Higher-order, partial hybrid stress, finite element formulation for laminated plate and shell analyses

A finite element formulation for arbitrarily curved orthotropic composite plate and shell analyses is presented here by using a higher order, partial hybrid stress method. The governing equation of the laminated plate is variationally derived from the Hellinger-Reissner principle. The flexural stress components are separated from the transverse shear stress components so that the continuity of interlaminar stress is enforced in the transverse shear stresses only. A general formulation is developed by using the shell geometry to suitably transform the plate equations into the shell equations. The partial hybrid stress method satisfies interface traction continuity conditions exactly in the transverse shear stress, and avoids the complexity of formulation that the normal hybrid stress method has. The validity of this method is demonstrated in various static deformation and free vibrations of plates and shells.