Zanaboni’s formulation of Saint-Venant’s principle extended to linear thermo-elasticity

Zanaboni’s formulation of Saint-Venant’s principle states that in a sufficiently elongated body of otherwise general geometry, the strain energy of those parts of the body remote from the load surface tend to zero. The extension to the coupled theory of linear thermo-elastostatics undertaken here explicitly for Dirichlet boundary conditions is non-trivial and involves both the construction of a generalised Poincaré inequality and the derivation of positive lower and upper bounds for certain bilinear forms. Modification of Zanaboni’s original argument is then possible and shows that the mechanical and thermal energies of parts of the body increasingly remote from the load surface likewise tend to zero.