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Non-classical aspects of Kirchhoff type shells

Abstract

Kirchhoff type shells are continuum models used to study the mechanics of thin elastic bodies; these are largely based on the theory of surfaces. Here, we report a reformulation of Kirchhoff shells using the theory of moving frames. This reformulation permits us to treat the deformation and the geometry of the shell as two separate entities. The structure equations which represent the familiar torsion and curvature free conditions (of the ambient space) are used to combine deformation and geometry in a compatible way. From such a perspective, Kirchhoff type theories have non-classical features which are similar to the equations of defect mechanics (theory of dislocations and disclinations). Using the proposed framework, we solve a boundary value problem and thus demonstrate, to an extent, the importance of moving frames.

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Notes

  1. A curve is regular if the tangent vector does not vanish.

  2. Even though this assumption is always made in a classical continuum theory, it is never explicitly stated.

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Acknowledgements

BD was supported by ISRO through the Centre of Excellence in Advanced Mechanics of Materials; grant No. ISRO/DR/0133. BD would also like to thank Prof. Arun Srinivasa, TAMU for helpful discussions.

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Correspondence to Debasish Roy.

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Dhas, B., Roy, D. Non-classical aspects of Kirchhoff type shells. Ann. Solid Struct. Mech. 12, 23–32 (2020). https://doi.org/10.1007/s12356-020-00057-5

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Keywords

  • Kirchhoff shells
  • Moving frame
  • Structure equations
  • Defect mechanics