wind turbine blade design using fem
DESCRIPTION
Wind turbine blade design using FEM. Afolabi Akingbe 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. - PowerPoint PPT PresentationTRANSCRIPT
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Wind turbine blade design using FEMAFOLABI AKINGBE
WEI CHENG
WENYU ZHOU
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OutlineBasics of wind turbine bladeBlade element theoryMembrane & plate bending modelShell element in FEMANSYS model
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How wind turbine blades work
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Essential blade conceptschord
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Twist angle
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Blade element theory
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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
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FEM triangular blade model
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Membrane element analysis
Assume linear displacements
◦ are 2x2 matrices
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Membrane element analysis
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Bending element analysis
Tranverse displacements and rotations are taken as degrees of freedom.◦
◦ are 4x4 matrices
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Bending element analysis
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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
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Shell element
(a) Plane deformation (b) bending deformation
The finite element solution
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Displacement model The displacement model for the flat shell is expressed as
Ni is the bilinear shape functions associated to node i,
and
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Strain and curvature The membrane εm and curvature κ are defined as
Transverse shear strain is
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Approximation of strain field
The membrane deformation, the approximation of the strain field is
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Discrete curvature field The discrete curvature field is
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Approximation of shear strain
The approximation of shear strain is written as
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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
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Load vector The load vector at each node i is of the form
fie = [Fxi Fyi Fzi Mxi Myi Mzi ]T
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Element stiffness matrix The element stiffness matrix at each node i
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ANSYS Modeling
• Angular velocity
• Surface pressure
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Deformation & stress contours
More stress at the blade root
Thicker material closer to root to endure high loads
(Displacement contour)
(Stress contour)
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Composite Can use commercial code like ANSYS to quickly change material properties and mesh sizing.