2010_01_12_3DBeam_CDT6

A preliminary design tool for composite A preliminary design tool for composite structures : 3D structures : 3D Beam II, v 5.51Beam II, v 5.51

CDT 6, Jan 15, 2010

Sung K. Ha, Mustafa Ghulam, Lei Xu & Stephen Tsai

Stanford Composite Design TeamStanford University

1

y

3D Beam II

MS Excel based User-friendly finite element analysis program

for beam or frame type structures

Structure with large slenderness ratio Structure with large slenderness ratio (long compared to cross-section)

Three dimensional grid, frame structures Tapered / Untapered beam structure Arbitrary ply drop off

A bit l d (3 f / 3 t ) t l ti Arbitrary loads (3 forces / 3 moments) at any location Multiply connected frames Modal analysis Modal analysis

An accurate, yet easy-to-use tool !!

2

Beam modeling of 3D structures

Beam analysis3D geometry- Fast

Si l- Slow

Complicated[A]n,[B]n,[D]n

- Simple- Complicated

[A]k,[B]k,[D]k

[A]2,[B]2,[D]2

[A]1,[B]1,[D]1

3

FEM formulation for a composite beam

1 1 3 2 2 3( , , )u x y z d x x

1) Displacement 3 3,d

At each node (6 dof)

2 2 3 1( , , )u x y z d x

3 3 2 1( , , )u x y z d x d

2 2,d Laminates

11 1 1

13

22

3 u d x x 22 2 2 0 u 33 3 3 0 u

2) strain-displacement

'n3 n1' ''

n3' n2''

1 1,d

11 1 11

31

21x x x, 22 2 2, 33 3 3,

12 1 2 2 1 3

2

13

1

1

12

12

( ), ,u u d

xx

x

n1n2=n2'

n3'

n1

n2'n1'=n1''

n3'' n2

13 1 3 3 1 2

3

12

1

1

12

12

( ), ,u u d

xx

x

23 2 3 3 2 1 112

12

0 ( ), ,u u

1 1 1 1

2 1 2 2 1 2 2

3 1 2 2 1 2 3

0d C S Dd S S C C S Dd S C S C C D

2 2

1 11 1 3 2 2 3

5 13 5 2 122

x xx

4

6 12 6 3 12 x


1

5

11 15 16

15 55 56

1

5

1

5

Local

C C CC C C C

3) Constitutive equation (stress-strain) 4) F.E. formulation

d d dT

1

MD'

5

6

15 55 56

16 56 66

5

6

5

6

local local local

Local

localC C C

1 11 16 15 2 15 3 16 3 11 2 11

1

6

C C C x C x C x C x C

d d d

1 5 6 5

6

MD

d N d N iih

a ai ih

aa ai

a

, , ,

1

2

1

2

1 2 3( )

5

6

15 56 55 2 55 3 56 3 15 2 15

16 66 56 2 56 3 66 3 16 2 16

5

1

2

3

C C C x C x C x C x CC C C x C x C x C x C

D'

k B DB B DBe T Txdx jd

e

( ) ( ) 12

11 16 15 11 12 131 1

66 56 21 22 232 6

A G G B B BFG G B B BF

G B B BF

Resultants Loads vs strains

k B DB B DBx

dx jde

( ) ( )

1155 31 32 333 5

11 12 131 1

22 232 2

333 3

.

G B B BFD D DM

sym D DMDM

2

1

1

1( )

e

e

xe

xN dx N jd

f f f

2 1( )

exe N dx N jd m m mM

e e e e ed d m +k f MD+KD F

1 1( )

exN dx N jd

m m m

F

3F

3M

2F 2M

11 2 3. .,e g A dx dx 11= CLaminates

5

d dm +k f MD+KD F1F

1M


3 3,d 3Q

3M

2 2,d

Laminates

1N2Q 2M

1 1,d 1

1M1x

5) strain-displacement

6) Constitutive equation (macro strain macro stress) MMF •Failure

SMM+

F b F i( )1 2 6

7) Failure criterion : Quadratic Tsai-Wu criterion

(macro strain macro stress) MMF •Fatigue Life

a F b F iij i j i i , ( , , )1 2 6

aR bR2 1 0 R

0 : safe0 : fail

kR

1 0 : fail0 : safe

Strength ratio

6

0 : fail

Coordinate Transformation for 3D Post-processingn

Plies

X3x3

t

(If = 0°, the reference X2-axis is parallel to the global X-Y plane.)

Z

L#n1

n2n

Bricksx2

Laminates n

bxs

TxI

J

J

X2

X1

X3

X3X1

t s nX2

b

,G Ix

I J

X1 Y

I

I

X2

X3X2

X2

X3

X1

t s n(1,0,0)s

h t

,g Ix Global coordinates (X-Y-Z)

X

J

S

,2B T bx x t xZ

, ,G I T g I x Tx x Reference coordinates (X1-X2-X3)

Local coordinates (x1-x2-x3)YX

, ,G g

T: a transformation matrix from (s, n,t) to (S,X2,X3)

local node#

1 46 7

85

n

tlocal node#

7

3D Beam v5.4x; worksheet : PostProcess-I 32 s

Coordinate systems and Layup direction

ZY

Structure

X₂X₃

Element

Ply

Fiber direction

X X₁ , ply angle

X1

, p y g

Cross Section

X

Plies

Bricks

X3

x2

x3

LaminatesLayup Sequence

Global coordinates (X-Y-Z)

X2

n2nt n3

y p qDirection, t

( )

Reference coordinates (X1-X2-X3)

L#n1

8

Local coordinates (x1-x2-x3)

Program Flow : 3D Beam II

Main Analysis ModulesInput Output

Step 1 : Section & Material• Cross Section

• Material property

• Displacement & Rotation

• Global Strains & Curvatures

Step 2 : Global Geometry

Material property

• Nodes (Global coordinates)

• Global Loadings & Moments

• In-Plane Strains

Step 3 : Loads

•Elements (node connectivity)

• Boundary conditions

• In-Plane Loads

• Strength Ratios

• Mode shape & NaturalStep 3 : Loadsy

• Global ForcesMode shape & Natural

Frequency

Step 4 : Solve

Graphical Post Processor:3D contour Plot tool

9

3D contour Plot tool,HUSAP

Version updated3D BEAM “M i ” h

Version 5.xx

3D BEAM “Main” sheet

Import and export input files(*.3db)

Modal analysis

Version 5.xx

Modal analysis (up to 10 mode)

10

Step 1 : Specification of Plies, Laminates and Sections3D BEAM “S i DB” h

[A]n,[B]n,[D]n3D BEAM “Section DB” sheet

(4)

[A] [B] [D]

[ ]n,[ ]n,[ ]n

[A]k,[B]k,[D]k

[A]2,[B]2,[D]2

pliesbricks

X3x3

Laminates

[A]1,[B]1,[D]1

bricks

X2

x2

(2 (3)

brick nodesMaterial DB sheet

• SI unit

Laminate nodes

)

(1)p8

Ply group number(2)

L2 L3

p1

p

…

(4)

(2)

•English unit

L1

L2

(3) (x2,x3)

11

Laminates in a rectangular thin-wall cross section

2

x3[03/45/-45/902]s

(2 , 1)(-2 , 1)

x3

a1a2 a1a2

Direction of ply sequencea1a2

n

t

1

x22" 3 x2

x1 t

2

4"

4

(-2 , -1) (2 , -1)

x1

Laminate #1

x1

Laminate #1

Laminate #2 a1a2

Laminate #3

Laminate #4

12

Base Line Option :0

Step 2 : Global Geometry (nodes and elements)3D BEAM “Gl b l h ”3D BEAM “Global geometry sheet”

[A]n,[B]n,[D]n

[A]k,[B]k,[D]k

[A]2,[B]2,[D]2

13

[A]1,[B]1,[D]1

Varying Sections

Z

21 3 4 Element #

X

1 2 32 Group #Section (group) #

[A]2[B]2[D]2

1 2 43 521 3 4

[A]1[B]1[D]1 [A]3[B]3[D]3

N d #

1 2 32

element #Section (group) #

1 2 43 5 Node #

14

Step 3 : Loads3D BEAM “L d h ”

Displacements & Rotations

3D BEAM “Loads sheet”


U3

Y

Z

X U

U2

X U1

Forces & Moments

[A]n,[B]n,[D]n

Forces & Moments

Z

F3

M3

M2

[A]k,[B]k,[D]k

[A]2,[B]2,[D]2

Y

X F1 M1

F2

15

[A]1,[B]1,[D]1 Global coordinates (X-Y-Z)

Step 4 : Results3D BEAM “R l h ”


Displacement chart Global resultant stress

3D BEAM “Results sheet”


U3

Y

Z

X U

U2

X U1

Forces & Moments

In plane load Strength ratio

Forces & Moments

Z

F3

M3

M2

Y

X F1 M1

F2

16

Global coordinates (X-Y-Z)

Step 4 : Results

Deflection along the X‐axis0.02

Cross‐sectionY 1kN

‐0.005

0

0.005

0 0.1 0.2 0.3 0.4 0.5 0.6

U₁

0.005

0.01

0.015

z_b

0.03m

0.5m

X

0 025

‐0.02

‐0.015

‐0.01U₁

U₂

U₃

‐0.015

‐0.01

‐0.005

0

‐0.02 ‐0.015 ‐0.01 ‐0.005 0 0.005 0.01 0.015 0.02

zT

zB

Cross-section:20 segments (laminates)

‐0.03

‐0.025

‐0.02

At each section, in-plan loads, strains and strength ratios

20 segments (laminates)

0 2

0.4

0.6

0.8

In Plane stress at Element # 1

N1

N2

N6 0.002

0.004

0.006

In Plane strain at Element # 1

e1

e2

e60.40.60.81

1.21

23

4

517

18

1920

Failure Index (1/R)

‐0.6

‐0.4

‐0.2

0

0.2

0 5 10 15 20 25

‐0.004

‐0.002

0

0 5 10 15 20 25

e6

00.2

6

7

8

913

14

15

16

‐0.8Laminate #

‐0.006

Laminate #

910

1112

13

Laminat #

Step 5 : 3D contour plotHUSAPHUSAP

18

Verification of 3D Beam – Comparison with analytic solution

Z 100 NCross-Section

X3 (x3)

7 cm.

X X2 (x2)

11 m

Comparison of three point bending results

0.0150.02

0.025with [010/9010]s

-0.0050

0.0050.01

0 0.2 0.4 0.6 0.8 1x) &

w'(x

)

0 025-0.02

-0.015-0.01

0 0.2 0.4 0.6 0.8 1

w(x

3D BEAM:w(x)

Analytic:w(x)

3D BEAM:w'(x)

A l ti '( )

19

-0.025X [m]

Analytic:w'(x)

Verification of 3D Beam –Case 2: Hollow Composite Beam with Circular Cross-section

Deformation under simple loadingVertical100 N Torsion

100 N · m

L 1 m

D = 0.1 m

[0/±45/90]S

L = 1 m

1

1.2

aqus

res

ult

Deflection

0 4

0.6

0.8

norm

aliz

ed b

y A

ba

3D Beam IIAbaqus

0

0.2

0.4

Def

orm

atio

n n

20

0Deflection Rotational Angle Rotational Angle

Verification of 3D Beam –Case 2: Hollow Composite Beam with Circular Cross-section

Natural frequencies & mode shapes

L 1

D = 0.1 m Mode 1

L = 1 m

[0/±45/90]S

M d 2

1400

1600

1800

Mode 2

800

1000

1200

1400

l Fre

quen

cy (H

z)

3D Beam IIAbaqus

Mode 3

200

400

600

Nat

ural

Abaqus

21

0Mode 1 Mode 2 Mode 3 Mode 4

Mode 4

Case 5: Hollow Composite Beam with Rectangular Cross-section

1.60E‐04

Load Case 1 : Max. Displacement

Results Results

Load Case 2 : Max. Rotation

0 00 002.00E‐054.00E‐056.00E‐058.00E‐051.00E‐041.20E‐041.40E‐0460 0

Dispalcemen

t (m)

Load Case 1 Load Case 2L = 1 m

1.00E‐042.00E‐043.00E‐044.00E‐045.00E‐046.00E‐047.00E‐048.00E‐04

Rotatio

n (radians)

0.00E+00

Abaqus (Shell Element) Abaqus (Beam Element) 3D Beam II5.50

H = 0.1m

100 N 100 N · m

H = 0.1m

0.00E+00

Abaqus (Shell Element) Abaqus (Beam Element)

3D Beam II5.50

W = 0.1m

Laminate Layup : [08/±458/908]SMaterial : AS/H3501

W = 0.1m

AbaqusAbaqus(Beam Element)(Beam Element)

AbaqusAbaqus(Shell Element)(Shell Element)

3D Beam II5.503D Beam II5.50

Load Case 1Load Case 1


Case 5: Hollow Composite Beam with Rectangular Cross-sectionResults : Natural Frequencies & Mode shapesResults : Natural Frequencies & Mode shapes




Laminate Layup : [08/±458/908]S

L = 1 mMode 1Mode 1

130.45 120.32 132.64

1200

1400

1600

1800

z)

Abaqus (Shell Element)

Abaqus (Beam Element)

3DBeam II5 50

Material : AS/H3501

Mode Mode 22705.49 972.93 743

0

200

400

600

800

1000

1200

1stMode 2ndMode 3rdMode 4thMode

Freq

uency (Hz 3D Beam II5.50

ModeMode 33 792 25 791 77 923 591st Mode 2nd Mode 3rd Mode 4th Mode Mode Mode 33 792.25 791.77 923.59

Mode Mode 441539.5 1648.8 1481.6

Case 6 :Ellipse Composite Circular Beam

8.00E‐03

Load Case 1 : Max. DisplacementD = 0.1 m

Results Results

2 50E 02

Load Case 2 : Max. Rotation

0 00 001.00E‐032.00E‐033.00E‐034.00E‐035.00E‐036.00E‐037.00E‐038 00 03

Dispalcemen

t (m)

Load Case 1 Load Case 2100 N 100 N · m

L = 1 m

0 00E 00

5.00E‐03

1.00E‐02

1.50E‐02

2.00E‐02

2.50E‐02

Rotatio

n (radians)

0.00E+00

Abaqus (Shell Element) Abaqus (Beam Element) 3D Beam II5.50

100 N

5 cm

100 N · m

5 cm

0.00E+00

Abaqus (Shell Element) Abaqus (Beam Element)

3D Beam II5.50

Laminate Layup : [0/±45/90]SMaterial : AS/H3501

10 cm 10 cm






Case 6 :Ellipse Composite Circular BeamResults : Natural Frequencies & Mode shapesResults : Natural Frequencies & Mode shapes

D = 0.1 m




Laminate Layup : [0/±45/90]S

L = 1 m

Mode 1Mode 1

61.46 61.61 61.93

700

Material : AS/H3501

Mode Mode 22103.88 101.95 104.93

200

300

400

500

600

Frequency (H

z)

Abaqus (Shell Element)

Abaqus (Beam Element)

3D Beam II5.50

ModeMode 33 366 15 379 43 371 56

0

100

1st Mode 2nd Mode 3rd Mode 4th Mode

Mode Mode 33 366.15 379.43 371.56

Mode Mode 44613.01 610.32 620.27

Verification of 3D Beam – Case 1: Composite plate

Deformation under simple loading

10 N Torsion

L = 1 m W = 7 cm

10 N · m

L 1 m

[08/±458/908]S

1

1.2

aqus

res

ult

Deflection

0 4

0.6

0.8

norm

aliz

ed b

y A

ba

3D Beam IIAbaqus

0

0.2

0.4

Def

orm

atio

n n

Rotational

26

0Deflection Rotational Angle

Rotational Angle

Verification of 3D Beam – Case 1: Composite plate

Natural frequencies & mode shapes

Mode 1

L 1 mW = 7 cm

L = 1 m

[08/±458/908]S

Mode 2

140

160

180

Mode 380

100

120

140

l Fre

quen

cy (H

z)

3D Beam IIAbaqus

20

40

60

Nat

ural

Abaqus

27

Mode 40Mode 1 Mode 2 Mode 3 Mode 4

Verification of 3D Beam – Case4: Composite Pi-Joint Deformation under simple loading

100 N

L = 1 m[08/±458/908]S

Torsion100 N · m

W = 7 cm

H = 3.5 cm

Deflection

1

1.2

1.4

aqus

res

ult

0.6

0.8

1

norm

aliz

ed b

y A

ba

3D Beam IIAbaqus

0

0.2

0.4

Def

orm

atio

n n

28

Rotational Angle

0Deflection Rotational Angle

Verification of 3D Beam – Case4: Composite Pi-Joint Natural frequencies & mode shapes

L = 1 m[08/±458/908]S

Mode 1

W = 7 cm

H = 3.5 cm

[08/±458/908]S

Mode 2

200

250

z)

Mode 3100

150

ral F

requ

ency

(Hz

3D Beam IIAbaqus

0

50

Nat

ur

29

Mode 40

Mode 1 Mode 2 Mode 3 Mode 4

Parametric Study-Easy to change the layup angles.

Pli

3D BEAM “Section DB” sheet

Laminates

Plies

Change ply angle for 3 cases

θ

C (1) 30°

•[0/±θ/90]s

Case (1) 30°

Case (2) 45°

Case (3) 60°

30

( )

Results: a clamped beam with circular cross-section

Displacement U3Z

Y

XZ

X

Case (2) : θ = 45° ; Deflection= -0.018 m

Case (1) : θ = 30° ; Deflection= -0.014 m

°Case (3) : θ = 60° ; Deflection= -0.020 m

31

Results: a clamped beam with circular cross-sectionR lt t th tA cantilever beam

under concentrated tip load

In plane loadBOTTOM

Results at the root

Fixed

p

TOPFixed

L3L4

L5L6L7

L8 TOPIn plane strain

BOTTOM

(Global coordinate)ZL1

L2

L8

L9

L10Z

TOP

TOP

BOTTOM

YL10

L11

L12

L20Y

XL12

L13L14

L15 L16 L17L18

L19

BOTTOM

- In plane load & strain are same for- In plane load & strain are same for case(1),(2) and (3).

32

Effect of fiber angles on stress distribution: Circular Beam

At root

L2

L3L4

L5L6L7

L8

FixedTOP

(Global coordinate)

Y

ZL1

L2L9

L10Y

Z

X

YL11

L12 L19

L20

BOTTOM XL13

L14L15 L16 L17

L18 Laminate #BOTTOM

TensionCompression

Small fiber angle reduces strength ratios

θFiber

33

Effect of ply angles on natural frequencies : Circular Beam

Natural frequencies & modal shapes

1st Mode shape1st Mode shape

2nd Mode shape

3rd Mode shape

Case(1): 30°

Case(2): 45°

Case(3): 60°

34

Application : PI joint

PI-Joint : One of most critical joints in aerospace structures

shaped Joint

35

p

Modeling of PI joint using 3D-BEAM

•No. of Laminates: 12

L12

•A section consists of several laminatesL1, L2, L7, L8, L11, L12 [0/45/-45/0]2s

L L L L [0/45/ 45/0]

•No. of Section Groups : 1•No of Nodes: 11L9

L10

L11 L2 ~ L6 , L9, L10 [0/45/-45/0]4s

•No. of Nodes: 11•No. of Elements: 10L1 L2 L3 L4 L5 L6 L7 L8

E10

E1E2

E3

36

Results : PI joint using 3D-BEAM

•No. of Laminates: 12

L1 L2 L7 L8 L11 L12 [0/45/ 45/90]L120.025

Deflection along X‐axis

L1, L2, L7, L8, L11, L12 : [0/45/-45/90]2s

L2 ~ L6 , L9, L10 : [0/45/-45/90]4sL10

L11

L12

0 01

0.015

0.02

U₁

U₂

L1 L2 L3 L4 L5 L6 L7 L8

L9

0

0.005

0.01

0 0 2 0 4 0 6 0 8 1 1 2

U₂

U₃

‐0.0050 0.2 0.4 0.6 0.8 1 1.2

0 50.6

1

212

Failure Index (1/R)Failure Index (1/R)

0.10.20.30.40.5

311

0 4

59

10

Laminate #3D contour plot tool for the 3D BEAM II

37

6

7

8for the 3D BEAM II

Parametric Study: PI-joint

L11

L12

Cross section

(Local coordinate)

Task : Minimize ply thickness for a layup sequence.

Restriction : Strength ratio(1/R) > 1

• No. of Section group : 1

• No. of Laminates: 12

N f N d 21

L9

L10 0.1mX₂

X₃

( )

• Load : 100kN

• Material : T300/N520

100kN

• No. of Nodes : 21

• No. of Elements : 20L1 L2 L3 L4 L5 L6 L7 L8 (: Laminate #)

0.2m

• Laminate sequence : [0/(±θ) /0]ns

Element #20

Node #21

1mY

θ x

Fixed

Angle of ply

N d #2

X

Y Case (1) 30°1/R > 1Case (2) 45°

C (3) 60°

38

Node #1Node #2

Element #1Element #2

Z(Global coordinate)

Case (3) 60°

Application: PI-joint (Stress & strength ratio).

Displacement at the end

L11

L12

Strength ratio

L9

L10

Strength ratio

L1 L2 L3 L4 L5 L6 L7 L8

39

Application: PI-joint ( Mode shape )

Natural frequencies

1st Mode shape

Mode shape

2nd Mode shape

3rd Mode shape

° C (2) θ 45° Case(3) : θ = 60°

40

Case(1) : θ = 30° Case(2) : θ = 45° Case(3) : θ = 60

Twisted PI joint

Twisted

How to twist sections (3D BEAM “Section DB” sheet) θ = 0° θ = 45°

PliesX₃

X₃

x₃ x₂45°

Laminates

X₂X₂

x₂ x₃

41

Application : Wing in aircraft Regional jet

Modeling in 3D BEAM

42

Problem statement : Wing in aircraft Task : Apply different fiber angle to reduce strength ratio and adjust natural frequency.

L4L5L6L7L8L9• No. of Section group : 19

• No. of Laminates: 20L1L2

L3L4L9L10L11

L12

L13

L25L26

L27

L28L29

L30


• No. of Elements : 19

• Airfoil : NACA 64A204Fixed

N d #14.4mZ

L13L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24

• Airfoil : NACA 64A204

• Wing load : Fz (5kN : distributed )

• Material : T300/N520

Node #1…

Element #1Node #2

Y

• Laminate sequence [05/(±θ)5/905]

θ Element #20

X

Case (1) 30°

Case (2) 45°

Case (3) 60°

Node #21

1m

43

Case (3) 60

Wing in aircraft : Stress analysis results.

Strength ratio

3L1L2

L3L4L5L6L7L8L9L10L11

L12L25

L26 L28L29

1

23 L12

L13L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24

L27L29

L30

1 2 3

To decrease strength ratio, make the fiber direction smaller.

Wing in aircraft : Modal analysis results

1st Mode shape

Natural frequency (Hz) Mode shape

2nd Mode shape

3rd Mode shape

As increase fiber direction, decrease natural frequency.

Case(1): 30°

Case(2): 45°

Case(3): 60°

45

, q y

Swung PI joint

3D contour plot tool for the 3D BEAM II

Helix twistHalf circle

46

Application : Fuselage with stringers and spars Fuselage with stringers and spar in aircraft structure

M d li i 3D BEAMModeling in 3D BEAM

47

Problem statement : Structure of aircraft Task : Minimize maximum displacement in structure changing fiber direction.

• No. of Section group : 8 • Load : 3.45kN θ



f l

• Material : AS/H3501

• Laminate sequence : [02/(±θ)2/02]s

Case (1) 30°Case (2) 45°Case (3) 60°• No. of Elements : 88 Case (3) 60

2 m

0.5m

L11

L12

2 m

L1 L2 L3 L4 L5 L6 L7 L8L9

L100.05 m

3 45kN

L1 L2 L3 L4 L5 L6 L7 L8

Fixed 0.1 m

48

3.45kN

Structure of aircraft : Problem statement

49

Structure of aircraft : Stress results Maximum displacement comparison Original shape

Case(1) : θ = 30°

Maximum displacement Deformed shapeCase(2) : θ = 45°

UyCase(2) : θ 45

Case(3) : θ = 60°

As smaller degree of fiber direction , less displacement

50

less displacement.

Structure of aircraft : Mode results Natural frequencies Mode shapes

1st Mode shape 2nd Mode shape

3rd Mode shape 4th Mode shape

As increase fiber direction decrease natural frequency

Case(1) : θ = 30° Case(2) : θ = 45° Case(3) : θ = 60°

51

As increase fiber direction, decrease natural frequency.

WindWind Turbine BladesTurbine BladesWind Wind Turbine BladesTurbine Blades

HSC

L Tu

rbin

e

52

Application: 5 kW Wind turbine blades

• Rated Power: 5 kW• Rated wind speed: 10 m/s• Hub height: 10 m

• Blades = 3• Orientation = Upwind• Rotation = Clockwise

D

• Rotor diameters: 2.5 m• Cut in wind speed: 4 m/s• Cut out wind speed: 25 m/s• Annual mean wind speed: 5 m/s

• Speed = Variable• Control = Pitch regulated

Hub height• Annual mean wind speed: 5 m/s• Average Reynolds # : 1.5 x 106

• Vertical Wind Shear: α = 0.2• Weibull Distribution: k = 2

*Reference: Finite element analysis with an improved failure criterionfor composite wind turbine blades, Forsch Ingenieurwes (2008) 72: 193–207

Hub height

Airfoil NACA 4412Rotor Radius = 2.5 m

Hub

Sections = 12Twist = 18o

Material:

0º

Neck

Sh llHub Metal and Composite*Neck Composite*Shell Composite*

18ºFig: Model of a wind turbine blade

Shell

* E-glass LY556 epoxy resin lamina Twistangle 0º

Application: Wind turbine blades

Distributed loads : Fz/length= 350N/ (2.5 m)

2.5mLayup sequence[ 0 / (±45) ][ 0 / (±45) ][ Al(4mm)/0 / (±45) ]

Material : E-glass LY556

Layup sequence[ 0 6/ (±45)2][ 0 8/ (±45)4][ Al(4mm)/0 8/ (±45)4]

Wing sections

0.04

0.06

0.08

Airfoil NACA 4412Twist = 18o

‐0.08

‐0.06

‐0.04

‐0.02

0

0.02

‐0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Application : Wind turbine blade

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Application : Wind turbine blade

0.01

0.02

0.03


N1

N2

N6 0.00002

0.00004

0.00006

0.00008


e1

e2

e6

0.005

0.01

0.0151

23

4

517

18

1920

Failure Index (1/R)Element #1

‐0.03

‐0.02

‐0.01

0

0 5 10 15 20 25

‐0.00008

‐0.00006

‐0.00004

‐0.00002

0

0 5 10 15 20 25

e60 6

7

8

91012

13

14

15

16

Laminate # Laminate # 11Laminat #

0.02

0.03

0.04


N1

N2

N6 0 0002

0.0004

0.0006


e1

e2 0.040.060.080.1

12

3

4

517

18

1920

Failure Index (1/R)

(4)

(8)Element #4

‐0.03

‐0.02

‐0.01

0

0.01

0 5 10 15 20 25

N6

0 0006

‐0.0004

‐0.0002

0

0.0002

0 5 10 15 20 25

e60

0.025

6

7

8

913

14

15

16

17

(1)

‐0.04Laminate #

‐0.0006

Laminate #

910

1112

13

Laminat #

0.04

0.06


N1

N2 0 001

0.0015


e10 1

0.15

0.21

23

418

1920

Failure Index (1/R)Element #8

0 04

‐0.02

0

0.02

0 5 10 15 20 25

N2

N6

‐0.0005

0

0.0005

0.001

0 5 10 15 20 25

e2

e60

0.05

0.15

6

7

814

15

16

17

56

‐0.06

‐0.04

Laminate #

‐0.001

Laminate #

910

1112

13

Laminat #

Application :3.5kW Wind turbine 3.5kW Wind turbine with blades and tower

Blade

Modeling in 3D BEAM

Tower

57

3.5kW wind turbine blades and tower Task : Analyze 3.5kW wind turbine for gravitational and aerodynamic load

• Rated power : 3.5kW • No. of Nodes : 57 • No. of Section group : 16

• Rated wind speed : 12m/s

• Load : gravitational and aerodynamic

• No. of Elements : 56

• Materials : Tower ( Steel ), Blade ( Steel, E-glass, IM6/epoxy)


8.3m

Wind turbine geometry Blade loads

12m

1m

0.6m

Airfoils : DU45 Gravitational load Aerodynamic load

58

3.5kW wind turbine : stress resultantsMaximum displacement

0.15m

Maximum strength ratioStrength ratio at blade

Strength ratio at root

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3.5kW wind turbine : mode results

Natural frequencies and mode shapes

2nd Mode shape : 1 28Hz 3rd Mode shape : 2 71Hz1st Mode shape : 1.02 Hz 2nd Mode shape : 1.28Hz 3rd Mode shape : 2.71Hz

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Effects of stiffeners thickness on wind turbine bladesT300/N5208Stiffener T300/N5208

E glass/LY556 Epoxy

Leading edge

Trailing edge

E-glass/LY556 Epoxy

[0/+45/0] 60 [0/+45/0]40 [0/+45/0]40 [0/+45/0]10

Trailing edge

Upper Spar Cap

Lower Spar Cap

Shear web [0/+45/0] 8 [0/+45/0] 8 [0/+45/0] 8 [0/+45/0] 8

Case (1) : n = 0;Case(2) : n = 10;Case(3) : n = 20.

[0n]Stiffener T300/N5208

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( )

Blade deflection : Ultimate load

Ultimate load at the tip4,000 N/m

Deflection

: No Stiffener

: Stiffener =[010] T300/N5208

: Stiffener =[020] T300/N5208

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Strength ratio : Ultimate load

(1) (2) (3)

(1) (2) (3)Strength ratio (Tsai-Wu)

L3L4L5L6L7L8L9L10

Laminate #

L1L2L3L4L9L10

L11L12

L13 L23 L24

L25L26

L27

L28L29

L30

L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24

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Vibration mode

: No Stiffener

Stiff [0 ] G hit1st mode shape

: Stiffener =[010] Graphite

: Stiffener =[020] Graphite

1st 2nd 3rd 4th

Vibration modesVibration modes

2nd mode shape 3rd mode shape 4th mode shape

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Summary and Conclusion

• The 3D beam can be used as a preliminary design tool• The 3D-beam can be used as a preliminary design tool.• Accurate, yet easy-to-use Tool for structural analysis of composite structures.• Calculate displacements, strains, stresses, failure index and natural vibration modes.p• It is based on a new composite beam theory, as accurate as 3D shell• Various applications, many structures can be treated as beams.

• A 3D-beam II- basic is available to the audience.• A smooth link from the 3D-beam to the SMM+ is under development• A smooth link from the 3D-beam to the SMM+ is under development.• Reliablity analysis tool will be linked.

Thank you for your attention !!!

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2010_01_12_3DBeam_CDT6

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