Abstract
Equations of equilibrium and four geometric and static boundary conditions are constructed for an entirely Lagrangian non-linear theory of shells. In the case of a linearly-elastic material and conservative surface and boundary loadings the shell relations are derivable as stationarity conditions of the Hu-Washizu free functional. For the geometrically non-linear first-approximation theory of elastic shells several consistently simplified versions of the shell equations are discussed. Several sets of equations for teories of shells undergoing moderate or large/small rotations are presented. The majority of the simplified versions allow an exact variational formulation using a Hu-Washizu free functional. A unified theory of superposition of non-linear deformations in thin shells is outlined and two equivalent incremental formulations of shell equations in the total Lagrangian and the updated Lagrangian descriptions are given.
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