Framework for the Buckling Optimization of Variable-Angle Tow Composite Plates

Abstract

The variable angle tow (VAT) technique allows bers to be steered curvilinearly.In doing so, it oers substantially enlarged freedom for stiness tailoring of composite laminates. Prior work has shown that VAT composite structures can have improved buckling and postbuckling load carrying capability when compared to straight ber composites. However, their structural analysis and optimal design is signicantly more computationally expensive than conventional laminates due to the exponential increase in number of variables associated with spatially varying planar ber orientations in addition to the usual stacking sequence considerations. In this work, an ecient two-level optimization framework using lamination parameters as design variables has been enhanced and generalised to the design of VAT plates. At the rst level, a computationally ecient Rayleigh-Ritz model is adopted to compute the buckling load of VAT plates and is used with a globally convergent gradient-based algorithm (GCMMA) to determine the optimal distribution of lamination parameters. As a result of this analysis, new explicit stiness matrices are found in terms of component material invariants and lamination parameters. The spatial variation of lamination parameters over the planform of VAT plates is represented in the form of B-splines.The convex hull property of B-splines ensures the point-wise feasibility of lamination parameters, and notably, ensures feasibility between control points as well as at them.

Optimisation of composite structures – Enforcing the feasibility of lamination parameter constraints with computationally-efficient maps

“…tens of thousand) of hyperplane constraints describing the convex hull geometry. In contrasts to numerical approaches, the analytical derivation of feasibility constraints leads to a compact description of the lamination parameters space boundaries [17,7]. The 22 non-linear constraints summarised in Eq.…”

“…ply orientation and thickness) is required to encompass the entire design space of a laminate whilst using CLT. By contrast, lamination parameters provide a compact and continuous parameterisation of a laminate's design space [7]. By taking advantage of material invariants, a set of twelve lamination parameters and a thickness variable are sufficient to express the stiffness properties of a laminate, as illustrated in Figure 1.…”

“…The number of feasibility constraints necessary to ensure that physically meaningful solutions are retrieved is expressed as 8 × N constr where N constr is the number of constraints per region. Although different formulations of these constraints have been proposed in the literature, N constr is typically expressed as either a set of non-linear constraints for orthotropic materials [7] (i.e. generally 22 constraints) or more generally as tens of thousand of linear constraints [13].…”

Analysis and Design for the Moderately Deep Postbuckling Behavior of Composite Plates

“…Recently, it was successfully applied to solve a challenge optimization problem for tow-steering composite laminates [35], which possess spatially varying material properties.…”

“…Consequently, an accurate boundary of the feasible region of lamination parameters is important for obtaining meaningful optimal solutions. Based on the work in Wu et al [34,35], such a boundary for ξ A 1,2 and ξ D 1,2 is dened by the following equations. …”