Analytical Solutions For Transient Thermoelastic Stress Fields Around A Borehole During Fluid Injection Into Permeable Media

1993 ◽  
Vol 32 (04) ◽  
Author(s):  
K. Hojka ◽  
M.B. Dusseault ◽  
A.D. Bogobowicz
Keyword(s):  
Analytical Solutions ◽  
Thermoelastic Stress ◽  
Stress Fields ◽  
Fluid Injection ◽  
Permeable Media

Analytical Solutions of Stresses in Functionally Graded Circular Hollow Cylinder with Finite Length

2004 ◽  
Vol 261-263 ◽  
pp. 651-656 ◽  
Author(s):  
Z.S. Shao ◽  
L.F. Fan ◽  
Tie Jun Wang
Keyword(s):  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Finite Length ◽  
Analytical Solutions ◽  
Radial Direction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Fields ◽  
Simply Supported

Analytical solutions of stress fields in functionally graded circular hollow cylinder with finite length subjected to axisymmetric pressure loadings on inner and outer surfaces are presented in this paper. The cylinder is simply supported at its two ends. Young's modulus of the material is assumed to vary continuously in radial direction of the cylinder. Moreover, numerical results of stresses in functionally graded circular hollow cylinder are appeared.

Thermoelastic Stresses in an Axisymmetric Thick-Walled Tube Under an Arbitrary Internal Transient

2004 ◽  
Vol 126 (3) ◽  
pp. 327-332 ◽  
Author(s):  
A. E. Segall
Keyword(s):  
Thermal Loading ◽  
Series Representation ◽  
Thermoelastic Stress ◽  
Internal Surface ◽  
Stress Fields ◽  
Element Analysis ◽  
Axisymmetric Solution ◽  
Thermoelastic Stresses ◽  
Stress States ◽  
Transient Thermal

A closed-form axisymmetric solution was derived for the transient thermal-stress fields developed in thick-walled tubes subjected to an arbitrary thermal loading on the internal surface with convection to the surrounding external environment. Generalization of the temperature excitation was achieved by using a versatile polynomial composed of integral-and half-order terms. In order to avoid the difficult and potentially error prone evaluation of functions with complex arguments, Laplace transformation and a ten-term Gaver-Stehfest inversion formula were used to solve the resulting Volterra integral equation. The ensuing series representation of the temperature distribution as a function of time and radial position was then used to derive new relationships for the transient thermoelastic stress-states. Excellent agreement was seen between the derived temperature and stress relationships, existing series solutions, and a finite-element analysis when the thermophysical and thermoelastic properties were assumed to be independent of temperature. The use of a smoothed polynomial in the derived relationships allows the incorporation of empirical data not easily represented by standard functions. This in turn permits an easy analysis of the significance of the exponential boundary condition and convective coefficient in determining the magnitudes and distribution of the resulting stress states over time. Moreover, the resulting relationships are easily programmed and can be used to verify and calibrate numerical calculations.

The Elastic Field Caused by a Circular Cylindrical Inclusion—Part I: Inside the Region x12+x22

1995 ◽  
Vol 62 (3) ◽  
pp. 579-584 ◽  
Author(s):  
Linzhi Wu ◽  
Shanyi Du
Keyword(s):  
Analytical Solutions ◽  
Elastic Field ◽  
Companion Paper ◽  
Elliptic Integrals ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Elastic Fields ◽  
Complete Elliptic Integrals ◽  
Nonsingular Surface ◽  
Surface Integrals

The displacement and stress fields caused by uniform eigenstrains in a circular cylindrical inclusion are analyzed inside the region x12+x22<a2,−∞<x3<∞ and are given in terms of nonsingular surface integrals. Analytical solutions can be expressed as functions of the complete elliptic integrals of the first, second and third kind. The corresponding elastic fields in the region x12+x22>a2,−∞<x3<∞ are solved by using the same technique (by Green’s functions) in the companion paper (Part II).

Magnetically Induced Stress Waves in a Conducting Solid—Theory and Experiment

1974 ◽  
Vol 41 (3) ◽  
pp. 641-646 ◽  
Author(s):  
F. C. Moon ◽  
S. Chattopadhyay
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Body Force ◽  
Capacitor Bank ◽  
Thermoelastic Stress ◽  
Compressional Wave ◽  
Stress Waves ◽  
Stress Fields ◽  
Radial Magnetic Field ◽  
Transient Magnetic Fields

The induction of stress waves by transient magnetic fields has been examined analytically for a conducting half space and experimentally for a cylindrical rod. The analytical model predicts both a body force generated compressional wave and a thermoelastic stress wave. The model shows the magnetic, temperature, and stress fields in the half space for various times after a prescribed magnetic field is applied at the boundary. In the experiment a transient, radial, magnetic field (up to 15 kilogauss) was applied to the end of a copper bar. The field was generated by discharging a small capacitor bank through a flat helical coil. The measured compressional stresses obtained in this manner were of the order of the measured magnetic pressure (B2/2μ0), at the end of the bar.

scholarly journals Stress fields around two pores in an elastic body: exact quadrature domain solutions

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150240
Author(s):  
Darren Crowdy
Keyword(s):  
Elastic Body ◽  
Analytical Solutions ◽  
Plane Elasticity ◽  
Stress Fields ◽  
Quadrature Domain ◽  
Mathematical Approach ◽  
Quadrature Domains ◽  
Planar Domains ◽  
Elastic Bodies ◽  
Prime Function

Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky–Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores.

The Elastic Field Caused by a Circular Cylindrical Inclusion—Part II: Inside the Region x12+x22>a2,−∞

1995 ◽  
Vol 62 (3) ◽  
pp. 585-589 ◽  
Author(s):  
Linzhi Wu ◽  
Shanyi Y. Du
Keyword(s):  
Stress Field ◽  
Elastic Medium ◽  
Analytical Solutions ◽  
Elastic Field ◽  
Numerical Results ◽  
Elliptic Integrals ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Complete Elliptic Integrals

Analytical solutions are presented for the displacement and stress fields caused by a circular cylindrical inclusion with arbitrary uniform eigenstrains in an infinite elastic medium. The expressions obtained and those presented in Part I constitute the solutions of the whole elastic field, −∞<x1,x2,x3<∞. In the present paper, it is found that the analytical solutions within the region x12+x22>a2,−∞<x3<∞ can also be expressed as functions of the complete elliptic integrals of the first, second, and third kind. When the length of inclusion tends towards the limit (infinity), the present solutions agree with Eshelby’s results. Finally, numerical results are shown for the stress field.

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