Laminated Tubes under Extension, Internal and External Pressure

2014 ◽  
Vol 30 (5) ◽  
pp. 455-466 ◽  
Author(s):  
W.-D. Tseng ◽  
J.-Q. Tarn ◽  
J.-H. Chang
Keyword(s):  
Transversely Isotropic ◽  
External Pressure ◽  
Axisymmetric Deformation ◽  
Elastic Tube ◽  
The State ◽  
Isotropic Layer ◽  
Stress Distributions ◽  
End Effect ◽  
Lateral Boundary Conditions ◽  
Symplectic Orthogonality

AbstractAn exact analysis of deformation and stress field in a laminated elastic tube under extension and uniform pressuring is presented. The problem of finite laminated tube is considered with emphasis on the end effect. The problem is formulated on the basis of the state space formalism for axisymmetric deformation of transversely isotropic layer. The transfer matrix transmits the state vector in radial direction from inner surface to outer surface and takes into account the interfacial continuity and lateral boundary conditions in a rigorous manner. Upon delineating the symplectic orthogonality relations of the eigenvectors and by using eigenfunction expansion, an exact solution which satisfies the end conditions is determined. The results show that the end effect is significant but confined to a local region near the base where the displacement and stress distributions are remarkably different from those according to the simplified solutions that only satisfy lateral BC.

A Circular Elastic Cylinder Under Extension

2011 ◽  
Vol 27 (3) ◽  
pp. 399-407 ◽  
Author(s):  
W.-D. Tseng ◽  
J.-Q. Tarn
Keyword(s):  
Transversely Isotropic ◽  
Elastic Cylinder ◽  
Axisymmetric Deformation ◽  
Axial Stiffness ◽  
Stress Distributions ◽  
End Effect ◽  
Rigorous Solution ◽  
Concentrated Load ◽  
End Conditions ◽  
Space Formalism

ABSTRACTAnalysis of deformation and stress field in a circular elastic cylinder under the extension is presented, with emphasis on the end effect. The problem is formulated on the basis of the state space formalism for axisymmetric deformation of transversely isotropic materials. A rigorous solution that satisfies the prescribed end conditions is determined by using symplectic eigenfunction expansion, thereby, the applicability of the Saint-Venant solution is examined. The results show that the end effect is significant but confined to a local region near the base of the cylinder where the end plane is perfectly bonded or subjected to a concentrated load. As the axial stiffness increases, the end effect on the stress state increases at the loaded end but decreases at the bonded end. The displacement and stress distributions across the section are uniform throughout the length of the cylinder except near the ends.

Anisotropic Porochemoelectroelastic Solution for an Inclined Wellbore Drilled in Shale

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Minh H. Tran ◽  
Younane N. Abousleiman
Keyword(s):  
Porous Media ◽  
Fluid Pressure ◽  
Transversely Isotropic ◽  
Biological Tissues ◽  
Analytical Models ◽  
Combined Effects ◽  
Saturated Porous Media ◽  
Stress Distributions ◽  
Shale Formations ◽  
Electrically Charged

The porochemoelectroelastic analytical models have been used to describe the response of chemically active and electrically charged saturated porous media such as clay soils, shales, and biological tissues. However, existing studies have ignored the anisotropic nature commonly observed on these porous media. In this work, the anisotropic porochemoelectroelastic theory is presented. Then, the solution for an inclined wellbore drilled in transversely isotropic shale formations subjected to anisotropic far-field stresses with time-dependent down-hole fluid pressure and fluid activity is derived. Numerical examples illustrating the combined effects of porochemoelectroelastic behavior and anisotropy on wellbore responses are also included. The analysis shows that ignoring either the porochemoelectroelastic effects or the formation anisotropy leads to inaccurate prediction of the near-wellbore pore pressure and effective stress distributions. Finally, wellbore responses during a leak-off test conducted soon after drilling are analyzed to demonstrate the versatility of the solution in simulating complex down-hole conditions.

Ultrasonic Measurement of Forced Diameter Variations in an Elastic Tube

1994 ◽  
Vol 16 (2) ◽  
pp. 124-142 ◽  
Author(s):  
Javier C. Berrios ◽  
Peder C. Pedersen
Keyword(s):  
Rigid Wall ◽  
External Pressure ◽  
Experimental Models ◽  
Elastic Tube ◽  
Ultrasonic Measurement ◽  
Time Shift ◽  
Correlation Technique ◽  
Pressure Function ◽  
Diameter Variation ◽  
Thin Walled Tube

This paper presents an ultrasonic measurement technique to determine an elasticity parameter, called the apparent compliance, in a thin-walled tube. The apparent compliance is obtained by ultrasound pulse-echo measurement of the diameter variation in response to an externally applied time-varying pressure function. Specifically, the diameter variation is obtained by tracking the time shift of the echoes from the front and back walls of the tube using a correlation technique. This technique is named the Forced Vibration Method (FVM). This approach to compliance measurement is distinctly different from compliance measurements using the blood function as excitation function, but is closely related to the elastic imaging concept. Two experimental models, termed the rigid wall model and the leg-like model, have been developed. These models allow the amplitude and frequency of the pressure function as well as the dimensions and properties of the tube to be varied. Results for the diameter variations vs. location along the tube and frequency of external pressure function are presented for both models.

The effect of transverse isotropy on isotropic traveltime inversion of vertical seismic profile data—A modeling study

Geophysics ◽  
1990 ◽  
Vol 55 (9) ◽  
pp. 1235-1241 ◽  
Author(s):  
Jan Douma
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Vertical Axis ◽  
Seismic Profile ◽  
Isotropic Layer ◽  
Low Velocity ◽  
Traveltime Inversion ◽  
Axis Of Symmetry ◽  
Transversely Isotropic Layer

Traveltime inversion of multioffset VSP data can be used to determine the depths of the interfaces in layered media. Many inversion schemes, however, assume isotropy and consequently may introduce erroneous structures for anisotropic media. Synthetic traveltime data are computed for layered anisotropic media and inverted assuming isotropic layers. Only the interfaces between these layers are inverted. For a medium consisting of a horizontal isotropic low‐velocity layer on top of a transversely isotropic layer with a horizontal axis of symmetry (e.g., anisotropy due to aligned vertical cracks), 2-D isotropic inversion results in an anticline. For a given axis of symmetry the form of this anticline depends on the azimuth of the source‐borehole direction. The inversion result is a syncline (in 3-D a “bowl” structure), regardless of the azimuth of the source‐borehole direction for a vertical axis of symmetry of the transversely isotropic layer (e.g., anisotropy due to horizontal bedding).

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