Acta Mechanica

, Volume 230, Issue 3, pp 851–869 | Cite as

Modified couple stress theory in orthogonal curvilinear coordinates

  • Hamed Farokhi
  • Mergen H. GhayeshEmail author
Original Paper


The formulations for the modified couple stress theory (MCST) are consistently derived in general orthogonal curvilinear coordinate systems. In particular, the expressions for the rotation vector, higher-order strain, and stress tensors, i.e., the rotation gradient tensor and the deviatoric part of the symmetric couple stress tensor, and the classical strain and stress tensors are derived for an arbitrary orthogonal curvilinear coordinate system. Additionally, using the theory of surfaces, the formulations for the MCST are derived for general doubly curved coordinates, which are more convenient to use for shells of arbitrary curvature. The expressions for special cases, i.e., cylindrical and spherical shells, are obtained. The MCST expressions derived in this study are comprehensive and generally and can be used for consistent utilisation of the MCST in any orthogonal curvilinear coordinate system.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Construction EngineeringNorthumbria UniversityNewcastle upon TyneUK
  2. 2.School of Mechanical EngineeringUniversity of AdelaideAdelaideAustralia

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