Boundary Integral Equation Formulation in Generalized Linear Thermo-Viscoelasticity With Rheological Volume

2002 ◽  
Author(s):  
Ahmed S. El-Karamany
Keyword(s):  
Integral Equation ◽  
Rheological Properties ◽  
Boundary Integral Equation ◽  
General Model ◽  
Relaxation Times ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Integral Equation Formulation ◽  
Special Cases ◽  
The Given

A general model of generalized linear thermo-viscoelasticity for isotropic material is established taking into consideration the rheological properties of the volume. As special cases the corresponding equations for the coupled thermo-viscoelasticity and the generalized thermo-viscoelasticity with one (Lord-Shulman theory) or with two relaxation times (Green-Lindsay theory) are obtained. The cases of thermo-viscoelasticity ignoring the rheological properties of volume can be obtained from the given model. The equations of the corresponding thermoelasticity theories result from the given model as special cases. A formulation of the boundary integral equation method, fundamental solutions of the corresponding differential equations are obtained and the dynamic reciprocity theorem is derived for this general model. Generalizations of Somiliana’s –Green and Maysels formulas are obtained. An example illustrating the BIE formulation is given. Special emphasis is given to the representation of primary fields, namely temperature and displacement.

Boundary Integral Equation Formulation in Generalized Linear Thermo-Viscoelasticity With Rheological Volume

2003 ◽  
Vol 70 (5) ◽  
pp. 661-667 ◽  
Author(s):  
A. S. El-Karamany
Keyword(s):  
Integral Equation ◽  
Rheological Properties ◽  
Boundary Integral Equation ◽  
Relaxation Times ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Phase Lag ◽  
Integral Equation Formulation ◽  
Special Cases ◽  
The Given

A general model of generalized linear thermo-viscoelasticity for isotropic material is established taking into consideration the rheological properties of the volume. The given model is applicable to three generalized theories of thermoelasticity: the generalized theory with one (Lord-Shulman theory) or with two relaxation times (Green-Lindsay theory) and with dual phase-lag (Chandrasekharaiah-Tzou theory) as well as to the dynamic coupled theory. The cases of thermo-viscoelasticity of Kelvin-Voigt model or thermoviscoelasticity ignoring the rheological properties of the volume can be obtained from the given model. The equations of the corresponding thermoelasticity theories result from the given model as special cases. A formulation of the boundary integral equation (BIE) method, fundamental solutions of the corresponding differential equations are obtained and an example illustrating the BIE formulation is given.

Fast Multipole Accelerated Boundary Integral Equation Method for Evaluating the Stress Field Associated with Dislocations in a Finite Medium

2012 ◽  
Vol 12 (1) ◽  
pp. 226-246 ◽  
Author(s):  
Degang Zhao ◽  
Jingfang Huang ◽  
Yang Xiang
Keyword(s):  
Integral Equation ◽  
Stress Field ◽  
Boundary Integral Equation ◽  
Fast Multipole Method ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Fast Multipole ◽  
Numerical Examples ◽  
Integral Equation Formulation ◽  
Finite Medium

AbstractIn this paper, we develop an efficient numerical method based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated with dislocations in a finite medium. Numerical examples are presented to examine the influence from material boundaries on dislocations.

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