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D Ý k H È Æ » i Ð ( k ï Û · 2013 SIMULIA Region al User Meeting D Ý k H È Æ » i Ð ( k...
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2013 SIMULIA Regional User Meeting ፄ ፄӝቫڙᛈၩΠϐന٫ϯी ᔎঅ 1 , च࠹ቺ 2 , ᝄ 2 1 ഌ۔Ꮲਠ βЕπำᏢ س2 ୯ҥԋфεᏢ βЕπำᏢ سᄔा ᠼᆢமϯ᠄ቫፄӝаځ፦ໆᇸǵமࡋଯᓬᗺǴ٬ளԜቶݱᔈҔܭૐϼǵ ٣ᄬǶ೭ᜪᄬӧ٬Ҕޑၸำύନڙ܍ᓉᄊख़ϐѦǴҭԖёڙ܍ᛈख़ǶΑ ډനԖਏޑᔈҔǴҁزஒଞჹፄӝቫڙ܍ᛈၩޑϸᔈՉϩᆶന٫ϯीǶ Ԗ᠘ܭԖज़ϡનϩ (FEA) ೯தਢٯϩǴᗲϿଛӝำԄՉന٫ϯϩ ǴҁزஒᒥൻPowellБݤϐᆒઓǴၸኗቪPythonဌҁ (script) ǴჴаAbaqusπ ڀޑന٫ϯБݤǴፄӝቫڙᛈፂᔐ᠄ޑቫࡋفന٫ϯᚒǴගٮࠔᇙޣа ׳ԖਏޑБԄԋࠔ፦׳ӳޑࠔीǶ ᜢᗖӷǺԖज़ϡનǵፄӝቫǵന٫ϯǵPowell БݤǵᛈၩǵAbaqusǵPython ဌҁ ABSTRACT Laminated fiber-reinforced composite materials are widely used in aeronautic engineering, military engineering, etc. thanks to its advantages like light weight, high strength and so on. These structures may stand for the blast loading besides normal static or dynamic loading. To get the most efficient use of materials, this research would focus on the analysis to the responds for the composite laminates under blast loading, and optimize its design. A common finite element analysis (FEA) usually focuses on the single analysis without aid by programming to perform an optimization analysis. So this research follows the spirit of Powell's method to achieve the optimization for composite laminates under blast loading by using Python script controlling Abaqus. With the algorithm developed in this thesis, the manufacturer can make better design for product in a more efficient way. Keywords: Finite element, Composite laminates, Optimization, Powell's method, Blast loading, Abaqus, Python Script ǵᆣፕ 1.1 زᐒᆶҞ ޑᠼᆢமϯ᠄ቫፄӝаځ፦ໆᇸǵ மࡋଯᓬᗺǴ٬ளԜቶݱᔈҔܭૐ ϼǵ٣ᄬǶ೭ᜪᄬӧ٬Ҕޑၸำύ ନڙ܍ᓉᄊख़ϐѦǴҭԖёڙ܍ᛈ ख़Ƕ ፄӝቫ᠄ቫࡋفᄬന٫ϯ ᚒǴЬाၸׯᡂቫϣӚ᠄ቫࡋفޑǴ Զׯᡂᡏޑ܄፦Ǵ٩ᏵҞޑғന٫ ᠄ޑቫࡋفಔӝǴวචന٫ϯБޑݤ٫ زሦୱǶځύǴΞҗܭፄӝቫڙΚ ܈ޑፕ୷ᘵၨഢǴԖၨӭޑزଞჹ ೭ኬڙΚచҹΠޑፄӝቫՉ᠄ቫന٫ ϯǹၨϐΠǴჹаᛈѦΚޑፄӝቫ ന٫ϯز߾ၨϿǶӢԜǴҁزᔕճҔ Ԗज़ϡનݤଞჹፄӝቫڙᛈख़Πϐ ϸᔈՉന٫ϯीǶ ฅԶǴፄӝቫ᠄ቫࡋفคݤၸ Abaqus ϣࡌϐܗᐆന٫ϯኳಔՉന٫ ϯǶԜǴҁزၸ Abaqus ܌ගޑٮဌ ҁфǴа Python ำԄᇟقኗቪǴ၂ว р࠼ᇙϯന٫ϯБ ݤǴаයԋ҂ 1/12
Transcript of D Ý k H È Æ » i Ð ( k ï Û · 2013 SIMULIA Region al User Meeting D Ý k H È Æ » i Ð ( k...
2013 SIMULIA Regional User Meeting
1, 2, 2
1 2
(FEA)
Powell Python (script) Abaqus
Powell Abaqus Python
ABSTRACT Laminated fiber-reinforced composite materials are widely used in aeronautic engineering,
military engineering, etc. thanks to its advantages like light weight, high strength and so on. These structures may stand for the blast loading besides normal static or dynamic loading. To get the most efficient use of materials, this research would focus on the analysis to the responds for the composite laminates under blast loading, and optimize its design.
A common finite element analysis (FEA) usually focuses on the single analysis without aid by programming to perform an optimization analysis. So this research follows the spirit of Powell's method to achieve the optimization for composite laminates under blast loading by using Python script controlling Abaqus. With the algorithm developed in this thesis, the manufacturer can make better design for product in a more efficient way. Keywords: Finite element, Composite laminates, Optimization, Powell's method, Blast loading,
Abaqus, Python Script
1.1
AbaqusAbaqus
Python
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1.1
1997 Soremekun[3] (genetic algorithm GA)
2000 G rdal [4]
Genin Birman[5] Ashby
Reda Taha [6] (quasi-Newton method)
Broyden-Fletcher-Goldfarb-Shanno (BFGS)
Kalavalapally [7, 8]
[3] (Newton method)
2.1
1. (fibrous composite
materials) 2. (laminated composite
materials) 3. (particulate composite
materials)
[9]
(lamina) (fiber)
(matrix)
[10]
1
laminate
[12] 2
2.2 Tsai-Hill
Hill[17]
HillAzzi Tsai[18]
Tsai[19]Hill
Tsai-Hill
ij ij X
(1 ) Y (2 ) S
1
2.3 Kevlar/Epoxy Kevlar/Epoxy
2.1
Kevlar
(Epoxy)
[14]Kevlar/Epoxy
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1
3.1
Tsai-HillTsai-Hill
Tsai-Hill
Powell
(golden section method) Powell
3.2 Powell
Powell[24] Powell
(pattern search method) (method of
conjugate directions)
Powell
[23]
Powell
PowellPowell
Powell 3
Si i Sp(j)
jB
n Powell
* X Si
Powell
3.3 (grid search method) (design
space)
x y 4 ( 4 ) 42=16
4.1
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2
Kevlar/Epoxy (1) 2.2 1.5 (2) 1.5 1.5
(1) (2) (3)
0.75 5
TNT 0.006
Tsai-Hill
4.2
5 6 1 0Z 1-2-3
1-2-n 5[0 /90 ] 6
[0 /90 /0 ] -90
90
0 180Z X
Abaqus CONWEP CONWEP
(free air blast ) (surface blast) CONWEP
P(t)[1]
Pincident(t)Preflect(t)
4.3
S4R
Tsai-Hill6
4[90 /90 ]
[90 /90 /0 ] 7 10
0.08 0.08504 0.07 0.07
484 2 3
Powell
5.1
PowellX
Powell 11
Powell 12 12
X_keepnew_X
situationnew_X
new_XX_keep f(X_keep)
Abaqus
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5.2
(local optimum)
12 (2)
0
0 Powell* 1
7
6.1 Powell
4 5Powell
Powell
6 6.2
Powell 7
8 1 1180 180
32400 13 17
6.3
Powell 9 13
Total time ErrorPowell
Powell 14 15
( 15)
-90 90
( 17)
0
( 14)
30.58% 31.08%
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Python
Abaqus
(1)
(2)
(3)
(4) (2)
Tsai-Wu
[1] Abaqus Inc., Abaqus Analysis User's
Manual, Version 6.11, 2011. [2] Abaqus Inc., Abaqus Scripting User's
Manual, Version 6.11, 2011. [3] G. A. Soremekun, "Genetic algorithms for
composite laminate design and optimization," Virginia Polytechnic Institute and State University, 1997.
[4] G. Soremekun, Z. Gurdal, R. T. Haftka, and L. T. Watson, "Composite laminate design optimization by genetic algorithm with generalized elitist selection," Computers & Structures, vol. 79, pp. 131-143, 2001.
[5] G. M. Genin and V. Birman, "Micromechanics and structural response of functionally graded, particulate-matrix, fiber-reinforced composites," International Journal of Solids and Structures, vol. 46, pp. 2136-2150, 2009.
[6] M. M. Reda Taha, A. B. Colak-Altunc, and M. Al-Haik, "A multi-objective optimization approach for design of blast-resistant composite laminates using carbon nanotubes," Composites Part B: Engineering, vol. 40, pp. 522-529, 2009.
[7] R. Kalavalapally, R. Penmetsa, and R. Grandhi, "Multidisciplinary optimization of a lightweight torpedo structure subjected to an underwater explosion," Finite Elements in Analysis and Design, vol. 43, pp. 103-111, 2006.
[8] R. Kalavalapally, R. Penmetsa, and R. Grandhi, "Configuration design of a lightweight torpedo subjected to an underwater explosion," International Journal of Impact Engineering, vol. 36, pp. 343-351, 2009.
[9] R. M. Jones, Mechanics of composite materials. Washington,: Scripta Book Co., 1975.
[10] R. C. Reuter, "Concise property transformation relations for an anisotropic lamina," Journal of Composite Materials, vol. 5, pp. 270-272, 1971.
[11] , "," ,
, , 2001. [12] E. Reissner and Y. Stavsky, "Bending
and stretching of certain types of heterogeneous aeolotropic elastic plates," J.
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Appl. Mech, vol. 28, pp. 402-408, 1961. [13] , "
," , , ,
2009. [14] ,
. . : , 1988. [15] M. E. Waddoups, "Advanced composite
material mechanics for the design and stress analyst," General Dynamics, Fort Worth Division FZM-4763, 1967.
[16] C. F. Jenkins, Report on materials of construction used in aircraft and aircraft engines. London,: H. M. Stationery off., 1920.
[17] R. Hill, The mathematical theory of plasticity. Oxford,: Clarendon Press, 1950.
[18] V. D. Azzi and S. W. Tsai, "Anisotropic strength of composites," Experimental Mechanics, vol. 5, pp. 283-288, 1965.
[19] S. W. Tsai, "Strength theories of filamentary structures," in Fundamental aspects of fiber reinforced plastic composites, R. T. Schwartz and H. S. Schwartz, Eds., ed New York: Interscience Publishers, 1968, pp. 3-11.
[20] O. Hoffman, "The brittle strength of orthotropic materials," Journal of Composite Materials, vol. 1, pp. 200-206, 1967.
[21] S. W. Tsai and E. M. Wu, "A general theory of strength for anisotropic materials," Journal of Composite Materials, vol. 5, pp. 58-80, 1971.
[22] R. F. Gibson, Principles of composite material mechanics, 3rd ed. Boca Raton, Fla.: Taylor & Francis, 2012.
[23] S. S. Rao, Engineering optimization : theory and practice, 4th ed. Hoboken, N.J.: John Wiley & Sons, 2009.
[24] M. J. D. Powell, "An efficient method for finding the minimum of a function of several variables without calculating derivatives," The Computer Journal, vol. 7, pp. 155-162, 1964.
[25] M. J. Vick and K. Gramoll, "Finite element study on the optimization of an orthotropic composite toroidal shell," Journal of Pressure Vessel Technology-Transactions of the ASME, vol. 134, 2010.
[26] , "
," , , , 2012.
[27] G. L. Rogers, Dynamics of Framed Structures. New York: John Wiley & Sons, Inc., 1959.
[28] , "," ,
, , 2010. [29] , "
," 992001INER012, 2010.
[30] CAE , Abaqus: , 2013.
1 Kevlar/Epoxy[25]
Property Value in metric
unit Property
Value in metric unit
Density 1.4 *10³
kg/m³
Axial tensile strength 1400 MPa
Axial tensile modulus (E1) 76 GPa
Transverse tensile
strength 12 MPa
Transverse tensile
modulus (E2=E3)
5.5 GPa Axial
compressive strength
235 MPa
Poisson ratio 0.34 Transverse
compressive strength
53 MPa
Shear modulus
(G12=G13) 2.3 GPa Shear
strength 34 MPa
Shear modulus
(G23) 1.4 GPa Ply thickness 0.127 mm
2
Meshsize
Element numbers
Displacement at center
Max Tsa i -Hill
value
CPU time
0.5 16 -3.92E-02 0.140956 00:03.4 0.44 24 -4.33E-02 0.20483 00:03.2 0.31 32 -4.47E-02 0.252645 00:03.2 0.3 48 -3.89E-02 0.287933 00:03.3
0.24 60 -3.51E-02 0.34115 00:03.3 0.21 80 -3.44E-02 0.322922 00:03.2 0.2 96 -3.78E-02 0.356578 00:03.3
0.16 140 -3.58E-02 0.463617 00:03.3
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0.14 160 -3.44E-02 0.57405 00:03.3 0.13 192 -3.56E-02 0.562026 00:03.4 0.12 216 -3.39E-02 0.562738 00:03.4 0.11 280 -3.70E-02 0.576095 00:03.4 0.1 352 -3.38E-02 0.608555 00:03.5
0.09 384 -3.60E-02 0.621836 00:03.5 0.08 504 -3.63E-02 0.650273 00:03.6 0.07 704 -3.65E-02 0.649386 00:03.7 0.06 936 -3.63E-02 0.673373 00:05.9 0.05 1320 -3.63E-02 0.687982 00:06.2 0.04 2128 -3.61E-02 0.702447 00:08.8 0.03 3700 -3.63E-02 0.696661 00:18.0
3
Meshsize
Element numbers
Displacement at center
Max Tsa i -Hill
value
CPU time
0.5 16 -3.64E-02 0.592174 00:03.8 0.3 36 -4.56E-02 1.057633 00:03.3
0.21 64 -4.65E-02 1.035343 00:03.3 0.16 100 -4.47E-02 1.036549 00:03.4 0.13 144 -4.52E-02 1.117504 00:03.4 0.11 196 -4.23E-02 1.131131 00:03.5 0.1 256 -4.34E-02 1.180647 00:03.6
0.08 324 -4.33E-02 1.194085 00:03.6 0.07 484 -4.30E-02 1.266949 00:03.8 0.06 676 -4.29E-02 1.311856 00:04.0 0.05 900 -4.28E-02 1.354367 00:06.3 0.04 1444 -4.28E-02 1.400983 00:06.9 0.03 2500 -4.27E-02 1.375831 00:10.0
4 Powell
[95.02, 96.53] [0, 82.62] [166.87,
22.43]
Tsa i -Hill
0.599180 2.146504 0.873323
8 4 4
3 54 1 59 1 59
5 Powell
[114.35,
84.98,0] [0, 91.18, 0]
Tsa i -Hill 1.219550 1.504972
3 9 1 34 4 36
6 Powell
[87.43, 97.38,
78.11] [91.18, 0,
91.92]
Tsa i -Hill 0.372935 1.501095
5 7 2 35 3 35
7
[95, 97] [34, 124] [12, 156]
Tsa i -Hill
0.592038 1.805015 0.844141
33 180
33 460
33 3224
8
[71, 92, 0] [20, 103, 0]
Tsa i -Hill 1.199936 1.484657
34 2521
34 23 05
9
Property ( )
Method Grid Search Powell Error
Position (theta) [95, 97] [95.02,
96.53]
Optimum Tsa i -Hill
Va lue 0.592038 0.59918 1.21%
Total time 33 hours 18 mins 0 sec
3 mins 54 secs
512.31
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10 Property ( )
Method Grid Search Powell
Error
Position (theta) [34, 124] [0, 82.62]
Optimum Tsa i -Hill
Va lue 1.805015 2.146504 18.92%
Total time 33 hours 46 mins 0 sec
1 mins 59 secs
1021.51
11
Property ( )
Method Grid Search Powell Error
Position (theta) [12, 156] [166.87,
22.43]
Optimum Tsa i -Hill
Va lue 0.844141 0.873323 3.46%
Total time 33 hours 32
mins 24 secs
1 mins 59 secs
1014.66
12
Property ( )
Method Grid Search Powell Error
Position (theta) [71, 92, 0] [114.35,
84.98,0]
Optimum Tsa i -Hill
Va lue 1.199936 1.21955 1.63%
Total time 34 hours 25
mins 21 secs
1 min 35 secs
1304.43
13
Property ( )
Method Grid Search Powell Error
Position (theta) [20, 103, 0] [0, 91.18,
0]
Optimum Tsa i -Hill
Va lue 1.484657 1.504972 1.37%
Total time 34 hours 23 mins 05 secs
4 mins 36 secs
448.50
14
Property ( )
Method Grid Search Powell Error
Position (theta) [71, 92, 0]
[87.43, 97.38, 78.11]
Optimum Tsa i -Hill
Va lue 1.199936 0.372935 X
Total time 34 hours 25
mins 21 secs
2 mins 35 secs
799.49
15
Property ( )
Method Grid Search Powell Error
Position (theta) [20, 103, 0] [91.18, 0,
91.92]
Optimum Tsa i -Hill
Va lue 1.484657 1.501095 1.11%
Total time 34 hours 23 mins 05 secs
3 mins 35 secs
575.74
1 [11]
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2 [11]
3 Powell [23]
4 pi = 4 [23]
5
6
7 -
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8 - Tsai-Hill
9 -
10 - Tsai-Hill
11 Powell
12 Powell
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15
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