Stress-focusing Effect in a Uniformly Heated Transversely Isotropic Piezoelectric Solid Sphere

2007 ◽  
Vol 20 (3) ◽  
pp. 255-275 ◽  
Author(s):  
H.L. Dai ◽  
Y.M. Fu
Keyword(s):  
Transversely Isotropic ◽  
Solid Sphere ◽  
Focusing Effect ◽  
Piezoelectric Solid

Penny-shaped and half-plane cracks in a transversely isotropic piezoelectric solid under arbitrary loading

2000 ◽  
Vol 70 (1-3) ◽  
pp. 201-229 ◽  
Author(s):  
E. Karapetian ◽  
I. Sevostianov ◽  
M. Kachanov
Keyword(s):  
Half Plane ◽  
Transversely Isotropic ◽  
Arbitrary Loading ◽  
Piezoelectric Solid

On Stress-Focusing Effect in a Uniformly Heated Solid Sphere

2003 ◽  
Vol 70 (2) ◽  
pp. 304-309 ◽  
Author(s):  
H. J. Ding ◽  
H. M. Wang ◽  
W. Q. Chen
Keyword(s):  
Temperature Rise ◽  
Stress Responses ◽  
Constant Pressure ◽  
Integral Transform ◽  
External Surface ◽  
Separation Of Variables ◽  
Solid Sphere ◽  
Uniform Temperature ◽  
Focusing Effect ◽  
Isotropic Solid

By using the separation of variables technique, the dynamic thermal stress responses in an isotropic solid sphere subjected to uniform temperature rise all over the sphere and a sudden constant pressure at the external surface are performed successfully. The analytical solutions of the radial and hoop dynamic stresses at the center are also obtained. By means of the present method, integral transform can be avoided. Numerical results denote that a very high dynamic stress peak appears periodically at the center of the isotropic solid sphere subjected to uniform temperature rise all over the sphere and a sudden constant pressure at the external surface.

A penny-shaped crack in a transversely isotropic piezoelectric solid: Modes II and III problems

1999 ◽  
Vol 15 (1) ◽  
pp. 52-58 ◽  
Author(s):  
Chen Weiqui ◽  
Ding Haojiang
Keyword(s):  
Transversely Isotropic ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Piezoelectric Solid

Stress-Focusing Effect in a Uniformly Heated Solid Sphere

1991 ◽  
Vol 58 (1) ◽  
pp. 58-63 ◽  
Author(s):  
Toshiaki Hata
Keyword(s):  
Arrival Time ◽  
Solid Sphere ◽  
Stress Waves ◽  
Ray Theory ◽  
Reflected Waves ◽  
Focusing Effect ◽  
Inverse Transform ◽  
Ray Path ◽  
Very High ◽  
Constant Period

The ray theory is applied to the stress-focusing effects in a uniformly heated solid sphere. The stress-focusing effect is the phenomenon that, under an instantaneous heating, stress waves reflected from the free surface of the sphere result in very high stresses at the center. Using the ray theory, the Laplace transformed solution of stress waves in the sphere is sorted out into rays according to the ray path of multiply-reflected waves. Inverse transform of each ray gives rise to the exact solution of the transient response up to the arrival time of the next ray. The numerical results reveal that stresses peak out periodically at a constant period and, unlike the case of cylinder, the radial stress at the center of the sphere is bounded.

Construction of Dynamic Fundamental Solutions for Piezoelectric Solids

1995 ◽  
Vol 48 (11S) ◽  
pp. S222-S229 ◽  
Author(s):  
Naum Khutoryansky ◽  
Horacio Sosa
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Point Of View ◽  
Integral Representations ◽  
Computational Point ◽  
Plane Wave Decomposition ◽  
Piezoelectric Solid ◽  
Piezoelectric Solids ◽  
Wave Decomposition

Fundamental solutions are derived within the framework of transient dynamic, three-dimensional piezoelectricity. The purpose of the article is to show alternate integral representations for such solutions. Thus, a representation over the unit sphere in accordance to a methodology based on the plane wave decomposition is provided. It is shown, however, that more efficient representations from a computational point of view can be achieved through appropriate coordinate transformations. Hence, representations of the fundamental solutions over surfaces of slowness are provided as novel alternatives to more classical approaches. The computational benefits of these new representations are displayed through a numerical example involving a transversely isotropic piezoelectric solid.

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