Wind turbine blade design using FEM AFOLABI AKINGBE WEI CHENG WENYU ZHOU
Outline Basics of wind turbine blade Blade element theory Membrane & plate bending model Shell element in FEM ANSYS model
How wind turbine blades work
Essential blade concepts chord
Twist angle
Blade element theory
Membrane & plate bending 3D structures under arbitrary loads Split element into two types for different calculations Membrane element for in-plane loads Plate bending elements for transverse loads and bending
FEM triangular blade model
Membrane element analysis
Bending element analysis
FEM for shell analysis A combination of a plate bending and membrane element The DOF of a plate and plane stress finite element in a local element-aligned coordinate system are considered
Shell element (a) Plane deformation (b) bending deformation The finite element solution
Displacement model The displacement model for the flat shell is expressed as N i is the bilinear shape functions associated to node i, and
Strain and curvature The membrane ε m and curvature κ are defined as Transverse shear strain is
Approximation of strain field The membrane deformation, the approximation of the strain field is
Discrete curvature field The discrete curvature field is
Approximation of shear strain The approximation of shear strain is written as
Linear system Combining simultaneously membrane and bending actions, a linear system for the vector of nodal unknowns q can be written where k e is the stiffness matrix composed of membrane and plate stiffness element matrices
Load vector The load vector at each node i is of the form f i e = [F xi F yi F zi M xi M yi M zi ] T
Element stiffness matrix The element stiffness matrix at each node i
ANSYS Modeling Angular velocity Surface pressure
Deformation & stress contours More stress at the blade root Thicker material closer to root to endure high loads (Displacement contour) (Stress contour)
Composite Can use commercial code like ANSYS to quickly change material properties and mesh sizing.