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Thermoelastic Processes and Equilibrium

  • Jean Salençon
Chapter

Abstract

As already observed, the equation of motion (1.1) results in a system of three first order partial differential equations for the tensor field σ Type="Italic">, that is, for the six scalar fields that are the components of the symmetric tensor σ, functions of the three space variables at each time t:
$$\left\{ {\begin{array}{*{20}{c}} {{\text{in a Galilean frame }},} \hfill \\ {{\text{div}}\underline{\underline \sigma } \left( {\underline x ,t} \right) + \rho \left( {\underline x ,t} \right)\left( {\underline F \left( {\underline x ,t} \right) - \underline a \left( {\underline x ,t} \right)} \right) = 0{\text{ on}}{{\Omega }_{{t,}}}} \hfill \\ {\left[\kern-0.15em\left[ {\underline{\underline \sigma } \left( {\underline x ,t} \right)} \right]\kern-0.15em\right] \cdot \underline n \left( {\underline x } \right) = 0{\text{ on }}{{\Sigma }_{{\underline{\underline {\sigma \cdot }} }}}^{1}} \hfill \\ \end{array} } \right.$$
(1.1)

Key Words

Quasi-static thermoelastic processes Thermoelastic equilibrium Boundary conditions Small displacements Small perturbations Linearisation Superposition principle Kinematically admissible fields Statically admissible fields Displacement method Stress method Torsion Saint Venant 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jean Salençon
    • 1
  1. 1.Laboratoire de Mécanique des SolidesÉcole PolytechniquePalaiseau CedexFrance

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