Local symmetry group in the general theory of elastic shells. (English) Zbl 1105.74019
Summary: We establish the local symmetry group of the dynamically and kinematically exact theory of elastic shells. The group consists of an ordered triple of tensors which make the shell strain energy density invariant under the change of reference placement. Definitions of the fluid shell, solid shell, and membrane shell are introduced in terms of the symmetry group. Within solid shells we discuss in more detail the isotropic, hemitropic and orthotropic shells, and the corresponding invariant properties of the strain energy density. For physically linear shells, when the density becomes a quadratic function of shell strain and bending tensors, reduced representations of the density are established for orthotropic, cubic-symmetric and isotropic shells. The reduced representations contain much less independent material constants to be found from experiments.
MSC:
| 74K25 | Shells |
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