In this research, using the Gateaux differential, an efficient computa
tional procedure is presented and a new functional with geometric and
dynamic boundary conditions is obtained for orthotropic cylindrical sh
ells. A mixed finite element (ORTHO36) is generated which is a conform
ing, rectangular (four-noded), isoparametric ''serendipity'' family el
ement and has 4 x 9 degrees of freedom. The existence of first order d
erivatives in the functional provides the advantage of using linear sh
ape functions. The formulation is applicable to orthotropic cylindrica
l shells with all kinds of boundary and loading conditions. The accura
cy of the ORTHO36 element is verified by applying the method to some t
est problems which exist in the literature.