1. Optimal design of composite pressure vessel by using genetic algorithm
Student : Nachaya Chindakham
Advisor : David T.W. Lin

2. Contents 1 Introduction 2
Finite element analysis of composite pressure vessel 3
Results and discussion 4
Conclusion

3. 1. Introduction (1/6) Various application of pressure vessel

4. 1. Introduction (2/6) Automotive industry Global warming
Reduce pollution

5. Basic requirement for the successful application.
1. Introduction (3/6)
Basic requirement for the successful application.
Low weight and low cost
Small volume
Efficiency
Reliable
Important
Safety

6. 1. Introduction (4/6) From the beginning to today.
1928
1974

7. Description of the contents
1. Introduction (5/6)
Type 4
Type of pressure vessel
Type 3
Type 2
Description of the contents
Type 1

8. Purpose of this research
1. Introduction (6/6)
Purpose of this research
Aim to reach the minimum stress concentration of composite pressure vessel.
Compare results with GA and **SCGM.
Section 1
Study a comparison the effect of population size, generation size, crossover rate and mutation rate in GA.
Section 2

9. Concept design and optimization
Previous
Paper*
Boundary
condition
Objective
Model
SCGM**
Results
Compare
the results
Optimization GA
Results
Effect of population size, generation size,
crossover and mutation rate in GA process
* Ping Xu, Jinyang Zheng, Honggang Chen, Pengfei Liu. Optimal design of high pressure hydrogen storage vessel using an genetic algorithm. International Journal of Hydrogen energy 2009 I-7, Elsevier.
** Pham Duy Hai, Optimal design composite pressure vessel with liner base on SCGM, Industry research master program, NUTN, 2011.

10. 2. Finite element analysis of composite pressure vessel (1/8)
2.1 The structure of the composite pressure vessel
The vessel is composed of an aluminum liner and carbon fiber/epoxy composite layer.
Aluminum
N=1
N=2
N=3
N=10 ..

11. 2. Finite element analysis of composite pressure vessel (2/8)
The winding angles at the cylinder are 90°, -90°, α0, -α0,…, α0, -α0, 90°, -90° in turn.
Aluminum
N=1
N=2
N=3
N=10 ..
N=4
-α0°
α0°
-90°
90°

12. 2. Finite element analysis of composite pressure vessel (3/8)
2.2 Material properties of the composite pressure vessel
The aluminum liner is considered to be isotropic.
The carbon fiber/epoxy composite is considered to be linear-elastic and transversely isotropic.

13. 2. Finite element analysis of composite pressure vessel (4/8)
The off-axis stress-strain relationship of the k (k = 1,2,3,…,1+ ns) layer under the defined cylindrical coordinate system are expressed as
(1)
Where
(1,2,3,6) : the off-axis elastic constants of the materials
: the off-axis axial, hoop, radial and shear stresses, respectively
: the corresponding strains

14. 2. Finite element analysis of composite pressure vessel (5/8)
2.3 Failure criteria
The maximum shear stress and Tsai-Wu failure criteria are considered for the liner material and carbon fiber/epoxy composite layer.
The quadratic Tsai-Wu failure surface for a 3D stress state is expressed as the following form
(2)
Where
: stressed under material coordinates
: second-order and fourth-order strength tensors depending on the tensile, compressive and shear strengths of the composites

15. 2. Finite element analysis of composite pressure vessel (6/8)
For the anisotropic composite laminate, the quadratic Tsai-Wu failure criterion can be written in the following form
(3)
Where
: on-axis stresses in the longitudinal and transverse directions, respectively
: the on-axis in-plane shear stress

16. 2. Finite element analysis of composite pressure vessel (7/8)
The parameters are given by
(4) (5)
(6)
Where
: longitudinal tensile and compressive strengths, respectively
: the transverse direction
S : the in-plane shear strength

17. 2. Finite element analysis of composite pressure vessel (8/8)
2.4 Modeling description
The inner radius and length of cylinder is 100 mm and 220 mm, respectively. The thickness of the liner is 3 mm. The number of composite layers are 10.
The working pressure inside is 70 MPa.
The material parameters are listed in Table 1 and 2
Table 1. Mechanical properties of 6061 Al
and T700/epoxy composite materials
Table 2. Strength parameters for T700/epoxy composite laminates E1
(GPa) E2
G12
v12
v23
6061 Al 70
26.92
0.3
T700/epoxy
181
10.3
5.17
0.28
0.49
Xt (MPa)
Xc (MPa)
Yt (MPa)
Yc (MPa)
S (MPa)
2150
298
778
J.Y. Zheng and P.F. Liu, Elasto Plastic stress analysis and burst strength evaluation of Al-carbon fiber/epoxy composite cylindrical laminates, Comput. Mat. Sci. 42, pp. 453–461, 2008.

18. Mesh elements number planning.
Mesh element number
The stress concentration
≈ CPU Time
(Hour)
1800
MPa
7.88
6000
MPa 34
9000
MPa
36.02
14400
MPa
62.56
18000
MPa
79.83

19. Generation of an ending population
3. Optimal method
Start
Define Parameters
Initial population
Selection and elitism
Crossover
i = i+1
Mutation NO
If generation
YES
Generation of an ending population

20. 3. Results and discussion (1/12)
3-1 Comparison of the simulation by using the genetic algorithm (GA) and the simplified conjugate gradient method (SCGM)
The winding angles of each composite layers from the inner layer to the outer layers are 90°, -90°, 18.9°, -18.9°, 90°, -90°, 18.9°, -18.9°, 90°, -90°

21. 3. Results and discussion (2/12)
The maximum stress profile by using GA with the generation in the optimal process at the winding angle [10˚ - 45˚] with the thickness of composite layer [ mm.], crossover rate: 0.6 and mutation rate: 0.01

22. 3. Results and discussion (3/12)
The maximum stress profile by using SCGM with the iteration number in the optimal process at the winding angle [10˚ - 45˚] with the thickness of composite layer [ mm.] and beta step size is 0.01

23. 3. Results and discussion (4/12)
The optimal result between SCGM and GA at the winding angle [10˚ - 45˚] with the thickness of composite layer is 1.6 mm.
SCGM
The winding angle
Max stress concentration
Min stress concentration
10º - 30º
MPa
MPa
13º º
MPa
36º º
MPa GA
The winding angle
Max stress concentration
Min stress concentration
10º - 30º
MPa
MPa
13º º
MPa
36º º
MPa

24. 3. Results and discussion (5/12)
Stress concentration of composite pressure vessel of SCGM and GA for 1.6 mm of the thickness of composite layer with the bounded at the winding angle is [30˚ - 45˚]
SCGM
The winding angle
Min stress concentration
36.2º
MPa
45º
MPa GA
The winding angle
Min stress concentration
36.54º
MPa
45 º
MPa

25. 3. Results and discussion (6/12)
The optimal process of the thickness of composite layer by using SCGM and GA with the thickness of composite layer [ mm.] at the winding angle is 18.9˚
SCGM
The thickness of composite layer
Min stress concentration
1.2 mm.
MPa
1.6 mm.
MPa GA
The thickness of composite layer
Min stress concentration
1.2 mm.
MPa
1.6 mm.
MPa

26. 3. Results and discussion (7/12)
The maximum stress contour with the thickness of composite layer [ mm.] at the winding angle [10˚ - 45˚] a) by using GA b) by using SCGM a) b)

27. 3. Results and discussion (8/12)
The result 30° cylinder part of optimal model

28. 3. Results and discussion (9/12)
3-2 Comparison of generation size, population size, crossover rate and mutation rate
Effect of population size and stress concentration in 30 generations and 100 populations and 100 generations and 30 populations
30 populations 100 generations
The winding angle
37.43º
The thickness of composite layer
1.6 mm.
The stress concentration
MPa
100 populations 30 generations
The winding angle
37.43º
The thickness of composite layer
1.6 mm.
The stress concentration
MPa

29. 3. Results and discussion (10/12)
Variation of stress concentration and number of generation at different mutation rate and crossover rate is 0.6
Mutation rate
The stress concentration
0.001
MPa
0.01
0.1
MPa

30. 3. Results and discussion (11/12)
Variation of stress concentration and number of generation at different crossover rate and mutation rate is 0.01
Crossover rate
The stress concentration
0.1
MPa
0.3
MPa
0.6
MPa
0.75
MPa
0.9
MPa

31. 3. Results and discussion (12/12)
The contour of mutation rate, crossover rate and stress concentration in 30 generations, 100 populations

32. 4. Conclusion (1/3) The obtain results of SCGM and GA Two variables
The thickness of composite layer from mm.
The winding angle of composite layer 10˚ - 45˚
Method
Variables
SCGM GA
The thickness of composite layer
1.6 mm.
The winding angle of composite layer
36.2˚
36.54˚
The stress concentration
MPa
MPa

33. Crossover and mutation rate, population and generation size
4. Conclusion (2/3)
Full range search
Random search GA
Crossover and mutation rate, population and generation size
Objective function
Initial data
Direct search
SCGM
Beta step

34. 4. Conclusion (3/3)
Generation size and population size have effect directly to approach the optimal result which is a large population size can access to the optimal point more rapidly than small population size.
Various mutation rates and crossover rates which mutation rate at 0.001, 0.01 and 0.1 are not much strong influence to find effect of mutation rate in small population size to perform the genetic algorithm.
Variety of crossover rates at 0.1, 0.3, 0.6, 0.75 and 0.9 shown that crossover rate from 0.75 to 0.9 has an impact to converge of the optimal result and improves the convergence rates of the genetic algorithm which has some correlation characteristic based on statistical measures.

35. Thank You!