Summary
For shells of finite deformations, a non-linear theory will be derived using the Kirchhoff-Love assumption. Its derivation is accomplished by a variational procedure ensuring a consistent formulation. Special attention is confined to the correct derivation of the dynamic boundary conditions which succeeds by introduction of a rotation vector connected with the rotational movement of the normal vector of the middle surface. The paper closes with the operator formulation of the theory which demonstrates the characteristic properties of the non-linear theories in a very general manner.
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Basar, Y., Krätzig, W.B. A consistent shell theory for finite deformations. Acta Mechanica 76, 73–87 (1989). https://doi.org/10.1007/BF01175797
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DOI: https://doi.org/10.1007/BF01175797