On the modeling of a nonlinear plate and a nonlinear shell

We consider modeling of a nonlinear thin plate and a nonlinear thin shell under the following assumptions: (a) the materials are nonlinear; (b) the deflections are small (linear strain displacement relations). For a plate with a planar middle surface, we consider the bending of the plate to establish the strain energy, the equilibrium equations, and the motion equations. For a shell with a curved middle surface in IR³, we derive a nonlinear model where a deformation in three-dimensions is concerned.