Solution in Elementary Functions to a BVP of Thermoelasticity: Green's Functions and Green's-Type Integral Formula for Thermal Stresses within a Half-Strip

2014 ◽  
Vol 37 (8) ◽  
pp. 947-968 ◽  
Author(s):  
Victor Seremet ◽  
Erasmo Carrera
Keyword(s):  
Green's Functions ◽  
Thermal Stresses ◽  
Green’S Functions ◽  
Integral Formula ◽  
Elementary Functions ◽  
Half Strip ◽  
Type Integral

Indefinite Green's Functions and Elementary Solutions

1963 ◽  
Vol 6 (1) ◽  
pp. 71-103 ◽  
Author(s):  
G. F. D. Duff ◽  
R. A. Ross
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Applied Mathematics ◽  
Integral Transforms ◽  
Source Distribution ◽  
Asymptotic Estimates ◽  
Elementary Functions ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Superposition Of Solutions

Linear differential equations both ordinary and partial are often studied by means of Green's functions. One reason for this is that linearity permits superposition of solutions. A Green's function describes the "effect" of a point source, and the description of line, surface, or volume sources is achieved by superposing, that is to say, integrating, this function over the source distribution.For equations with constant coefficients the use of integral transforms permits the calculation of such source functions in the form of integrals. Only in the simplest cases is explicit evaluation by elementary functions possible, and this has perforce led to the use of asymptotic estimates, which so thoroughly pervade the domain of applied mathematics.

Thermal Stresses in an Orthotropic Elastic Semispace

1972 ◽  
Vol 39 (1) ◽  
pp. 87-90 ◽  
Author(s):  
A. Y. Ako¨z ◽  
T. R. Tauchert
Keyword(s):  
Temperature Field ◽  
Green's Functions ◽  
Thermal Stresses ◽  
Green’S Functions ◽  
Elastic Solid ◽  
Displacement Boundary ◽  
Steady State Temperature ◽  
Method Of Solution ◽  
Displacement Potentials ◽  
General Method

The thermal stresses in an orthotropic semi-infinite elastic solid subject to plane strain are investigated. A general method of solution based upon displacement potentials is presented for the case of a steady-state temperature field. Results are presented for both stress-free and zero-displacement boundary conditions. The stresses are written in terms of Green’s functions, where the Green’s functions represent stresses induced by a line source of temperature on the bounding plane.

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