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A generalization of the Saint-Venant’s principle for an elastic body with dipolar structure

  • Marin MarinEmail author
  • Andreas Öchsner
  • Eduard M. Craciun
Original Article
  • 9 Downloads

Abstract

This study is concerned with the linear elasticity theory for bodies with a dipolar structure. In this context, we approach transient elastic processes and the steady state in a cylinder consisting of such kind of body which is only subjected to some boundary restrictions at a plane end. We will show that at a certain distance \(d=d(t)\), which can be calculated, from the loaded plan, the deformation of the body vanishes. For the points of the cylinder located at a distance less than d, we will use an appropriate measure to assess the decreasing of the deformation relative to the distance from the loaded plane end. The fact that the measure, that assess the deformation, decays with respect to the distance at the loaded end is the essence of the principle of Saint-Venant.

Keywords

Dipolar bodies Thermoelastostatics Saint-Venant’s principle Spatial decay 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTransilvania University of BrasovBrasovRomania
  2. 2.Faculty of Mechanical EngineeringEsslingen University of Applied SciencesEsslingenGermany
  3. 3.Faculty of Mechanical, Industrial and Maritime EngineeringOvidius University of ConstantaConstantaRomania

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