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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093, Brasov, Romania

    Marin Marin

  2. Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, 73728, Esslingen, Germany

    Andreas Öchsner

  3. Faculty of Mechanical, Industrial and Maritime Engineering, Ovidius University of Constanta, 900527, Constanta, Romania

    Eduard M. Craciun

Authors
  1. Marin Marin
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  2. Andreas Öchsner
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  3. Eduard M. Craciun
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Correspondence to Marin Marin.

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Communicated by Andreas Öchsner.

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Marin, M., Öchsner, A. & Craciun, E.M. A generalization of the Saint-Venant’s principle for an elastic body with dipolar structure. Continuum Mech. Thermodyn. 32, 269–278 (2020). https://doi.org/10.1007/s00161-019-00827-6

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  • DOI: https://doi.org/10.1007/s00161-019-00827-6

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