STRESS- AND ROTATION-BASED HIERARCHIC MODELS FOR LAMINATED COMPOSITES

A hierarchic sequence of equilibrium models in terms of stresses assumed to be not a priori symmetric is derived for cylindrical bending of laminated composites, using first-order stress functions. The stress field of each hierarchic model satisfies a priori (i) the translational equilibrium equations and the stress boundary conditions of two-dimensional elasticity, and (ii) the continuity requirement for the transverse shear and normal stresses at the lamina interfaces. The levels of hierarchy correspond to the degree to which the two first-order compatibility equations and the rotational equilibrium equation of two-dimensional elasticity are satisfied. The numerical solution is based on Fraeijs de Veubekeʹs dual mixed variational principle, employing the p-version of the finite element method. The number of degrees of freedom is independent of the number of the layers in the laminate. Results are obtained directly for the stresses and rotations; the displacement field is obtained in the post-processing phase by integration. Numerical results with comparisons show the capability of the mathematical and numerical models proposed