Mekanika Struktur Komposit 06. Teori Lamina Dwi Hartini, S.T., M.T.
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Mekanika Struktur Komposit06. Teori Lamina
Dwi Hartini, S.T., M.T.
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.
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
Or:
12
2
1
22
22
12
2
1
00
011
011
G
EE
EE
Stiffness Matrices for Isotropic Materials
Where:
12
EG
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
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
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
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
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
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
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
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
DISPLACEMENT CHARACTERISTICS
Isotropic Orthotropic Off-axis Lamina
(Anisotropic)
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
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
Pengaruh sudut orientasi serat terhadap
kekuatan bahan komposit.
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