Dynamic Green’s functions in anisotropic piezoelectric, thermoelastic and poroelastic solids

1994 ◽  
Vol 447 (1929) ◽  
pp. 175-188 ◽  
Keyword(s):  
Time Domain ◽  
Unit Sphere ◽  
Green's Functions ◽  
Green’S Functions ◽  
Fundamental Solutions ◽  
Anisotropic Elasticity ◽  
Field Equations ◽  
One Dimensional ◽  
Time Harmonic ◽  
Point Forces

A procedure is described to generate fundamental solutions or Green’s functions for time harmonic point forces and sources. The linearity of the field equations permits the Green’s function to be represented as an integral over the surface of a unit sphere, where the integrand is the solution of a one-dimensional impulse response problem. The method is demonstrated for the theories of piezoelectricity, thermoelasticity, and poroelasticity. Time domain analogues are discussed and compared with known expressions for anisotropic elasticity.

Fundamental solutions and analysis of an interfacial crack in a one-dimensional hexagonal quasicrystal bi-material

2020 ◽  
Vol 25 (5) ◽  
pp. 1124-1139
Author(s):  
CuiYing Fan ◽  
Shuai Chen ◽  
QiaoYun Zhang ◽  
Ming Hao Zhao ◽  
Bing Bing Wang
Keyword(s):  
Differential Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Crack Opening ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Delta Function ◽  
Numerical Approach ◽  
Fundamental Solutions ◽  
One Dimensional

Using the Stroh formalism, Green’s functions are obtained for phonon and phason dislocations and opening displacements on the interface of a one-dimensional hexagonal quasicrystal bi-material. The integro-differential equations governing the interfacial crack are then established, and the singularities of the phonon and phason displacements at the crack tip on the interface are analyzed. To eliminate the oscillating singularities, we represent the delta function in terms of the Gaussian distribution function in the Green’s functions and the integro-differential equations, which helps reduce these equations to the standard integral equations. Finally, a boundary element numerical approach is also proposed to solve the integral equation for the crack opening displacements, the asymptotic expressions of the extended intensity factors, and the energy release rate in terms of the crack opening displacements near the crack tip. In numerical examples, the effect of the Gaussian parameter on the numerical results is discussed, COMSOL software is used to validate the analytical solution, and the influence of the different phonon and phason loadings on the interfacial crack behaviors is further investigated.

scholarly journals Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

2019 ◽  
Vol 24 (1) ◽  
pp. 26 ◽  
Author(s):  
Sergey Davydov ◽  
Andrei Zemskov ◽  
Elena Akhmetova
Keyword(s):  
Half Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Local Equilibrium ◽  
Linear Equations ◽  
Integral Form ◽  
External Effects ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
The Laplace Transform

This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green’s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green’s functions. The obtained Green’s functions was analyzed. Test calculations were performed on the examples of some technological processes.

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