Stress-based hierarchic models for laminated composites Original Research Article

Derivation of hierarchic sequence of equilibrium models for cylindrical bending of composite laminates is presented. The levels of hierarchy correspond to the degree to which the second-order compatibility equation of the two-dimensional elasticity is satisfied. The stress fields of the hierarchic models satisfy a priori the equilibrium equations and the stress boundary conditions of two-dimensional elasticity, and the continuity requirements for the transverse shear and normal stresses at the lamina interfaces are also a priori satisfied for each member of the hierarchy. The numerical solution is based on the principle of minimum complementary energy. The number of degrees of freedom in the finite element approximation is independent of the numbers of the layers in the laminate. The results are obtained directly for stresses, whereas the displacements are calculated in the post-processing phase, by integration. Numerical results with comparisons present the performance of the mathematical and numerical models proposed.