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

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)73-86
Number of pages14
JournalJournal of Engineering Mathematics
Volume95
Issue number1
DOIs
Publication statusPublished - Dec 2015

Fingerprint

Saint-Venant's Principle
Thermoelasticity
Elasticity
Tend
Elastostatics
Formulation
Strain Energy
Zero
Bilinear form
Strain energy
Thermal energy
Dirichlet Boundary Conditions
Upper and Lower Bounds
Boundary conditions
Geometry
Energy

Keywords

  • General elongated geometries
  • Linear thermo-elastostatics
  • Saint-Venant’s principle
  • Zanaboni

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

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abstract = "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 Poincar{\'e} 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.",
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Zanaboni’s formulation of Saint-Venant’s principle extended to linear thermo-elasticity. / Knops, R. J.

In: Journal of Engineering Mathematics, Vol. 95, No. 1, 12.2015, p. 73-86.

Research output: Contribution to journalArticle

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