On the Finite Element Discretization of Continuous Tow-Sheared Structures

Tow-steered laminates, those in which the fiber angle varies as a function of in-plane coordinates, represent a substantial numerical modeling problem. In the Continuous Tow Shearing (CTS) process, the tows are deformed by in-plane shearing that generates a non-linear orientation-thickness coupling, which needs to be accounted for when analyzing CTS structures. In this manuscript, an investigation into the Finite Element discretization of CTS structures is conducted to ascertain the most appropriate element choice in terms of computational cost and accuracy. First, natural frequency and buckling eigenvalue analyses are conducted on constant-thickness flat plates and thin-walled cylinders ((±45/0/90)_s layup), in order to set a baseline. Next, multiple discretization strategies are implemented to investigate a CTS plate and a thin-walled CTS cylinder by means of two- and three-dimensional shell elements, in linear frequency and buckling analyses. Two CTS stacking sequences are considered, with the first ((±0⟨0|70⟩¹⁰)_2s) having identical steering across plies, and the second with variable steering across plies ((±0⟨0|70⟩¹⁰/±90⟨0|70⟩¹⁰)_s) to increase the discretization difficulty. The use of three-dimensional shell elements allows for greater fidelity in representing the geometry of a CTS structure, as they allow the asymmetric thickness build-ups to be discretized accurately. We show that three-dimensional shell elements enable the use of lower mesh resolutions whilst maintaining solution accuracy, in comparison to two-dimensional shell element meshes of the same geometric in-plane resolution. Moreover, a relation between element type and mesh resolution is presented to appropriately align element centroids and nodal coordinates, for two- and three-dimensional shell elements, respectively, with the maxima of a specific thickness distribution.