06 msk teori lamina dh
DESCRIPTION
Teori Lamina,,KompositTRANSCRIPT
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Mekanika Struktur Komposit06. Teori Lamina
Dwi Hartini, S.T., M.T.
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PENDAHULUAN
Lamina diartikan sebagai lapisan komposit tunggal yang hanya mempunyai satu arah serat.
Lamina merupakan elemen pembangun struktur komposit, karena itu pengetahuan mengenai sifat-sifat mekanika lamina ini sangat penting untuk mengetahui lebih lanjut mengenai struktur komposit.
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PLATE UNDER MULTI-AXIAL LOADINGS
1 1
1
2
0
.
12
112
11
E
E
(Isotropic)
11
2
2
12
12
12
2
1
12
2
1
100
01
01
G
EE
EE
Constitutive Equations for Isotropic
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Or:
12
2
1
22
22
12
2
1
00
011
011
G
EE
EE
Stiffness Matrices for Isotropic Materials
Where:
12
EG
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PLATE UNDER MULTI-AXIAL LOADINGS
1 1
1
2
0
.
12
1
1121122
1
11
E
E
(Orthotropic)
11
2
2
12
12
12
2
1
12
22
21
1
12
1
12
2
1
100
01
01
G
EE
EE
Constitutive Equations for Orthotropic
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Or:
12
2
1
12
2112
2
2112
212
2112
121
2112
1
12
2
1
00
0.1.1
0.1.
.1
G
EE
EE
Stiffness Matrices for Orthotropic Materials
Where:
121
221 .
E
E
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COMPLIANCE MATRIX FOR ORTHOTROPIC
12
2
1
66
2212
1211
12
2
1
00
0
0
S
SS
SS
Where:
1266
222
2
21
1
1212
111
1 ;
1
; 1
GS
ES
EES
ES
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STIFFNESS MATRIX FOR ORTHOTROPIC
12
2
1
66
2212
1211
12
2
1
00
0
0
Q
Where:
12662112
222
2112
121
2112
21212
2112
111
; 1
11 ;
1
GQE
Q
EEQ
EQ
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EXAMPLE
Carbon-epoxy T300/5208 has properties as follows: E1 = 19.2 Msi ; E2 = 1.56 Msi ; v12 = 0.24 ; G12 = 0.82 Msi
Therefore, the compliance coefficients are (in 1/Msi):
0
2195.11
641.01
0125.0 05208.01
2616
1266
222
1
1212
111
SS
GS
ES
ES
ES
And the stiffness coefficients are (in Msi)
0
820.0 567.1
376.0 29.19
2616
6622
1211
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TRANSFORMED STIFFNESS MATRICES
x
y
12
Transformation of stress and strains in arbitrary direction:
xy
y
x
xy
y
x
TT
2
12
2
1
1
12
2
1
and
sin cos ;
22
2
2
22
22
22
222
22
22
1
nm
nmmnmn
mnmn
mnnm
T
nmmnmn
mnmn
mnnm
T
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From the stiffness matrix equation:
11 Q
Therefore, we find:
xx TQT 21
1
or
xy
y
x
xy
y
x
T
Q
T
2
66
2212
12111
1
00
0
0
Now we define:
xx Q
21
1 TQTQ
and
or
xy
y
x
xy
y
x
QQQ
QQQ
QQQ
662616
262212
161211
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The individual ijQ terms are given below:
)()22(
)2()2(
)2()2(
)()4(
)2(2
)2(2
4466
226612221166
3662212
366121126
3662212
366121116
4412
2266221112
422
226612
41122
422
226612
41111
mnQnmQQQQQ
nmQQQmnQQQQ
mnQQQnmQQQQ
mnQnmQQQQ
mQnmQQnQQ
nQnmQQmQQ
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DISPLACEMENT CHARACTERISTICS
Isotropic Orthotropic Off-axis Lamina
(Anisotropic)
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EXAMPLE (2)
Carbon-epoxy T300/5208 has properties as follows: E1 = 19.2 Msi ; E2 = 1.56 Msi ; v12 = 0.24 ; G12 = 0.82 Msi and fiber angle 30o to the global axis
Therefore, the compliance coefficients are (in 1/Msi):
465.1 ;3636.0
8434.0 5878.0
1065.0 2933.0
2616
6622
1211
SS
SS
SS
And the stiffness coefficients are (in Msi)
017.2 658.5
975.3 843.2
531.3 75.11
2616
6622
1211
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OFF-AXIS ENGINEERING CONSTANTS
Xx
y1
2
X
44
12
22
121
12
21
4
2
22
1
12
12
4
1
22
1221
44
1
12
4
2
22
1
12
12
4
1
114222
1
12111
111
12111
nmG
nmGEEEG
mE
mnEG
nEE
nmGEE
mnE
E
nE
mnEG
mEE
xy
y
xxy
x
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Pengaruh sudut orientasi serat terhadap
kekuatan bahan komposit.