PPT

```Wind turbine blade
design using FEM
A FOL A BI A KI N G BE
W E I CHE N G
W E N YU ZHOU
Outline
Membrane & plate bending model
Shell element in FEM
ANSYS model
chord
Twist angle
Membrane & plate bending
Split element into two types for different calculations
Plate bending elements for transverse loads and bending
Membrane element analysis
Assume linear displacements
◦  ,  = 1 + 2  + 3
◦  ,  = 4 + 5  + 6
11  12
◦    = 21  22
31  32
◦  are 2x2 matrices

13
23
33

Membrane element analysis
1
1
2
2
3
3
=

1
1
2
2
3
3
Bending element analysis
Tranverse displacements and rotations are taken as degrees
of freedom.
◦  ,  = 1 + 2  + 3  + 4  2 + 5  + 6  2 +
7  3 + 8  2  +  2 + 9  3
11  12  13
◦    = 21  22  23
31  32  33
◦   are 4x4 matrices
Bending element analysis
1
1
−1
1
2
2
=
−2
2
3
3
−3
3

1
1
−1
1
2
2
−2
2
3
3
−3
3
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
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.
```