A finite element for the linear analysis of laminated circular plates

A new finite element for modeling axiysymmetric circular plates is developed. The element is based upon Mindlin's shear-deformable plate theory, and elements may be stacked on top of one another to model laminated plate by the addition of only rotational degrees of freedom for each lamina. The elements assure continuity of the displacements between the layers, but not continuity of the traction vectors. Neither interlaminar slip nor debonding between the layers is considered.

The plate element is more efficient at modeling laminated structures than conventional plate elements or solid elements because it accurately models the structure while keeping the degrees of freedom per element to a minimum. If one were to use solid elements to model a laminated circular plate, many more elements would have to be used in the model to avoid loss of accuracy due to a large aspect ratio. Each layer in the laminated plate is allowed an independent rotation: hence, the model gives more accurate results than classical lamination theory models. The new element is also immune from shear locking at least for radius-to-thickness ratios up to 500 without having to incorporate reduced numerical integration schemes. In fact, the element's stiffness matrix may be integrated in closed form: this is not possible for most plate elements in the literature.