Title 非線形構造解析技術の社会的普及に関する研究( 本文(Fulltext) )

Author(s) 小林, 卓哉

Report No.(DoctoralDegree) 博士(工学) 乙第075号

Issue Date 2015-12-31

Type 博士論文

Version ETD

URL http://hdl.handle.net/20.500.12099/54098

※この資料の著作権は、各資料の著者・学協会・出版社等に帰属します。

Social Dissemination of Nonlinear Structural Simulation Technologies

2015 12

1 ······················································································· 1

2 2.1 ················································································· 6 2.2 ··················································· 7 2.3 Ogden ·········································································· 9 2.4 ······································································ 11 2.5 Ogden ························ 15 2.6 ·············································· 18 2.7 ················································· 21 2.8 ································································ 25 2.9 ·············································· 27 2.10 ····················································································· 27

3

3.1 ··············································································· 29 3.2 Maxwell ··························································· 30 3.3 - ····································································· 32 3.4 ····························································· 39 3.5 Maxwell ·· 41 3.6 ·························································· 45 3.7 ··················································································· 47

4

4.1 ··············································································· 48 4.2 ············································································ 50 4.3 2 ······················································· 51 4.4 ··················· 54 4.5

Yamaki ························· 59 4.6

Esslinger ························ 61 4.7 ····································· 63 4.8 ····················································································· 68

5

5.1 ··············································································· 69 5.2 ···················································· 71 5.3 ······················································· 72 5.4 ············································································ 74 5.5 ········································ 76 5.6 ··································································· 78 5.7 ····················································································· 81

6

6.1 ··············································································· 82 6.2 ···················································· 82 6.3 ····························································· 84 6.4 ·············································· 89 6.5 ·············································· 95 6.6 ················································· 99 6.7 ···················································································· 100

7 ·························································································· 101

8 ···················································································· 104

9 ·························································································· 116

1

1 (1-1)

1950 60

1983(1-2)

2

3 8

550

(1-3)

(1-4)

3

FEM

900

20 1500

2 3

6

2

FEM

4

3

Maxwell -

FEM

4

5

6

6

5

50

6

2

2.1

O

Fig.2-1

Fig.2-1 4 (2-21)

1939 1940

7

FEM

2.2

%

1940 (2-1)

2

(1)

(2)

0

8

Hyperelastic (2-2), (2-3), (2-4)

2-1

Fig.2-2

2-2

Fig.2-2

9

2-2

2-3

2-4 2-3 2-5

2-4

2-5

2-5

(2-2)

2.3 Ogden Fig.2-3 Ogden

Neo-Hookean Mooney(2-2), (2-7)

Fig.2-3

Valanis Landel(2-5), (2-6)

2-6

10

1

(2-8) Ogden N(2-9), (2-10), (2-11)

2-7

Ogden Treloar(2-12)

2-7 2-7

2-5

2-8

Fig.2-3

11

2.4

2.4.1 Simple Tension

2-4

2-9

2-8

2-10

2-10

2-11

2-12

Fig.2-4 FEM

1

Ogden 2-7

12

2-12 -

2-1

2-12

2-13

2-14

Mooney(2-7) 2-14

Ogden

2-15

2-14

2-15

Fig.2-4

13

2.4.2 Pure Shear

Fig.2-5

2-16

2-17

2-8

2-18

2-18 2-19

Fig.2-5

14

2-20

2-19

2-20

Fig.2-5 Ogden Treloar(2-12) FEM

75mm 5mm

2.4.3 Equi-Biaxial Tension

Fig.2-6

Ogden(2-6), (2-8), (2-12)

Fig.2-6

(1) Ogden

Valanis 2-6

(2)

(3) 2-21

15

2-21

2-8

2-22

2-22 1= 1=

2-23

2-24

2.5 Ogden FEM 1940

Mooney(2-13) Mooney Hencky 1993

Love 1920

2-25

, Mooney 2

200%

16

Mooney Treloar(2-14)

2-26

G

Neo-Hookean Mooney

Mooney Neo-Hookean

Treloar

Rivlin (2-15) 1950

Mooney-Rivlin

2-27

2-28

Rivlin Mooney Treloar

Mooney 2-25

2-29

Rivlin Green (2-16), (2-17)

17

2-30

2-31

Cauchy-Green

2-32

2-28

Mooney-Rivlin

Arruda-Boyce (2-20)

Ogden

.

2-29 Mooney-Rivlin

18

Ogden

Ogden(2-9), (2-18)

Mooney-Rivlin

Ogden

Ogden

Arruda-Boyce

Excel Ogden

Ogden

FEM

2.6 Fig2-7 3

Ogden 2-7

(2-12) (2-20) (2-24) Fig.2-8(a)

Fig.2-3

(2-9) (2-16) (2-21) Fig.2-8(b)

Fig.2-8(a)

2 1.5

3 3

Fig.2-8(a) 3

2.9

19

JIS

K6251,K6254 K6254

2.4.3

FEM

Fig.2-7

(a) (b)

Fig.2-8

20

Fig.2-9 Ogden

3 2-12 2-20 2-24

1.5 50

Fig.2-8(b)

1 3

FEM Ogden

Ogden 2 3

Fig.2-9

( 1 0.69, 1= 0.186, 2 -1.07, 2=0.0460, 3 4.14, 3= 0.000643)

2-12

2-20

2-24

21

(1) 10%

0.5 FEM 0.48 0.49

JIS

0.5

(2) 50 100 Neo-Hookean

1

100 -

(3) Arruda-Boyce

FEM

(4) (2-18) 3

2-29 Mooney

0.05 0.1

Williams(2-19) 0.2

2.7

22

JIS

JIS

FEM

JIS FEM

3

JIS K 6251

1

JIS K 6254

JIS K 6254

Fig.2-10 Fig.2-12 Ogden

2-7

Ogden 2-13

2-33

Fig.2-13 Excel

FEM

23

-

JIS K 6254

Fig.2-12

10%

Ogden FEM

Ogden

2-14

Fig.2-10 3 JIS K 6251

Fig.2-11 1 JIS K 6254

Fig.2-12 JIS K 6254

24

2-34

2-7

Fig.2-14 Fig.2-13 2-34

Ogden 2-33 2-34

-

Fig.2-15

100% 1

10% 40%

Fig.2-14

Fig.2-13

Fig.2-13

25

2.8

(2-16) Ogden (2-9)

Fig.2-16 ,

2 2-24

2-35

2-36 2-35 2-37

, 2-36, 2-37

2-24 2-37 2-38

Fig.2-15

26

2-38

=100mm, =1mm Ogden 2-7

Fig.2-17 2-38

2

2 FEM

Fig.2-17 FEM Abaqus Marc

Fig.2-16 3

Fig.2-16 Fig.2-17

27

2.9 2.2 2.7 Excel

Fig.2-18

Ogden

Abaqus Marc LS-DYNA

2.10

1940

1970 Ogden

Fig.2-18Ogden

28

FEM 1980

FEM

3 Excel

40

29

3

3.1

Hooke 1678 Newton 1687

(3-1) 1835

elastic after-effect

Weber

30

Maxwell 1868

viscoelastic fluid

Kelvin 1875

viscoelastic solid

1950 1980 FEM

(3-20)

3.2 Maxwell FEM Fig.3-1

Maxwell (3-2), (3-6) Maxwell

Maxwell

3-1

3-1

3-2

31

Maxwell

Fig.3-2 0

( )

FEM Maxwell

10 20 Maxwell

1

10

20

Fig.3-1 Maxwell Fig.3-2 Maxwell

32

3.3 - 3.3.1

50

Thermo-rheological Simplicity

Fig.3-3

10 1000sec

Fig.3-3 109 Pa

109 Pa

Fig.3-3 1/1000

Fig.3-3

1013 poise

33

1940 1950

Fig.3-3 Fig.3-3

0.01sec

109sec 30

10 1000sec 0.01sec

30 Fig.3-3

Fig.3-3

3-3

Fig.3-3

34

-

WLF

WLF

WLF Williams Landel Ferry

3-4

50

3-4

Fig.3-4 a 3-4 260

a WLF ( =260 K) b ( =260 K)

Fig.3-4 -

35

Fig.3-4 3-5 260

3-5

Fig.3-4 b

3-5

3.3.2

-

RSA TA (3-7)

30 5 1mm

-40 60 =233 333

= 3.16 10 31.6 100 0.5 16Hz

JIS(3-8) RSA

36

0.1 1%

storage modulus E' loss

modulus E" Fig.3-5 =3.16 10 31.6 100

E'

E"

Fig.3-5

37

3.3.3

Fig.3-5

Fig.3-5

3-3

3-3 3-6

[K] 0[K]

3-6

-

WLF Fig.3-5

3-4

3-6

Fig.3-5

Fig.3-6

3-4

3-4

g

g -40 -14

g -14 WLF

38

b Tg -14 ( )a Tg -40 ( )Fig.3-6

-

WLF 3-4 1 2

g g

tan = /

Fig.3-5 g -10 -20 Excel g

Fig.3-6 g

(3-9)

39

3.4

1950 hereditary

integral

1 106sec

10-6 1sec

loss tangent

Fig.3-7

40

Maxwell

Fig.3-7

3-9

Fig.3-7

3-7

3-8

41

3-2 3-8

Maxwell

3-10

3-11

Fig.3-6 b

3-10 3-11

Maxwell

3.5 Maxwell (3-10), (3-11),

(3-20) 3-10 3-11

Maxwell 3

(1) i

(2) Maxwell

(3)

(1)

Maxwell

FEM

42

(2) Maxwell

10 20

Maxwell

2 Maxwell

2 Maxwell

= 100Pa

1 = 100Pa 1 = 1sec

Fig.3-8

Maxwell

Maxwell

10

Maxwell 10

Fig.3-8 2

43

(3)

Emri(3-12)

3-12

Fig.3-9

Fig.3-10 b

Fig.3-6 b

Maxwell

Fig.3-11

Optimization

Fig. 3-6 b 12

Maxwell 12

e i i Maxwell

Abaqus MSC.Marc LS-DYNA

44

Fig.3-9

(a) ( ) (b)

Fig.3-10

Fig.3-11Maxwell

E E

45

3.6 (3-13)

Fig.3-12 200 150 5.3

mm 2

610Hz 1 720Hz 2

Fig.3-13 (3-14), (3-16)

t =0.22mm t

=1.44mm t =0.12mm

Fig.3-14

20Hz 20kHz tan

Abaqus Abaqus Maxwell

*VISCOELASTIC

Fig.3-15

(3-17), (3-19)

46

Fig.3-12

Fig.3-13 (3-14)

(a) (b)

Fig.3-14

47

3.7

Maxwell

1920(3-1), (3-5)

1950 60

(3-21)

FEM 1980

FEM

Maxwell

-

Excel

110

Fig.3-15 FEM

(a) (b)

48

4.1

-

49

FEM

(4-1), (4-2)

(4-3) Yamaki (4-4) 1

2 2 1

Esslinger(4-5), (4-6)

(4-7)

50

4.2

Abaqus(4-8) ADINA ANSYS Marc FEM

FEM

Abaqus 4-1

4-2

4-1

4-2

* = /

1 ~ 10 %

4-1

Abaqus

dissipated energy fraction

2.E-4

dissipated energy fraction c

51

dissipated energy fraction 2.E-4

1/100 ~ 1/1,000

4.3 2 2 (4-9) Fig.4-1

2

4-3 1

2 Fig.4-1

4-4

4-3

4-4

= 1000 mm, = 100 mm

100 mm2

2.E5 MPa

1 N

Fig.4-1

52

Fig.4-2

Fig.4-2

Fig.4-3 a

Fig.4-3 b

Fig.4-2 b

Fig.4-3 b 200mm

Fig.4-4 Abaqus/Standard

HHT Newmark- Fig.4-4 a

100 ~ 300 mm

p

U2

U1

1 2x

yW W

HH

y

x

W

U1

p

U2

W

1 2

Fig.4-1 2

53

Abaqus/Standard HHT

Fig.4-4 b

1

0 0 Fig.4-4

a(4-10)

Fig.4-3 b Fig.4-4 b

4-1 4-2

Fig.4-2 2

(a (b

54

4.4

(b

-15

-10

-5

0

5

10

15

0 100 200 300

Load

pro

porti

onal

ity fa

ctor

1

Displacement U2 [mm]

Theory

Abaqus, Artificial damping

U2 [mm]

Abaqus

(a

Fig.4-3 2

-15

-10

-5

0

5

10

15

0 100 200 300

Load

pro

porti

onal

ity fa

ctor

a

Displacement U2 [mm]

Theory Abaqus, Implicit dynamic

U2 [mm]

Abaqus

(a (b

Fig.4-4 2

0.0E+00

5.0E+05

1.0E+06

1.5E+06

2.0E+06

0 100 200 300

Ener

gy [N

mm

]

Displacement U2 [mm]

Theory

Strain energy

External work

Kinematic energy

U2 [mm]

[Nm

m]

0.0E+00

5.0E+05

1.0E+06

1.5E+06

2.0E+06

0 100 200 300

Ener

gy [N

mm

]

Displacement U2 [mm]

Theory

Strain energy

External work

Artificial dampingenergy

U2 [mm]

[Nm

m]

55

4-5

4-5

4-5

4-5 10 60% (4-12)

2 4-5

(4-14)

(4-15)

Yamaki (4-4) 4-5 1

2

4-5

4-5

4-5

Yamaki

56

5.4 5.6

[MPa]

[mm]

[mm]

[mm]

Batdorf parameter

[mm]

[N]

[N]

[N]

[MPa]

[MPa]

[MPa]

Fig.4-5 Karman Tsien(4-12), (4-15)

=26

4-5

1

57

1

1

2

Yamaki (4-4)

Mylar DuPont PET Mylar

=5560 MPa =0.3

Batdorf parameter Z

4-6

Fig.4-6 a Z =500 =100mm =0.247mm =113.9mm

=0.606mm

FEM

Diamond buckling pattern

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 2 4 6 8 10 12 14 16 18 20

Axial Shortening /t

Axi

al S

tress

r/Et

n=26

n=20 n=15

n=13n=12

n=11n=10 r/t=1000

Fig. 4-5 Karman Tsien(4-12) , (4-15)

58

Fig.4-6 a =2 =10

=2 Two-tier diamond pattern

=2 (4-6)

Two-tier diamond pattern

Fig.4-6 b

Fig.4-6 a

=1

One-tier mode

Yamaki

Fig.4-6 b

1

900N 4-5

1290N 30% (4-3)

Yamaki 0.247mm 10%

(a (b

Fig. 4-6 Yamaki (4-4)

Axi

al L

oad

P[N

]

n=12

Asymmetric

1000

Axial Shortening [mm]

800

600

400

200

0 1.00.80.60.40.2

n=11 n=10n=9

Z=500

Symmetric

n=11n=10

n=9n=8 n=7

wrt. cross-section atmid-length of cylindrical shell.

59

1

=12

=11 2

2

=9

4.5 Yamaki FEM Abaqus 6.8 Yamaki

Fig.4-7 Abaqus

S4R

80 400

Fig.4-8 4-5

1.01 1.04 100

FEM

Koiter Circle (4-14), (4-16)

Hunt (4-17) 4-7

Yamaki (4-4) Esslinger (4-18)

Timoshenko (4-12)

Fig. 4-7 Yamaki

60

4-7

Fig.4-9 FEM

=18 FEM

4-7

FEM 1 Fig.4-8 Fig.4-9

=13 =0

4-8 (4-12) FEM =13 4-8

4-7 =0

4-8

FEM Fig.4-9

Fig. 4-9

02468

101214161820

0 2 4 6 8 10 12 14Number of axial half-waves m

Num

ber o

f circ

umfe

rent

ial

full-

wav

es n

Hunt et al.Abaqus

1st Mode(m=13, n=0)

77th Mode(m=4, n=17) 63rd Mode

(m=10, n=15)

Fig. 4-8

61

4.6 Esslinger Fig.4-10 Esslinger (4-5), (4-6) (4-2)

Abaqus S4R

0.3( ) (4-2), (4-7) Yamaki

Mylar =5400 MPa

100mm 330mm 0.254mm

1 msec

A 0.33msec 1

B

0.83msec C 1.3msec

=18 (4-12)

D 2.8msec

E 24msec =9

=2 "two-tier

diamond pattern"

1

(4-19)

Esslinger 5200

(4-12) Esslinger

0.039mm/sec (4-6)

Yamaki(4-4)

Singer(4-6)

Mylar

62

Fig.4-10 C (1.3msec)

18

800Hz

msec

Fujii (4-13)

FEM

Fig.4-10

63

4.7 (4-20)

Mylar

Mylar

2%

100°C

Fig.4-11 (4-11) DMA

tan TA Instruments RSA

30°C 200°C

2°C/min 3.16, 10, 31.6,

100 rad/sec

Fig.4-11 70°C

- WLF WLF

Mylar

3

4-9

Maxwell

Maxwell 4-10

64

4-10

4-10 Fig.4-11

4-11 4-12

Fig.4-11(4-11)

4-11

4-12

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

0 50 100 150 200

tan

[-]

E',E

'' [P

a]

[deg.C]

E'E''tan

6070

80E'

Fig.4-11 Mylar

65

Fig.4-11

60°C 70°C = 80°C 3

Fig.4-12 a Fig.4-12 c

4-10

4-9 -

4-9

Fig.4-12

a Fig.4-12 c 300sec

1sec 300sec

3

Fig.4-13 80mm

100mm 0.30mm

5mm 300sec

3

Fig.4-14

60°C

Yamaki (4-4) 1

2 =8 =6

66

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1E-01 1E+02 1E+05 1E+08 1E+11

Rel

axat

ion

Mod

ulus

[Pa]

a

Time [sec]

T = 60 deg.C

[sec]

[Pa]

(a 60 °C;

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1E-09 1E-06 1E-03 1E+00 1E+03

Rel

axat

ion

Mod

ulus

[Pa]

a

Time [sec]

T = 80 deg.C

[sec]

[Pa]

(c 80 °C;

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1E-05 1E-02 1E+01 1E+04 1E+07

Rel

axat

ion

Mod

ulus

[Pa]

a

Time [sec]

T = 70 deg.C

[sec]

[Pa]

(b 70 °C;

Fig.4-12 Mylar Fig.4-13 Mylar

(a 60 °C;

(b 70 °C;

(c 80 °C;

67

70°C =8 Fig.4-12

b 2

2 Fig.4-13 b

80°C Fig.4-12(c

2

Fig.4-14

=8

Fig.4-12 3

0

10

20

30

40

50

0

100

200

300

400

500

0 1 2 3 4 5

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deg.

C )

[N]

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Exp. 80 deg.C FEM 80 deg.C

(a) 60 deg.C ( )

(b) 70 deg.C ( )

(c) 80 deg.C ( )

n = 8 n = 6n = 7

Fig.4-14 Mylar

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1sec

(4-2)

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1994

1981

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529

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71

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kg

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200

FW=5000 kg

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kg 3 Fig.5-6

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360

Table 5-1

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Temp.

[ ]

Young’s

Modulus

[kg/mm2]

Poisson’s

Ratio

[ ]

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Expansion

[ -1]

Yield

Stress

[kg/mm2]

Hardening

Slope

[kg/mm2]

20 19900 0.26 1.52E-5 24.5 300

360 17500 0.29 1.92E-5 15.5 300

510 16100 0.30 2.03E-5 14.3 300

5 1.59E-3 2.16E-8 3.04E-13

10 2.18E-3 4.08E-6 2.87E-10

CREEP LAW

78

5.6

(1)

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200

365

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6 kg/mm2

5000

79

kg 450

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(3)

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93

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Frank 1884 1966(6-84)

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101

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1950

1960

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4.

5.

103

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104

1 (1-1) S. P. Timoshenko, , , , , , 1977, p.1.

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(1) Takaya Kobayashi and Motoharu Tateishi, Hot Clamp Design for LMFBR Piping Systems,

Journal of Pressure Vessel Technology, ASME, Vol.115, 1993, pp.47-52. 1 6

(2) Takaya Kobayashi, Yasuko Mihara and Fumio Fujii, Path-tracing Analysis for

Post-buckling Process of Elastic Cylindrical Shells under Axial Compression, Thin-Walled Structures, Vol.61, 2012, pp. 180 187. 5

(3)

A2( ), Vol.70, No.2 ( Vol.17), 2014, pp. I_419-I_428.

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(3) : PBT

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2013, pp. 1791-1806

(1) 1999 Poster Award The Polymer Processing Society

Kenichi Funaki Chisato Nonomura (Toyobo), Takaya Kobayashi Yoichi Watanabe

(Mechanical Design & Analysis Corporation), Sigeo Mita and Kuniaki Shoji (Tokyo

University of Marine Science and Technology), Development of New Material Protective Device against Ship Collisions The 15th annual meeting of the Polymer Processing

Society, 's Hertogenbosch, The Netherlands, 1999.

(2) 2002

115

Mate2002 2002

(3) 2003

Mate2003 2003

(4) 2005 Co-Authoring the Outstanding Technical Paper from the Computer Technology

Technical Committee ASME

Takaya Kobayashi and Tomotaka Ogasawara Post-Buckling Analyses of Elastic

Circular Cylindrical Shells Under Axial Compression ASME 2005 Pressure Vessels and

Piping Conference Denver, Colorado, USA 2005.

(5) 2011 Best Conference Paper, ICTWS

Takaya Kobayashi, Yasuko Mihara and Fumio Fujii, Path-Tracing Analysis for Postbuckling Process of Elastic Cylindrical Shells under Axial Compression

International Conference on Thin-Walled Structures - ICTWS2011, pp.945-952, 2011,

Timisoara, Romania.

(6) 2015

(7) 2015

20

(1) Takaya Kobayashi, Masami Sato and Yasuko Mihara, Application of Thermo-Viscoelastic

Laminated Plate Theory to Predict Warpage of Printed Circuit Boards, Viscoelasticity -

From Theory to Biological Applications, ISBN: 978-953-51-0841-2, InTech, 2012.

116

CAE 2001

2008

10

2013

117