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

QQ

QQ

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

QQ

QQ

QQ

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

QQ

QQ

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

QQ

QQ

QQ

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.