1. Wind turbine blade design using FEM AFOLABI AKINGBE WEI CHENG WENYU ZHOU

2. Outline  Basics of wind turbine blade  Blade element theory  Membrane & plate bending model  Shell element in FEM  ANSYS model

3. How wind turbine blades work

4. Essential blade concepts chord

5. Twist angle

6. Blade element theory

7. 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

8. FEM triangular blade model

9. Membrane element analysis

11. Bending element analysis

13. 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

14. Shell element (a) Plane deformation (b) bending deformation The finite element solution

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

16. Strain and curvature The membrane ε m and curvature κ are defined as Transverse shear strain is

17. Approximation of strain field The membrane deformation, the approximation of the strain field is

18. Discrete curvature field The discrete curvature field is

19. Approximation of shear strain The approximation of shear strain is written as

20. 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

21. 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

22. Element stiffness matrix The element stiffness matrix at each node i

23. ANSYS Modeling Angular velocity Surface pressure

24. Deformation & stress contours More stress at the blade root Thicker material closer to root to endure high loads (Displacement contour) (Stress contour)

25. Composite Can use commercial code like ANSYS to quickly change material properties and mesh sizing.