Buckling analysis and optimisation of variable angle tow composite plates

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