Closure to “Discussion of ‘Point Force Solution for an Infinite Transversely Isotropic Solid’” (1977, ASME J. Appl. Mech., 44, pp. 514–515)

1977 ◽  
Vol 44 (3) ◽  
pp. 515-515
Author(s):  
Y.-C. Pan ◽  
T.-W. Chou
Keyword(s):  
Transversely Isotropic ◽  
Point Force ◽  
Isotropic Solid

Point Force Solution for an Infinite Transversely Isotropic Solid

1976 ◽  
Vol 43 (4) ◽  
pp. 608-612 ◽  
Author(s):  
Y.-C. Pan ◽  
T.-W. Chou
Keyword(s):  
Elastic Constants ◽  
Numerical Evaluation ◽  
Systematic Approach ◽  
Transversely Isotropic ◽  
Potential Functions ◽  
Point Force ◽  
Isotropic Materials ◽  
Isotropic Solid ◽  
Individual Term ◽  
Transversely Isotropic Materials

The solution for a point force applied at the interior of an infinite transversely isotropic solid is obtained by introducing three potential functions which govern the displacements. Unlike previous publications where the solutions are expressed in different forms depending on the conditions satisfied by the elastic constants, the present paper provides a systematic approach to obtain a unified solution which is applicable for all stable transversely isotropic materials. The expression obtained does not have the deficiency suffered by previous solutions, namely, each individual term in the present expression does not tend to infinity on the z-axis. Thus accurate numerical evaluation of the Green’s function can be directly performed without the need to resolve the singularity algebraically.

Elastic waves through a simulated fractured medium

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 964-977 ◽  
Author(s):  
Chaur‐Jian Hsu ◽  
Michael Schoenberg
Keyword(s):  
Normal Stress ◽  
Stress Level ◽  
Elastic Waves ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Static Stress ◽  
Ultrasonic Velocities ◽  
Bulk Properties ◽  
Isotropic Solid ◽  
Fractured Medium

Ultrasonic velocities were measured on a block composed of lucite plates with roughened surfaces pressed together with a static normal stress to simulate a fractured medium. The measurements, normal, parallel, and oblique to the fractures, show that for wavelengths much larger than the thickness of an individual plate, the block can be modeled as a particular type of transversely isotropic (TI) medium that depends on four parameters. This TI medium behavior is the same as that of an isotropic solid in which are embedded a set of parallel linear slip interfaces, specified by (1) the excess compliance tangential to the interfaces and (2) the excess compliance normal to the interfaces. At all static stress levels, we inverted the data for the background isotropic medium parameters and the excess compliances. The background parameters obtained were basically independent of stress level and agreed well with the bulk properties of the lucite. The excess compliances decreased with increasing static closing stress, implying that increasing static stress forces asperities on either side of a fracture into greater contact, gradually eliminating the excess compliance that gives rise to the anisotropy. A medium with such planes of excess compliance has been shown, theoretically, to describe the behavior of a medium with long parallel joints, as well as a medium with embedded parallel microcracks.

FREE VIBRATION OF TRANSVERSELY ISOTROPIC SOLID AND THICK-WALLED TOROIDAL SHELLS

2006 ◽  
Vol 06 (03) ◽  
pp. 359-375 ◽  
Author(s):  
YAN JANE LIU ◽  
GEORGE R. BUCHANAN
Keyword(s):  
Finite Element ◽  
Coordinate System ◽  
Transversely Isotropic ◽  
Element Formulation ◽  
Isotropic Materials ◽  
Isotropic Solid ◽  
Transversely Isotropic Materials ◽  
Toroidal Coordinates ◽  
Hexagonal Crystals ◽  
Toroidal Shells

The frequency of vibration of thick-walled toroidal shells is studied using a finite element formulation wherein the finite element is derived directly in toroidal coordinates. Hexagonal crystals of thallium and cadmium are used as representative transversely isotropic materials. The shell is assumed to be transversely isotropic with respect to the toroidal radial direction, and results based on that assumption are contrasted to a shell that is transversely isotropic with respect to the circumferential toroidal coordinate. It is established that an analysis based on a toroidal coordinate system is superior to an axisymmetric coordinate system and has some advantages over a commercial finite element code. Tables of results are presented that compare frequency of vibration for the above mentioned transversely isotropic materials and isotropic materials.

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