Modelling of fibre steered plates with coupled thickness variation from overlapping continuous tows

Abstract

Previous research has hinted on further improvements of the buckling behaviour of variable-stiffness laminates by incorporating overlaps, resulting in a variable thickness profile that is non-linearly coupled to the steering angles. The present study compares two modelling strategies to consider the variable thickness distribution: 1) as manufactured with discrete thicknesses; and 2) smoothed with a continuous thickness distribution. The as-manufactured discrete thickness created by overlapping tows is obtained by means of virtually manufactured laminates. The smeared approximation is much simpler to implement, whereby the local thickness is a non-linear function of the local steering angle. Linear buckling analyses are performed by means of fast semi-analytical models based on the Ritz method using hierarchical polynomials and classical plate formulation. By assuming a smooth manufacturing mould on one side, a one-sided thickness variation is produced, resulting in non-symmetric laminates for which the mid-plane surface is varied accordingly. Modelling guidelines are provided regarding the use of the smeared model in a study covering a wide range of geometries, loading and boundary conditions. With these guidelines, one can apply the smeared thickness technique in semi-analytical models to reach a correlation within ±5% compared to a costly discrete-thickness finite element model.

Lightweight design of variable-angle filament-wound cylinders combining Kriging-based metamodels with particle swarm optimization

“…(2) As explained in Wang et al (2020), for VAFW cylinders the thickness distribution of the kth ply given by h k (x) changes due to filament bending, filament shearing or any combination of both (Wang et al 2020), and the thickness increase is necessary to keep a constant volume (Castro et al 2019;Vertonghen and Castro 2021), leading to the following nonlinear dependence of h k (x) with the winding angle distribution (x):…”

Design of Compressed Variable Stiffness Panels with Steering-thickness Coupling

“…The main advantage of the smeared thickness approach regarding finite element modeling is that local thickening is simplified by a continuous thickness distribution over the plane, avoiding extremely refined meshes to model local thickening regions properly. The smeared thickness assumption for AFP panels has been compared with a discrete representation where all overlaps are modelled, leading to very close results [22,34].…”

“…Using a classical genetic algorithm, the panel geometry, fiber path and laminate stacking sequence are optimized in a single step to minimize the structural weight. The single-step optimization approach allows a straightforward description of the actual fiber orientations and steering angles, whereby the coupled thickness variation can be calculated based on constant volume requirements [4,22]. By employing a Lagrangian interpolation scheme and treating the reference fiber orientation angles as design variables, the variable thickness coupling is simplified once the steering angle is directly obtained.…”

“…Vescovini and Bisagni [24,25] also demonstrate a fast semi-analytical buckling model for the buckling of constant-stiffness composite panels with omega stiffeners. For variable-stiffness plates, Vertonghen and Castro [22] presented a suitable semi-analytical formulation for the purposes of the present study, which, however, cannot be used due to the stiffening plate elements, unless some strategy of connecting multiple domains is implemented, such as penalizing the strain energy [25][26][27]. Given the complications aforementioned complications with implementing a semi-analytical model, the linear buckling analyses are herein performed by means of finite elements with MSC Nastran ® .…”

Overlap-Stiffened Panels for Optimized Buckling Performance Under Minimum Steering Radius Constraints

“…This smeared out thickness distribution was the basis for Equation 1. Lander and Castro [10,11] compared the differences in modelling the exact thickness distribution vs. the smeared thickness distribution, demonstrating the good correlation and equivalence in buckling response of the smeared approach compared to a discrete representation of the overlaps.…”