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Variational Methods in Linearised Thermoelasticity

  • Jean Salençon
Chapter
  • 689 Downloads

Abstract

In Sect. 2 of Chap. VIII, we stated the small perturbation hypothesis (S.P.H.). This allows a physical, then geometrical linearisation of the constitutive law and leads to a linearised expression for the equations governing a quasi-static thermoelastic process relative to the known reference configuration. The equations obtained in this way (Chap. VIII, Sect. 2.3) show that the thermal problem decouples (so that the temperature change field becomes one of the known fields), and define at each instant of time a thermoelastic equilibrium problem that depends only on the current excitations and the initial state.

Key Words

Kinematically admissible displacement fields Statically admissible stress fields Dualisation Virtual work theorem Convexity Variational principles Theory of minimum potential energy Theory of minimum complementary energy Uniqueness Energy bounds Numerical methods Approximation Clapeyron equation Reciprocity theorem Self-equilibrating stress fields Redundant unknowns Loading parameters Castigliano theorem Minimum potential theorem 

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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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