A modified Hellinger-Reissner variational functional including only two independent variables for large displacement of thin shallow shell

The variational functional of the Hellinger-Reissner variational principle for thelarge displacement problem of a thin shallow shell with an arbitrary shape is firstestablished. Then the functional of the modifed principle suitable for the finite elementmethod is derived. In the .functional only two independent variables, the deflection wand the stress function F are inchuded. The displacement expressions in the middlesurface on the boundary of the shell is also derived by means of the previous twovariables.