Mixed least-squares finite element models for static and free vibration analysis of laminated composite plates

New mixed least-squares finite element models are developed for static and free vibration analysis of laminated composite plates. Both models consider the first-order shear deformation theory with generalized displacements and stress resultants as independent variables, using equal and high-order C0 basis functions. The mixed least-squares formulation is a useful alternative to mixed weak form models, as it develops into an unconstrained minimization variational problem and thereby allows the finite element approximating spaces to be chosen independently. Ultimately, the model for static analysis yields a symmetric positive-definite system of linear equations, and the latest innovative model for free vibration analysis yields a symmetric quadratic eigenvalue problem. The predictive capabilities of the proposed models are assessed by comparison with analytical solutions, considering selected examples of both static and free vibration analysis of rectangular laminated composite plates, with different boundary conditions and a range of side-to-thickness ratios (from 10 to 500). In particular, these mixed least-squares models using high-order basis functions are shown to be insensitive to shear-locking.