scholarly journals Green's Functions of an External Circular Crack in a Transversely Isotropic Piezoelectric Medium.

1999 ◽  
Vol 42 (1) ◽  
pp. 73-79 ◽  
Author(s):  
Weiqiu CHEN ◽  
Tadashi SHIOYA
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Piezoelectric Medium ◽  
External Circular Crack

Anti-plane time-harmonic Green’s functions for a coated circular inhomogeneity in a piezoelectric medium with spring- or membrane-type imperfect interfaces

2016 ◽  
Vol 22 (9) ◽  
pp. 1813-1846 ◽  
Author(s):  
Yin Shi ◽  
Yongping Wan ◽  
Zheng Zhong
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Transversely Isotropic ◽  
Piezoelectric Medium ◽  
Two Phase ◽  
Imperfect Interfaces ◽  
Time Harmonic ◽  
Special Cases ◽  
Circular Inhomogeneity ◽  
Membrane Type

Two-dimensional anti-plane time-harmonic dynamic Green’s functions for a coated circular inhomogeneity in an infinitely extended matrix with spring- or membrane-type imperfect interfaces are presented. The inhomogeneity, coating and matrix are all assumed to be piezoelectric and transversely isotropic. By using the Bessel function expansions, explicit solutions for the electromechanical fields induced by a time-harmonic anti-plane line force and line charge located in the unbounded matrix, the annular coating and the circular inhomogeneity are derived. The present solutions can recover the anti-plane Green’s functions for some special cases, such as the dynamic or quasi-static Green’s functions of piezoelectricity with perfect interfaces, as well as the dynamic or quasi-static Green’s functions for a two-phase composite with perfect or imperfect interfaces. By means of detailed discussions, selected calculated results are graphically shown to demonstrate the dependence of the electromechanical fields on the circular frequency and the interface properties as well as the coating and size of the inclusion.

scholarly journals The Fundamental Solutions for the Stress Intensity Factors of Modes I, II And III. The Axially Symmetric Problem

2015 ◽  
Vol 20 (2) ◽  
pp. 345-372
Author(s):  
B. Rogowski
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Green's Functions ◽  
Green’S Functions ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Engineering Practice ◽  
Crack Plane ◽  
Axially Symmetric ◽  
Intensity Factors

Abstract The subject of the paper are Green’s functions for the stress intensity factors of modes I, II and III. Green’s functions are defined as a solution to the problem of an elastic, transversely isotropic solid with a penny-shaped or an external crack under general axisymmetric loadings acting along a circumference on the plane parallel to the crack plane. Exact solutions are presented in a closed form for the stress intensity factors under each type of axisymmetric ring forces as fundamental solutions. Numerical examples are employed and conclusions which can be utilized in engineering practice are formulated.

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