Boundary Integral Equation Formulation for Fractional Order Theory of Thermo-Viscoelasticity

2021 ◽  
pp. 149-168
Author(s):  
M. A. Elhagary
Keyword(s):  
Integral Equation ◽  
Fractional Order ◽  
Boundary Integral Equation ◽  
Order Theory ◽  
Boundary Integral ◽  
Equation Formulation ◽  
Integral Equation Formulation

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.

To: “Full wave logging in an irregular borehole” by Michel Bouchon and Denis P. Schmitt (GEOPHYSICS, 54, 758–765, June 1989)

Geophysics ◽  
1989 ◽  
Vol 54 (11) ◽  
pp. 1514-1514
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Displacement Vector ◽  
Radial Force ◽  
Boundary Integral ◽  
Equation Formulation ◽  
Full Wave ◽  
Integral Equation Formulation

The boundary‐integral equation formulation described by Bouchon and Schmitt is exact, but the derivation of the formulas for the components of the displacement vector in the formation due to circular radial force are erroneous. The correct derivation follows.

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