Mixed Least-Squares Finite Element Model for the Static Analysis of Laminated Composite Plates

A mixed finite element model for the static analysis of laminated composite plates is presented. The formulation is based on least-squares variational principles, which is an alternative approach to the mixed weak form finite element models. The least-squares-based finite element model considers the first-order shear deformation theory, with the generalized displacements and the stress resultants as independent variables. Moreover, high-order C° Lagrange interpolation functions and full integration are used to develop the discrete finite element model, which by the least-squares formulation, results in a symmetric and positive-definite system of algebraic equations. The predictive capability of the proposed mixed plate finite elements is demonstrated by numerical examples of the static analysis of rectangular laminated composite plates with a variety of boundary conditions and side-to-thickness ratios. Particularly, the high-order mixed plate elements based on this formulation are shown to be insensitive to shear-locking.