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.

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.

A New Boundary Integral Equation Formulation for Linear Elastic Solids

1992 ◽  
Vol 59 (2) ◽  
pp. 344-348 ◽  
Author(s):  
Kuang-Chong Wu ◽  
Yu-Tsung Chiu ◽  
Zhong-Her Hwu
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral Equations ◽  
Analytic Solutions ◽  
Boundary Integral ◽  
Tangential Displacement ◽  
Infinite Body ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Elasticity Problems

A new boundary integral equation formulation is presented for two-dimensional linear elasticity problems for isotropic as well as anisotropic solids. The formulation is based on distributions of line forces and dislocations over a simply connected or multiply connected closed contour in an infinite body. Two types of boundary integral equations are derived. Both types of equations contain boundary tangential displacement gradients and tractions as unknowns. A general expression for the tangential stresses along the boundary in terms of the boundary tangential displacement gradients and tractions is given. The formulation is applied to obtain analytic solutions for half-plane problems. The formulation is also applied numerically to a test problem to demonstrate the accuracy of the formulation.

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