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

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

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

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

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

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

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

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

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.

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 ..

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°

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.

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

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

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

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

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.

Mesh elements number planning. Mesh element number The stress concentration ≈ CPU Time (Hour) 1800 490.002 MPa 7.88 6000 490.320 MPa 34 9000 489.940 MPa 36.02 14400 489.794 MPa 62.56 18000 489.810 MPa 79.83

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

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°

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 [1.2 - 1.6 mm.], crossover rate: 0.6 and mutation rate: 0.01

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 [1.2 - 1.6 mm.] and beta step size is 0.01

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 497.616 MPa 498.283 MPa 13º - 36.5º 490.056 MPa 36º.5 - 45º 496.556 MPa GA The winding angle Max stress concentration Min stress concentration 10º - 30º 497.918 MPa 498.679 MPa 13º - 36.5º 489.941 MPa 36º.5 - 45º 496.075 MPa

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 490.056 MPa 45º 496.556 MPa GA The winding angle Min stress concentration 36.54º 489.941 MPa 45 º 489.075 MPa

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 [1.2 - 1.6 mm.] at the winding angle is 18.9˚ SCGM The thickness of composite layer Min stress concentration 1.2 mm. 634.561 MPa 1.6 mm. 495.997 MPa GA The thickness of composite layer Min stress concentration 1.2 mm. 634.606 MPa 1.6 mm. 486.382 MPa

3. Results and discussion (7/12) The maximum stress contour with the thickness of composite layer [1.2-1.6 mm.] at the winding angle [10˚ - 45˚] a) by using GA b) by using SCGM a) b)

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

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 490.002 MPa 100 populations 30 generations The winding angle 37.43º The thickness of composite layer 1.6 mm. The stress concentration 490.002 MPa

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 0.001 490.002 MPa 0.01 0.1 490.013 MPa

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 0.1 490.449 MPa 0.3 490.108 MPa 0.6 490.002 MPa 0.75 490.001 MPa 0.9 490.010 MPa

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

4. Conclusion (1/3) The obtain results of SCGM and GA Two variables The thickness of composite layer from 1.2 - 1.6 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 490.056 MPa 489.941 MPa

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

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.

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