Cylindrical Thin Shell Kinematics

Due to the less complicated geometry, the representation of the kinematic relations may be simplified with the following substitutions  

Accordingly, the strain measures as well as rotations have to be renamed. Then the introduction of Eqs. (6.11) into Eqs. (6.8) and (6.9) yields  

with Eqs. (6.12) and (6.15), the complete set of strain measures in terms of displacements is established for thin cylindrical shells. By neglecting the underlined terms of Eqs. (6.15), this formulation based on the theory of Sanders [158] and Koiter [114], may be reduced to the also well-known formulation of Donnell [64] or Girkmann [84]. Theories similar to the latter likewise have been developed by Mushtari and Vlasov, see Novozhilov [134]. The inspection of the constituents of terms involving the radius shows that 

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