On the Finite Element Discritization of Continuous Tow Sheared Structures

Abstract

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.

Increasing reliability of axially compressed cylinders through stiffness tailoring and optimization

“…S4R elements with enhanced hourglassing control are used with the mesh size informed by a convergence study. For a discussion on the discretization of fibre angles and thicknesses for RTS structures, the reader is directed to [ 51 ]. The optimization is carried out on SF- and RTS-designed cylinders with geometry and material properties as listed in table 1 .…”

Mechanical Cloaking of Cutouts in Laminated Plates

“…Furthermore, this choice of 𝜙 𝑘 = [0°, 90°] is that in which Gürdal et al identified as promising configurations in load path redistribution through structural stiffness tailoring [20]. Moreover, previous work identified the choice of 𝜙 𝑘 = 0°or 𝜙 𝑘 = 90°to allow for relatively simple and efficient numerical discretization strategies to be employed [17]. Examples of several steering directions, periodicities and their resulting fiber orientation distributions are presented in Fig.…”

“…The CTS process instead shears material tows in-plane to fiber steer. By shearing tows in-plane, tessellation is possible and hence a ply can be fully covered without the need for gaps or overlaps, leading to a simplification of both the geometric discretization and computational analysis [17]. This in-plane shearing mechanism used by the CTS process gives rise to a mechanically nonlinear fiber orientation-ply thickness coupling, where due to material volume conservation pre-and post-shearing, a thickness change occurs [14].…”