Wind turbine blade design using FEM

Wind turbine blade design using FEM AfolabiAkingbe 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 • 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 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 Ni is the bilinear shape functions associated to node i, and

Strain and curvature • The membrane εm and curvature κare 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 = [FxiFyiFziMxiMyiMzi]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.

Wind turbine blade design using FEM

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