Dynamic Modelling of Blades Based on a Novel Curved Thin Walled Beam Theory
There are several Thin-Walled Beam models for straight beams, but few TWB models consider beams with arbitrary curvatures. Although, a curved beam can be modelled using finite elements, the number of degrees of freedom is too large and a nonlinear dynamic solution is very cumbersome, if not impossible. In this work, a general description of arbitrary three-dimensional curves, based on the Frenet-Serret field frame, is applied to determine the dynamic stresses in wing turbines blades. The dynamic model is developed using the Isogeometric Analysis (IGA) and the in plane and out-of-plane curvature’s gradients are found in an Euler-type formulation, allowing the treatment of cases with highly-curved geometry. An Isogeometrical (IGA) formulation relies on a linear combination of Non-Uniform Rational B-Splines (NURBS) to represent not just the model’s geometry, a standard practice in most Computer-Aided Design (CAD) platforms, but also the unknown solution field of each sought variable. For the unified model hitherto described, these variables are represented by a NURBS curve.