Wind turbine blade design using FEM AFO LA

Wind turbine blade design using FEM AFO LA BI A KINGBE WEI CHEN G 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 § 3 D 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 The finite element solution (a) Plane deformation (b) bending deformation

Displacement model The displacement model for the flat shell is expressed as Ni is the bilinear shape functions associated to node i, and

Strain and curvature The membrane εm 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 ke 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 fie = [Fxi Fyi Fzi Mxi Myi Mzi ]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.