Generalization of Green’s functions and Green’s formulae onto a case of boundary value problems in the classical theory of static and dynamical thermal stresses are suggested i this
article.These result has been obtained for the first time and are the generalization of the well known Green’s integral formulae for the theories of heat conduction and elasticity onto static and
dynamical theories of uncoupled thermoelastisity . They can also be explained as a generalization of a classical integral Maysel’s formulae onto those cases when the temperature field satisfies the
equation of heat conduction, the field being caused by the internal heat source and temperature or heat flux prescribed on the boundary. The advantage is that it allows us to unite the two-stage
process of solving the boundary value problems in the theory of thermal stresses (the first stage comprise the determination of temperature fields and second stage comprises the determination of
thermoplastic displacements). The investigations have shown that the possibilities of realizing the concrete solutions which have the form given generalization are so vast that they could be a
subject for a whole handbook on influence functions and integral solutions of boundary value problems in the theory of thermal stresses. They are, for example, the solutions for locally mixed
boundary value problems for canonic elastic bodies for Cartesian, polar, cylindrical, spherical and other systems of orthogonal coordinate. In doing so most of them can be expressed in terms of
elementary functions, that are very important for practical calculations.
Date
2004-08-31
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Additional Notes
Sheremet V., Generalization of Green's Formulae in Thermoelasticity. An electronic publication at National Institute of Standards and Technology (NIST) of USA, 2003, 4
p.
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