Variable Angle Tow (VAT) placed composite laminates, where the fibre orientations continuously varying over the plane of each ply, generally exhibit variable stiffness properties. The stiffness tailoring of VAT plates through the design of fibre orientation distributions can substantially improve the buckling resistance, which is mainly due to the benign, non-uniform, in-plane load redistribution. In this work, a new mathematical definition is proposed to represent the general variation of fibre-orientation in the VAT plate. In this definition, the coefficients of polynomials are directly equal to the designed fibre angles at pre-selected control points. A Rayleigh-Ritz approach is used to determine the prebuckling loads distributions and critical buckling load of VAT plates. It provides a more efficient means to evaluate the buckling load of VAT laminates, compared with other numerical solutions. Subsequently, preliminary optimisation of VAT plates for maximum buckling load is done using the proposed definition of nonlinear variation of fibre angles. Results obtained for simply supported square VAT plates are compared with optimal results reported in the literature. Finally, long VAT plates with one free edge and others simply supported are studied to demonstrate the viability of the proposed modelling strategy

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.

The concept of Variable angle tow placement is explored for enhancing the buckling resistance of composite plates subjected to axial compression under different plate boundary conditions. The buckling problem of VAT plate is complicated because of variation in stiffness properties across planform of the plate due to curvilinear fiber path distribution. The problem requires prebuckling analysis to be performed first to determine the non-uniform stress distribution and then the buckling analysis of VAT plates. In the present work, a solution methodology based on the Differential quadrature method (DQM) is developed for solving the partial differential equations of VAT plates with linear fiber angle orientations. Within the framework of DQM, a stress function formulation for inplane analysis and displacement formulation for buckling analysis was employed to derive the governing differential equations based on classical laminated plate theory. The novel aspect of the present work is the use of Airy's stress function to model the prebuckling analysis of VAT plates which considerably reduces the problem size and computational effort. This approach provides more generality to handle pure stress and mixed boundary conditions more effectively when compared to the exisiting analytical models. Furthermore, the governing differential equation derived for buckling analysis of VAT panels considers the effect of bendingtwist coupling terms on the buckling load. DQM was applied first to solve the inplane elasticity problem of VAT plates subjected to cosine distributed compressive loads. DQM was then extended to solve the inplane problem of VAT plates under uniform end shortening for which the unknown stress distribu- * Corresponding author Email address: paul.weaver@bristol.ac.uk (Paul Weaver) December 7, 2011 tions are non-uniform. Stress distributions along the edges of the plate were expanded using Legendre polynomials and the unknown coefficients were determined using a least square approach such that the displacment boundary conditions are satisfied. Later, the DQM was applied to solve the buckling problem of rectangular VAT plates subjected to axial compression under different boundary conditions, viz., simply supported, clamped and free edge boundary conditions. Comparisons were made with finite element results obtained using ABAQUS and the accuracy and efficiency of the proposed DQM approach were studied. Preprint submitted to Composite Structures

Variable angle tow (VAT) placement techniques provide the designer with the ability to tailor the point-wise stiffness properties of composite laminates according to structural design requirements. Whilst VAT laminates exhibit-

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