Locking-free curved elements with refined kinematics for the analysis of composite structures

A new class of refined curved beam elements is proposed for the accurate stress analysis of composite structures. The element possesses three-dimensional capabilities and it is suited for the study of curved laminates and fiber-reinforced composites at the microscopic scale. The numerical issues associated with membrane and shear lockings are overcome by means of assumed interpolations of the strain components based on the mixed interpolation of tensorial components method (MITC). Higher-order expansions with only displacement unknowns are employed for the cross-section assumptions at the component level, enabling the computation of component-wise stress fields. For this purpose, a hierarchical set of Legendre functions is implemented, which allows the user to tune the kinematics of the element through the polynomial order input. The detrimental effects of locking in composite modeling are investigated and the robustness and efficiency of the beam element is assessed through comparison against solutions from the literature and refined solid models.