A 2D equivalent single-layer fomulation for the effect of transverse shear on laminated plates with curvilinear fibres

The Hellinger–Reissner mixed variational principle in conjunction with Lagrange multipliers is used to model transverse shear stresses, in bending of variable stiffness laminated plates, using a reduced two-dimensional formulation. The effect of transverse shear stresses on the bending deflection of variable angle tow (VAT) laminates is assessed. The novel formulation features multiple shear correction factors that are functions of the bending rigidity terms Dij, their first and second derivatives and the Timoshenko shear factor χ. The new set of governing equations are solved, in their strong form, using the Differential Quadrature Method (DQM) and the accuracy and robustness of the solution technique verified using a 2D “thick” shell and 3D high-fidelity finite element model. The derived theory is superior to the “thick” 2D shell model in capturing transverse shear effects and shows good accuracy compared to the full 3D solution for thicknesses within the range of practical engineering laminates. The derived equations degenerate to Classical Laminate Analysis for very thin configurations but discrepancies as large as 43% are observed for span-to-thickness ratios of 10:1. Finally, the specific VAT panels under investigation are affected more by transverse shear deformation than a corresponding homogeneous quasi-isotropic laminate.