Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics

This paper presents a numerical implementation and evaluation of a new nonlinear beam finite element model appropriate for highly flexible wind turbine blades made of composite materials. The underlying model uses the geometrically exact beam theory (GEBT) and spatial discretization is accomplished with Legendre spectral finite elements (LSFEs). The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures with geometric nonlinearity. LSFEs are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. The LSFE code is implemented in the software module called BeamDyn in the new FAST modularization framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for simulations of wind turbines in operating conditions. In this paper, we verify BeamDyn for static and dynamic nonlinear deformation of composite beams and compare BeamDyn LSFE performance against common low-order finite elements found in a commercial code. Comparisons show that the BeamDyn LSFEs can provide dramatically more accurate results for a given model size.