutions are accurate at Pe´cle´t number of order one. While several restrictions are necessary, the closed-form expressions offer considerable numerical savings relative to evaluations of the convolution integral.

Thermoelastic Solutions for Thermal Distributions Moving Over Half Space Surfaces and Application to the Moving Heat Source

1988 ◽  
Vol 55 (1) ◽  
pp. 87-92 ◽  
Author(s):  
M. D. Bryant
Keyword(s):  
Fourier Transform ◽  
Heat Source ◽  
Half Space ◽  
Elastic Half Space ◽  
Temperature Wave ◽  
Exact Results ◽  
Moving Heat Source ◽  
Exponential Fourier Transform

A method is developed for obtaining fundamental thermal and thermoelastic solutions for thermal distributions moving over the surface of an elastic half space. This method uses the concept of a moving temperature wave along with a novel form of an exponential Fourier transform. The technique is developed and then demonstrated on the example of a moving heat source. Exact results are matched with results from Carslaw and Jaeger (1959) and Barber (1984).

scholarly journals Surface Displacements due to a Steadily Moving Point Force

1996 ◽  
Vol 63 (2) ◽  
pp. 245-251 ◽  
Author(s):  
J. R. Barber
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Elastic Half Space ◽  
Point Force ◽  
Two Dimensional ◽  
Normal Surface ◽  
Displacement Fields ◽  
Linear Superposition ◽  
Surface Displacements ◽  
Stress And Displacement Fields

Closed-form expressions are obtained for the normal surface displacements due to a normal point force moving at constant speed over the surface of an elastic half-space. The Smirnov-Sobolev technique is used to reduce the problem to a linear superposition of two-dimensional stress and displacement fields.

Surface Displacement of a Convective Elastic Half-Space Under an Arbitrarily Distributed Fast-Moving Heat Source

1965 ◽  
Vol 87 (3) ◽  
pp. 729-734 ◽  
Author(s):  
F. F. Ling ◽  
V. C. Mow
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Fast Moving ◽  
Constant Velocity ◽  
Surface Displacement ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Two Dimensional ◽  
Moving Heat Source ◽  
Thermoelasticity Theory

A solution of the normal displacement of the elastic half-space under an arbitrarily distributed fast-moving heat source of constant velocity within the two-dimensional quasi-static, uncoupled thermoelasticity theory is presented. The surface of the half-space is allowed to dissipate heat by convection. Moreover, an example associated with the problem of elastohydrodynamics is given.

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