Acta Mechanica

, Volume 225, Issue 3, pp 647–661 | Cite as

Two-dimensional linear model of elastic shell accounting for general anisotropy of material

  • Petr E. Tovstik
  • Tatiana P. TovstikEmail author


A two-dimensional linearly elastic model of shells made of an anisotropic material described by 21 elastic moduli is developed. For this aim, the generalized Timoshenko–Reissner hypotheses are used. In contrast to the ordinary shell models, the tangential stress-resultants here depend not only on the tangential strains but also on the transverse shear. An asymptotic analysis of the obtained equations is fulfilled. The typical stress-strain states, namely the membrane state, the edge effect state, and the boundary layer, are constructed. The system of the Donnell type is delivered. As an example of general anisotropy, a composite material consisting of a matrix reinforced by the system of fibers inclined to the mid-surface is studied. Certain simple static problems and free vibration problems are solved for a cylindrical shell made of this material.


Boundary Layer Cylindrical Shell Free Vibration Timoshenko Beam Elasticity Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Institute of Problems of Mechanical EngineeringSt. PetersburgRussia

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