Semi-Analytical Buckling and Optimisation of Variable Stiffness, Variable Thickness Laminates

Abstract

Variable Angle Tow designs have shown to improve structural performance by providing a better stiffness distribution. However, additional manufacturing constraints are involved compared to straight fibre laminates: mainly the maximum fibre steering curvature that can be achieved. Moreover, if a gap free laminate is constructed, overlaps will be formed depending on the relative fibre orientation when the continuous tows are bent to follow a reference path in Automated Fibre Placement and a one-sided irregular thickness profile is created. To counter the latter effect and still obtain uniform thickness laminates, a cut and restart strategy of the tows is often used in industry, leaving the final product with small gap areas. However, previous research has hinted both numerically and experimentally on further buckling improvements of variable stiffness laminates incorporating overlaps, resulting in a variable thickness profile. To investigate these possible benefits and their extent, the thickness build-up and overlap locations are specially considered in this proposed framework on Variable Angle Tows. In first instance, a virtual manufacturing surrogate of the laminate is produced to represent the discrete thickness profile due to the overlaps. This is performed by plotting each tow graphically and subsequently retracing the total thickness based on the superimposed opacity over the laminate. The tow paths are obtained from the interpolated fibre orientation, which simultaneously incorporates the steering limit of the manufacturing process. The surrogate information is then compared to a smeared approximation of the thickness build-up, based solely on the steering angle. The linear buckling simulation is performed by means of a semi-analytical model on a plate formulation, where the one-sided thickness profile variation is modelled by incorporating an offset from the geometrical varying midplane to a common one, around which the laminate stiffnesses are calculated. These adapted stiffnesses are then used in solving the neutral equilibrium buckling problem, where the displacements are approximated by means of the Ritz method, with a set of Legendre polynomial shape functions and numerical integration of the stiffness matrices. The semi-analytical smeared model correlates to within ± 5% of the discrete thickness Finite Element Model for a range of geometries, loading and boundary conditions. This verifies the thickness approximation for linear buckling of small tow widths compared to the laminate's dimensions, yet was inconclusive for larger tow width ratios. Finally, laminates with a varying thickness profile are optimised alongside the variable stiffness for different cases and compared to uniform thickness counterparts at isomass. The results show small improvements in the symmetric problem, but a higher gain is obtained for unsymmetrical conditions with an unrestricted layup sequence, as the thickness increase can be highly tailored together with the variable fibre orientation to locations requiring higher stiffness.