Multiple Artificial Geothermal Cracks in a Hot Dry Rock Mass for Extraction of Heat

1985 ◽  
Vol 107 (2) ◽  
pp. 274-279 ◽  
Author(s):  
Y. Shibuya ◽  
H. Sekine ◽  
Y. Takahashi ◽  
H. Abe´
Keyword(s):  
Rock Mass ◽  
Stress Distribution ◽  
Theoretical Analysis ◽  
Boundary Conditions ◽  
Singular Integral ◽  
Inversion Formula ◽  
Singular Integral Equations ◽  
Fluid Temperature ◽  
Two Dimensional ◽  
Dimensional Theory

Theoretical analysis is made for multiple geothermal cracks. A periodic array of two-dimensional cracks is considered as a model of the multiple geothermal cracks, and is anlayzed on the basis of the two-dimensional theory of quasi-static thermo-elasticity. The singular integral equations are derived from the boundary conditions, and they are solved by applying the combination of inversion formula and collocation method. Numerical results for the fluid temperature at an outlet, the rock mass temperature, the shape of the geothermal cracks and the stress distribution around the geothermal cracks are shown in graphs.

A Mixed Boundary-Value Problem of Elasticity With Parabolic Boundary

1957 ◽  
Vol 24 (1) ◽  
pp. 122-124
Author(s):  
Gunadhar Paria
Keyword(s):  
Stress Distribution ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Complex Variable ◽  
Hilbert Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Mixed Boundary Value Problem ◽  
Parabolic Boundary

Abstract The problem of finding the stress distribution in a two-dimensional elastic body with parabolic boundary, subject to mixed boundary conditions, has been reduced to the solution of the nonhomogeneous Hilbert problem following the method of complex variable. The result has been compared with that for a straight boundary.

Contact Temperature in Dry Bearings. Three Dimensional Theory and Verification

1981 ◽  
Vol 103 (2) ◽  
pp. 243-251 ◽  
Author(s):  
A. Floquet ◽  
D. Play
Keyword(s):  
Fourier Transform ◽  
Boundary Conditions ◽  
Experimental Verification ◽  
Three Dimensional ◽  
Contact Temperature ◽  
3D Analysis ◽  
New Work ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Infra Red

Boundary conditions were arbitrarily specified in an earlier two dimensional (2D) analysis of contact temperature. In this new work a general three dimensional (3D) Fourier transform solution is obtained from which for specific cases, the boundary conditions can be estimated. Further, experimental verification of 3D analysis was performed using infra-red technique.

SINGULAR INTEGRAL EQUATION METHOD FOR MULTIPLE FLAT PUNCH PROBLEM FOR AN ELASTIC HALF-PLANE

2009 ◽  
Vol 06 (04) ◽  
pp. 605-614
Author(s):  
Y. Z. CHEN ◽  
Z. X. WANG ◽  
X. Y. LIN
Keyword(s):  
Stress Distribution ◽  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Integral Equation Method ◽  
Angle Distribution ◽  
Flat Punch ◽  
Singular Stress ◽  
Punch Problem

When a flat punch is indented on elastic half-plane, the singular stress distribution at the vicinity of the punch corners is studied. The angle distribution for the stress components is also achieved in an explicit form. From obtained singular stress distribution, the punch singular stress factor is defined. The multiple punch problem can be considered as a superposition of many single punch problems. Taking the stress distribution under the punch base as the unknown function and the deformation under punch as the right-hand term, a set of the singular integral equations for the multiple punch problem can be achieved. After the singular integral equations are solved, the stress distributions under punches can be obtained. In addition, the exerting locations of the resultant forces under punches can also be determined. Two numerical examples with the calculated results are presented.

Two-dimensional symmetric double contacts of elastically similar materials

2015 ◽  
Vol 230 (10) ◽  
pp. 1626-1633 ◽  
Author(s):  
P Ghanati ◽  
S Adibnazari
Keyword(s):  
Contact Problem ◽  
Singular Integral ◽  
Analytical Approach ◽  
Flat Surface ◽  
Consistency Condition ◽  
Singular Integral Equations ◽  
Two Dimensional ◽  
End Points ◽  
Side Condition ◽  
Similar Materials

The two-dimensional contact problem for an elastic body indenting an elastically similar half plane resulting in double contacts is important for various applications. In this paper, a generic quasi-static two-dimensional symmetric double contact problem with nonsingular end points between two elastically similar half planes, under the constant normal and oscillatory tangential loading, is analyzed. The classical singular integral equations approach is utilized to extract the pressure and shear functions in the contact zones; subsequently boundary conditions at end points are applied and a new side condition is derived and titled “the consistency condition” for symmetric double contacts. This condition is necessary for determining the extent of the contact and stick zones. Next, this analytical approach is applied to the symmetric indentation of a flat surface by two rigidly interconnected wedge-shaped punches.

Exact Stress Distribution in Standard Gear Teeth and Geometry Factors

1973 ◽  
Vol 95 (4) ◽  
pp. 1159-1163 ◽  
Author(s):  
C. N. Baronet ◽  
G. V. Tordion
Keyword(s):  
Stress Distribution ◽  
Gear Tooth ◽  
Theory Of Elasticity ◽  
Tooth Profile ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Concentrated Load ◽  
Gear Teeth ◽  
Pressure Angle ◽  
Surface Stresses

Using the two-dimensional theory of elasticity and an appropriate transform function, the stress distribution in a gear tooth acted on by a concentrated load has been obtained. Computations were carried out for the 20 and 25-deg pressure angle, standard full-depth system, for numbers of teeth ranging from 20 to 150. The intensities of the maximum static surface stresses along the root fillets are given for different loading positions on the tooth profile. Some of the results are compared with others found in the literature.

scholarly journals POLYNOMIAL SPLINE COLLOCATION METHOD FOR NONLINEAR TWO‐DIMENSIONAL WEAKLY SINGULAR INTEGRAL EQUATIONS

1997 ◽  
Vol 2 (1) ◽  
pp. 122-129 ◽  
Author(s):  
Arvet Pedas
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Polynomial Spline ◽  
Two Dimensional ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations

„Polynomial spline collocation method for nonlinear two‐dimensional weakly singular integral equations" Mathematical Modelling Analysis, 2(1), p. 122-129

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