Wind turbine blade design using FEMAFOLABI AKINGBE

WEI CHENG

WENYU ZHOU

OutlineBasics of wind turbine bladeBlade element theoryMembrane & plate bending modelShell element in FEMANSYS model

How wind turbine blades work

Essential blade conceptschord

Twist angle

Blade element theory

Membrane & plate bending3D 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

Assume linear displacements

◦ are 2x2 matrices

Membrane element analysis

Bending element analysis

Tranverse displacements and rotations are taken as degrees of freedom.◦

◦ are 4x4 matrices

Bending element analysis

FEM for shell analysisA 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

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.