X - JEC Composites

A Preliminary Design Tool for Composites 

Beam Structures : 3D-Beam II 

JEC, Paris 

March, 2011 

Sung K. Ha 

Hanyang University, Korea 

Stanford Composite Design Group 

1

Beam Type Structures of Composites 

Wind Turbine Blades and Tower 

Wings 

Non Crimp Fabrics (NCF) 

HSCL Turbine 

Courtesy of Chomarat 

Sporting Goods 

Box beams 

2

3D Beam 

Analysis of Composite Strucutres Needs Ply-by-ply inputs such as 

thickness, ply orientation, and material properties. 

MS Excel based User-friendly FEA program for beam type structures. 

An accurate, yet easy-to-use tool , greatly simplifying data input 

procedures. 

 

 

 

 

 

 

Long Structures (compared to cross-section) 

Any cross-sections 

Tapered / Untapered beam structure 

Loads (3 forces / 3 moments) at any location 

Multiply connected frames 

Modal analysis 

3

FEM formulation for a composite beam: 3D-Beam 

At each node (6 dof) 

d , 

3 3 

1) Displacement 

u ( x, y, z) 

d x 

x 

1 1 3 2 2 3 

d 

, 

 

1 1 

d 

, 

 

2 2 

 

u ( x, y, z) 

d x 

2 2 3 1 

u ( x, y, z) 

d x 

3 3 2 1 

2) strain-displacement 

d1 

 

2 

 

3 

u 

, 

x3 

x2 

22 

u 2, 2 

0 33 

u 3, 

3 

0 

x x x 

11 1 1 

1 

1 

1 

n 3 ' 

n 3 

 

n2 =n 2 ' 

n 

n 1 ' 

3 ' 

n 3 '' 

 

n 1 

n 1 '=n 1 '' 

d1 C1 0 S1 D1 

 

d 

 

2 

S1S2 C2 CS 

 

 

 

1 2D2 

d SC S CC D 

 

3 1 2 2 1 2 3 

n 2 '' 

n 2 ' 

 

 

1 

1 d2 

 

1 

( u 

, 

u 

, 

) 

x3 

 

2 

2 x1 

x1 

 

1 

1 d3 

 

1 

( u 

, 

u 

, 

) 

x2 

 

2 

2 x x 

12 12 21 3 

13 1 3 3 1 2 

1 

1 

 

23 

( u2, 3 

u3, 

2 

) 1 

 

1 0 

2 

2 

 

x 

x 

 

1 11 1 3 2 2 3 

 

2 x 

 

5 13 5 2 1 

 

2 x 

 

6 12 6 3 1 

1 

1 

4

FEM formulation for a composite beam 

3) Constitutive equation (stress-strain) 

 

1 

 

 

5 

 

 

 

6 

C C C 

 

 

 

C C C 

 

C C C 

11 15 16 

15 55 56 

 

 

 

 

 

1 

 

 

5 

 

 

 

6 

local 16 56 66 local local 

C 

Local 

 

1 

 

 

5 

 

 

 

6 

 

1 C C C x C x C x C x C 

 

 

5 

 

 

C C C x C x C x C x C 

 

 

 

6 

C C C x C x C x C x C 

local 

11 16 15 2 15 3 16 3 11 2 11 

15 56 55 2 55 3 56 3 15 2 15 

16 66 56 2 56 3 66 3 16 2 16 

Resultants Loads vs strains 

 

 

 

1 

 

 

6 

 

 

 

 

5 

 

D' 

 

1 

 

 

 

 

2 

 

 

3 

4) F.E. formulation 

 

T 

d 

 

 

 

1 

 

 

1 

 

5 

 

6 

 

5 

d MD' d 

 

 

6 

 

 

h 

h 

d N d , N ( i 1, 2, 

3) 

i 

2 

 

a1 

a ai i 

2 

 

a1 

a 

ai 

Laminates 

F 

A G G B B B 

 

 

1 11 16 15 11 12 13 1 

 

G 

2 66 

G56 B21 B22 B 

 

F 

 

23 

 

6 

F 

G 

3 55 

B31 B32 B 

 

 

 

33 

5 

 

 

M 

D 

1 

11 

D12 D13 

1 

 

M 

sym. 

D D 

 

2 22 23 2 

 

 

M 

D 

3 

33 

3 

M 3 

eg . ., A11 = C11dxdx 

2 3 

F 3 

M 1 

F 1 

F2 

M 

2 

e 

2 

T T 

k B DBdx 

B DB jd 

e ( ) ( ) 

 

 

x 

x 

1 

e 

e 

2 

x 

e 

1 

1 

 

1 

f e 

N f dx 

N( ) f jd 

x 

 

e 

2 

x 

e 

1 

 

1 

1 

m e 

N m dx 

N( ) m jd 

x 

 

1 

1 

e e e e e 

m d 

+k d f MD+KD 

 

F 

5

FEM formulation for a composite beam 

Laminates 

x 1 

d 

, 

 

1 1 

d 

, 

 

3 3 

d 

, 

 

2 2 

M 3 

Q 3 

N 1 

M 1 

Q2 

M 

2 

5) strain-displacement 

6) Constitutive equation 

(macro strain macro stress) 

7) Failure criterion : Quadratic Tsai-Wu criterion 

SMM+ 

MMF 

•Failure 

•Fatigue Life 

a F , b F 

( i 1, 2, 6) 

aR 

2 

ij i j i i 

bR 1 0 R 

 

 

 

0 :safe 

0 :fail 

Strength ratio 

1 0 :fail 

k 

R 0 :safe 

6

Coordinate systems and Layup direction 

Z 

Global 

Y 

Element 

X₃ 

X₂ 

Fiber direction 

Ply 

X 1 

X 

X₁ (S) 

, ply angle 

Cross Section 

 

Global coordinates (X-Y-Z) 

Element coordinates (X 1 -X 2 -X 3 ) 

Local coordinates (x 1 -x 2 -x 3 ) 

Layup Sequence 

Direction, t 

t 

n 

S 

n1 

n2 

L# 

n3 

Laminates 

Bricks 

x 3 

 

t sn 

X 3 

Plies 

x 2 

 

X 2 

7

Program Flow : 3D Beam 

Input 

• Cross Section 

• Material property 

• Nodes (Global coordinates) 

•Elements (node connectivity) 

• Boundary conditions 

• Global Forces 

Main Analysis Modules 

Step 1 : Section & Material 

Step 2 : Global Geometry 

Step 3 : Loads 

Step 4 : Solve 

Output 

• Displacement & Rotation 

• Global Strains & Curvatures 

• Global Loadings & Moments 

• In-Plane Strains 

• In-Plane Loads 

• Strength Ratios 

• Mode shape & Natural 

Frequency 

•Ply Stresses & Strains 

3D Graphical Post Processor: 

iPost.exe 

8

3D Beam– Main Sheet 

3D BEAM “Main” sheet 

2010-07-30 

9

Step 1 : Specification of Material Properties 

Material DB sheet 

10

Step 1 : Sections: Coordinates, Plies, and Laminates 

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

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

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

L1 

L2 

(x2,x3) 

 

L3 

 

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

Laminates bricks 

x 3 

 

X 3 

plies 

x 2 

 

X 2 

Laminate brick nodes 

nodes 

11

Step 1 : Sections: Coordinates, Plies, and Laminates 

3D BEAM “Section DB” sheet 

(4) 

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

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

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

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

L2 

 

L3 

(4) 

(3) 

(2) 

(3) 

L1 

(x2,x3) 

 

Material DB sheet 

• SI unit 

(1) 

Ply group number 

p8 

… 

p1 

(2) 

Laminates 

bricks 

x 3 

 

X 3 

plies 

x 2 

•English unit 

 

X 2 

brick nodes 

Laminate nodes 

12

e.g., A rectangular thin-wall cross section 

a2 

n 

a1 

t 

a2 

2 

Direction of ply sequence 

[0 3 /45/-45/90 2 ] s 

a1 

(-2 , 1) 

(2 , 1) 

a2 

x 3 

x 2 

a1 

x1 

x 3 

x 2 

t 

1 

2" 

3 

4 

(-2 , -1) 

(2 , -1) 

x1 

4" 

Laminate #1 

Laminate #2 

a1 

a2 

Laminate #3 

Laminate #4 

Base Line Option :0 

13

Step 2 : Global Geometry (nodes and elements) 

3D BEAM “Global geometry sheet” 

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

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

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

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

14

3D BEAM “Loads sheet” 

Step 3 : Loads: forces and moments 

[A] n 

,[B] n 

,[D] n 

[A] k 

,[B] k 

,[D] k 

[A] 2 

,[B] 2 

,[D] 2 

Displacements & Rotations 

 

U 3 

[A] 1 

,[B] 1 

,[D] 1 

Z 

Y 

U 2 

 

X U 1 

Forces & Moments 

M 3 

F 3 

M 2 

Z 

Y 

F 2 

X F 1 M 1 

 

Global coordinates (X-Y-Z) 

15

Step 4 : Results: Deflections, in-plane loads, etc. 

Y 

X 

0.5m 

1kN 

0.03m 

•Displacements & 

•Forces 

•Moments 

 

M 

• Rotations 

3 

U 3 

F 3 

Z 

 

Z 

M 2 

U 2 

F 

Y 

2 

Y 

X U 1 

X F 1 M 1 

Cross-section: 

20 segments (laminates) 

‣ resultant forces 

0.005 

0 

‐0.005 

‐0.01 

‐0.015 

‐0.02 

‐0.025 

‐0.03 

Deflection along the X‐axis 

0 0.1 0.2 0.3 0.4 0.5 0.6 

U₁ 

U₂ 

U₃

Step 4 : Results: failure index, in-plane loads, etc. 

3D BEAM “Results sheet” 

at each section 

Cross‐section 

0.02 

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

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

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

N 1 

N 2 

N 6 

0.015 

0.01 

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

0.005 

0 

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

‐0.005 

z_b 

zT 

zB 

‐0.01 

‐0.015 

‐0.02 

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

0.8 

0.6 

0.4 

0.2 

0 

‐0.2 

‐0.4 

‐0.6 

‐0.8 

In Plane stress at Element # 1 

N1 

N2 

N6 

0 5 10 15 20 25 

Laminate # 

0.006 

0.004 

0.002 

0 

‐0.002 

‐0.004 

‐0.006 

In Plane strain at Element # 1 

e1 

e2 

e6 

0 5 10 15 20 25 

Laminate # 

17 

16 

15 

Laminat # 

18 

14 

19 

13 

201.2 

1 

0.8 

0.6 

0.4 

0.2 

0 

‣Strength 12 ratio 

1 

11 

2 

10 

3 

9 

Failure Index (1/R) 

4 

5 

6 

7 

8 

17

Installation : 3D-beam and iPost (Graphic Post Processor) 

1 – Copy and Paste the 3D-beam and iPost into your folder. 

2. If needed, Install JRE (Java Runtime Environment) on your system to run JAVA Post 

Processor. You can download JRE from http://java.sun.com/javase/downloads/index.jsp 

This application is available for all operating systems. 

3 – Be sure to place “iPost.exe” file at same location as the 3D Beam II.xlsm software. 

Figure : 3D-beam & iPost 

18

iPost – Overview 

Post Process File Selection 

Parameter Setting 

Display Setting 

Graphics Area 

Field Output: 

Contour Values 

Note!! 

Current generated Post Process file will be automatically called. 

19

iPost– Parameter Setting 

Parameter Setting 

Scale Factor: 0.1 Scale Factor: 1 

Field Outputs: 

Nstress: stress from node 

Disp: displacement distribution 

Mode: mode shape 

Mat Number: 

All: elements with all mat 

1: elements with mat 1 

2: elements with mat 2 

& so on… 

Scale Factor: 

Any value 

20

iPost– Display Setting 

Display Setting 

On 

Off 

Window: 

1, 2, 4 

Wire Fram: 

On/Off 

Deformed 

Deformed & Undeformed 

Background: 

White/Black 

Deformed/Undeformed 

21

Comparison between 3D Beam and 

commecial FEA tools 

22

Case : Hollow Composite Beam with Circular Cross-section 

Deformation under simple loading 

Vertical 

100 N 

Torsion 

100 N · m 

D = 0.1 m 

L = 1 m 

[0/±45/90] S 

1.2 

Deflection 

Deformation normalized by Abaqus result 

1 

0.8 

0.6 

0.4 

0.2 

3D Beam II 

Abaqus 

0 

Deflection 

Rotational Angle 

Rotational Angle 

23

Case : Hollow Composite Beam with Circular Cross-section 

Natural frequencies & mode shapes 

D = 0.1 m 

L = 1 m 

[0/±45/90] S 

Mode 1 

Mode 2 

Natural Frequency (Hz) 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

3D Beam II 

Abaqus 

Mode 3 

200 

0 

Mode 1 Mode 2 Mode 3 Mode 4 

Mode 4 

24

Case : Hollow Composite Beam with Square Cross-section 

Results 

L = 1 m 

Load Case 1 Load Case 2 

100 N 100 N · m 

Load Case 1 : Max. Displacement 

Dispalcement (m) 

1.60E‐04 

1.40E‐04 

1.20E‐04 

1.00E‐04 

8.00E‐05 

6.00E‐05 

4.00E‐05 

2.00E‐05 

0.00E+00 

Abaqus (Shell Element) 

A 

3D Beam II5.50 

Load Case 2 : Max. Rotation 

Rotation (radians) 

8.00E‐04 

7.00E‐04 

6.00E‐04 

5.00E‐04 

4.00E‐04 

3.00E‐04 

2.00E‐04 

1.00E‐04 

0.00E+00 



H = 0.1m 

H = 0.1m 

W = 0.1m 

W = 0.1m 

Laminate Layup : [0 8 /±45 8 /90 8 ] S 

Material : AS/H3501 

Abaqus 

(Shell Element) 


Load Case 1 

Load Case 2

Case : Hollow Composite Beam with Square Cross-section 

Results : Natural Frequencies & Mode shapes 

Abaqus 


Abaqus 

(Beam Element) 


L = 1 m 

Laminate Layup : [0 8 /±45 8 /90 8 ] S 


Mode 1 

130.45 120.32 132.64 

Frequency (Hz) 

1800 

1600 

1400 

1200 

1000 

800 

600 


Abaqus (Beam Element) 


Mode 2 

705.49 972.93 743 

400 

200 

0 

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

Mode 3 

792.25 791.77 923.59 

Mode 4 

1539.5 1648.8 1481.6

Case :Ellipse Composite Beam 

Results 

D = 0.1 m 

L = 1 m 

Load Case 1 Load Case 2 

100 N 

100 N · m 

Load Case 1 : Max. Displacement 

Dispalcement (m) 

8.00E‐03 

7.00E‐03 

6.00E‐03 

5.00E‐03 

4.00E‐03 

3.00E‐03 

2.00E‐03 

1.00E‐03 

0.00E+00 

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

Load Case 2 : Max. Rotation 

Rotation (radians) 

2.50E‐02 

2.00E‐02 

1.50E‐02 

1.00E‐02 

5.00E‐03 

0.00E+00 


Abaqus (Beam 

Element) 


5 cm 

5 cm 

10 cm 

Laminate Layup : [0/±45/90] S 


10 cm 

Abaqus 


Abaqus 



Load Case 1 

Load Case 2

Case :Ellipse Composite Beam 

Results : Natural Frequencies & Mode shapes 

D = 0.1 m 

Abaqus 


Abaqus 



L = 1 m 

61.46 61.61 61.93 

Laminate Layup : [0/±45/90] S 


Mode 1 

Frequency (Hz) 

700 

600 

500 

400 

300 

200 

100 


Abaqus (Beam Element) 


Mode 2 

Mode 3 

103.88 101.95 104.93 

366.15 379.43 371.56 

0 

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

Mode 4 

613.01 610.32 620.27

Parametric study using 3D Beam 

29

. 

Parametric Study-Easy to change the layup angles 

3D BEAM “Section DB” sheet 

Plies 

Laminates 

Change ply angle for 3 cases 

θ 

Case (1) 30° 

Case (2) 45° 

Case (3) 60° 

•[0/±θ/90]s 

30

Results: a clamped beam with circular cross-section 

Y 

Z 

Displacement U3 

Z 

X 

X 

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



31

Results: a clamped beam with circular cross-section 

A cantilever beam 

under concentrated 

tip load 

Results at the root 

In plane load 

BOTTOM 

Fixed 

TOP 

L9 

L10 

L11 

L8 

Y 

L7 

L6 L5 

L4 

L3 

TOP 

Z 

L2 

(Global Z coordinate) 

L1 

Y 

L20 

In plane strain 

BOTTOM 

L12 

L13 

L14 

BOTTOM 

L15 L16 

L17 

X 

L18 

L19 

TOP 

- In plane load & strain are same for 

case(1),(2) and (3). 

32

Effect of fiber angles on stress distribution: Circular Beam 

At root 

Fixed 

L8 

L7 

L6 

TOP 

L5 

L4 

L3 

L9 

L10 

Z 

(Global Z coordinate) 

L2 

L1 

L11 

Y 

Y 

L20 

L12 

L13 

L14 

BOTTOM 

L15 

L16 

L17 

X 

L18 

L19 

Laminate # 

Tension 

Compression 

Small fiber angle reduces strength ratios 

θ 

Fiber 

33

Effect of ply angles on natural frequencies : Circular Beam 

Natural frequencies & modal shapes 

1 st Mode shape 

2 nd Mode shape 

3 rd Mode shape 

Case(1) 

: 30° 

Case(2) 

: 45° 

Case(3) 

: 60° 

34

Analysis of a Bend-Twisting Coupled 

Box Beam 

35

Tension-Shear Coupling in a laminate 

A tension-shear coupling term, 

A 16 

Balanced 

x 2 

x 1 

A16 0 

6 0 

N 1 

1 

1 A11 A12 0 N1 

 

 

A A 0 N 

2 21 22 2 

 

 

6 

0 0 A 

66 

N 

 

 

 

6 

 

 

Unbalanced 

x 2 

x 1 

A16 0 

 

6 

0 

N 1 

1 

1 A11 A12 A 

16 N1 

 

 

A A A N 

2 21 22 26 

2 

 

 

6 

A61 A62 

A 

66 

N 

 

 

 

6

Bend-Twist Coupling 

M 

EI 

C 2 

 

T 

 

C GJ 

 

1 

 

[0 / ] 100 

A 

16 

0 

If isotropic or balanced, 

For unbalanced, C 0 

C 0 

Twist 

Bend 

[0 / ] 100 

A 

16 

0 

37

A composite bend/twist coupled box beam. 

A bend/twist coulpled box-beam. 

Tip 

y 

x 

z 

 

Z 

ply thickness: 0.1 mm 

composite material : IM6/ep 

[ 45 80] 

[0 / ] 100 

[0 / ] 100 

bidirectional upper NCF: 

bidirectional lower NCF: 

length:10 m 

height:0.5 m 

width:0.5 m 

[0 / ] m 

[0 / ] m

Bend/twist coupling using birectional NCF 

Analysis tool : 3D-beam 

4 

L#3 

3 

0.24 

0.14 

0.04 

L#4 

‐0.252 ‐0.152 ‐0.052 0.048 0.148 0.248 

Base line 

Top line 

Bottom line 

[0 / ] m 

‐0.06 

L#2 

‐0.16 

[ 45] n 

[0 / ] m 

[ 45] n 

L#1 

‐0.26 

1 2

Bend/twist coupling using birectional NCF 

Analysis tool : 3D-beam 

twist/bend coupling, 

Z 

 

d 

d 

twisting angle, deg 

bending angle, deg 

Bidirectional NCF can be used to cause an intrinsically bend/twist coupling. 

0.25 

0.2 

bending angle, deg 

0.5 

0 

Z 

 

d 

d 

[ 45] n 

[0 / ] m 

[0 / ] m 

[ 45] n 

0.15 

0.1 

0.05 

0 

twisting angle, deg 

0 15 30 45 60 75 90 

-0.5 

-1 

-1.5 

-2 

twist/bend coupling 

outer ply angle, , deg

Zero displacement using Bend-Twist coupling 

Deflection, m 

Rotation, deg 

[ 4580] 

[0100 / 100] 

[ 45 ] 

80 

[0100 / 100] 

Top : [0 / 45 ] 

100 100 

Bottom : [0 / 45 ] 

100 100 

, deg 

Bending + Torsion 

No deflection 

Bending force only 

P 

+ 

P 0.78N 

0.78N 

Torsion only T 1 Nm T 1 Nm

Application to Braided Composite Beams 

42

Beam Type Composite Applications: Braided composites 

 

Braided Composites 

Airbeams, framing 

aircraft maintenance hangars 

Composite Bridge Arches 

 

High Tech Hockey Stick 

 

Baseball composites bats 

by courtesy of A&P Technology 

43

Braided structure with varying cross-sections 

30° 

2θ 

 

45° 

60° 

length 

width 

44 

2011,03,021

Variation of Material Properties with Braid angle 

45

Baided Beam with Varying Cross-sections 

[ / 

] m 

46

Application to Design of Wind Turbine 

Blades 

HSCL Turbine 

47

Application: 5 kW Wind turbine blades 

• Rated Power: 5 kW 

• Rated wind speed: 10 m/s 

• Hub height: 10 m 

• 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 

• Average Reynolds # : 1.5 x 10 6 

• Vertical Wind Shear: α = 0.2 

• Weibull Distribution: k = 2 

• Blades = 3 

• Orientation = Upwind 

• Rotation = Clockwise 

• Speed = Variable 

• Control = Pitch regulated 

*Reference: Finite element analysis with an improved failure criterion 

for composite wind turbine blades, Forsch Ingenieurwes (2008) 72: 193–207 

Hub 

D 

Hub height 

Airfoil NACA 4412 

Rotor Radius = 2.5 m 

Sections = 12 

Twist = 18 o 

Neck 

0º 

Material: 

Hub Metal and Composite* 

Neck Composite* 

Shell Composite* 

Fig: Model of a wind turbine blade 

* E-glass LY556 epoxy resin lamina Twist 

angle 

Shell 

18º 

0º

Application: Wind turbine blades 

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

[ Al(4mm)/0 8 / (±45) 4 ] 

[ 0 8 / (±45) 4 ] 

2.5m 

[ 0 6 / (±45) 2 ] 

Layup sequence 

Material : E-glass LY556 

Wing sections 

Airfoil NACA 4412 

Twist = 18 o 

0.08 

0.06 

0.04 

0.02 

0 

‐0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 

‐0.02 

‐0.04 

‐0.06 

‐0.08

Application : Wind turbine blade 

50

Application : Wind turbine blade 

Element #1 


0.03 

N1 

0.02 

N2 

0.01 

N6 

0 

‐0.01 

0 5 10 15 20 25 

‐0.02 

‐0.03 

Laminate # 

Element #4 


0.04 

N1 

0.03 

N2 

0.02 

N6 

0.01 

0 

‐0.01 0 5 10 15 20 25 

(1) 

‐0.02 

‐0.03 

‐0.04 

Laminate # 

Element #8 


0.06 

N1 

0.04 

N2 

0.02 

N6 

0 

‐0.02 

0 5 10 15 20 25 

‐0.04 

‐0.06 

Laminate # 


0.00008 

0.00006 

0.00004 

0.00002 

e1 

e2 

e6 

0 

‐0.00002 0 5 10 15 20 25 

‐0.00004 

‐0.00006 

‐0.00008 

Laminate # 

(8) 


0.0006 

(4) 

0.0004 

0.0002 

e2 

e6 

0 

‐0.0002 

0 5 10 15 20 25 

‐0.0004 

‐0.0006 

Laminate # 


0.0015 

0.001 

e1 

e2 

0.0005 

e6 

0 

0 5 10 15 20 25 

‐0.0005 

‐0.001 

Laminate # 

e1 

19 

18 

17 

16 

15 

14 

13 

Laminat # 

19 

18 

17 

16 

15 

14 

13 

Laminat # 

19 

18 

17 

16 

15 

14 

13 

Laminat # 

1 

20 0.015 

0.01 

0.005 

0 

12 

11 

1 

200.1 

0.08 

0.06 

0.04 

0.02 

0 

12 

11 

1 

200.2 

0.15 

0.1 

0.05 

0 

12 

11 

2 

10 

2 

10 

2 

10 


3 

4 

5 

6 

7 

8 

9 


3 

4 

5 

6 

7 

8 

9 


3 

4 

5 

6 

7 

8 

9 

51

Effects of stiffeners thickness on wind turbine blades 

Stiffener T300/N5208 [0 n ] 

E-glass/LY556 Epoxy 

Leading edge 

Trailing edge 

Upper Spar Cap 

Lower Spar Cap 

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

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

Stiffener T300/N5208 

Case (1) : n = 0; 

Case(2) : n = 10; 

Case(3) : n = 20. 

52

Blade deflection : Ultimate load 

Ultimate load at the tip 

4,000 N/m 

Deflection 

: No Stiffener 

: Stiffener =[0 10 ] 

T300/N5208 

: Stiffener =[0 20 ] 

T300/N5208 

53

Strength ratio : Ultimate load 

(1) (2) (3) 

Strength ratio (Tsai-Wu) 

(1) (2) (3) 

Laminate # 

L8 L7 L6 L5 

L10 L9 

L4 

L3 

L11 

L25 

L2 

L1 

L12 L26 

L28 

L29 

L27 

L30 

L13 

L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 

54

Vibration mode 

: No Stiffener 

: Stiffener =[0 10 ] Graphite 

: Stiffener =[0 20 ] Graphite 

1 st mode shape 

1 st 2 nd 3 rd 4 th 

Vibration modes 

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

55

Summary and Conclusion 

• The 3D-beam can be used as a preliminary design tool for compoiste structures. 

• It is based on a composite beam theory, yielding as accurate results as 3D modeling. 

• Yet easy-to-use tool. 

• Calculate displacements, strains, stresses, failure index and natural vibration modes. 

• Biaxial unbalanced laminates and beams, 

• Braided Composite Beams 

• A “3D Beam II5.55p” (public version) is available to the audience. 

Thank you for your attention !!! 

sungha@hanyang.ac.kr 

title: 3DBEAM 

56

X - JEC Composites

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