A state space finite element for laminated composite plates Original Research Article

This paper presents a semi-analytical finite element solution for the stress analysis of cross-ply laminated composite plates. The method is based on a mixed variational principle that includes the variations of both displacements and stresses. Finite element approximation is introduced only for the in-plane variations of displacements and stresses, while the through-thickness distributions of them are obtained by using the method of state equation. Numerical tests show that the results obtained approach the analytical three-dimensional solutions. Moreover, the use of the recursive formulation of the state equation leads to the solution of an algebra equation system whose order does not depend on the number of material layers of the laminate. Compared with the traditional finite element method, the new solution always provides continuous distributions of both displacements and transverse stresses across material interfaces.