A mixed element for laminated plates and shells

Formulation and numerical evaluation of a simple shear-flexible four-noded quadrilateral laminated composite plate/shell finite-element is presented. The element developed is based on a generalized mixed variational principle with independently assumed displacement and laminate internal strain fields. For the latter, a layer-number-independent polynomial interpolation is utilized, together with a judicious selection of the in-plane (spanwise) distributions for the strain components. This was facilitated by the use of a set of bubble functions as additional kinematic degrees of freedom, which was shown to be crucial for eliminating the locking phenomenon. For dynamic applications, a simplified lumped mass matrix is employed. Finally, an extensive number of critical test cases are given to access the element's preformance and to illustrate its effectiveness in static as well as vibration problems for anisotropic laminated plates and shells.