david roylance mechanics of materials Part 2 pdf
david roylance mechanics of materials Part 2 pdf
... 1.8 22 –33
aramid 124 3.6 2. 3 1.45 86 2. 5 22 –33
boron 400 3.5 1.0 2. 45 163 1.43 330–440
HS graphite 25 3 4.5 1.1 1.80 140 2. 5 66–110
HM graphite 520 2. 4 0.6 1.85 28 1 1.3 22 0–660
Of course, these materials ... neck.
5
INTRODUCTION TO COMPOSITE MATERIALS
David Roylance
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambrid...
david roylance mechanics of materials Part 1 docx
... written
7
ATOMISTIC BASIS OF ELASTICITY
David Roylance
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 021 39
January 27 , 20 00
Introduction
The ... ELASTICITY
David Roylance
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 021 39
January 21 , 20 00
Introduction
Th...
david roylance mechanics of materials Part 4 pot
... Strength of Materials, McGraw-Hill, New York, 19 52
12
The Kinematic Equations
David Roylance
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 021 39
Septemb ... is:
U
∗
=
τdγ=
1
2
τγ =
τ
2
2G
=
1
2G
Tr
J
2
This is then integrated over the specimen volume to obtain the total energy:
U =
V
U
∗
dV =
L
A
1
2G
T...
david roylance mechanics of materials Part 5 ppt
... as
σ
x
σ
y
τ
x
y
=
c
2
s
2
2sc
s
2
c
2
−2sc
−sc sc c
2
− s
2
σ
x
σ
y
τ
xy
(4)
1
R.M. Jones, Mechanics of Composite Materials, McGraw-Hill, 1975.
2
I
3
=det|σ|=
1
3
σ
ij
σ
jk
σ
ki
(21 )
These ... σ
x
sin
2
θ + σ
y
cos
2
θ − 2
xy
sin θ cos θ
τ
x
y
=(σ
y
−σ
x
)sinθ cos θ + τ
xy
(cos
2
θ − sin
2
θ)
Or
...
david roylance mechanics of materials Part 6 ppt
... sequence of nine equations, since each
component of
ij
is a linear combination of all the components of σ
ij
. For instance:
23
= S
23 11
σ
11
+ S
23 12
σ
12
+ ···+S
23 33
33
Based on each of the ... E
2
=4,G
12
=2. 8(allGPa)and
ν
12
=0 .25 . The compliance matrix S in the 1 -2 (material) direction is:
S =
1/E
1
−ν
21
/E
2
0
−ν
12
/E
1
1/E
2
0
001/G...
david roylance mechanics of materials Part 7 ppsx
... diff(U,F);
The result of these manipulations yields
δ
F
=
LF
12 L
2
G − 12GL
2
cos
2
θ +9Gr
2
2
cos
2
θ +10r
2
2
E−10 r
2
2
E cos
2
θ
9 r
1
r
3
2
Eπ G
This displacement is in the direction of the applied ... σ
2
/2E over the specimen
volume:
U
b
=
V
U
∗
dV =
L
A
σ
2
x
2E
dA dL
=
L
A
1
2E
−My
I
2
dA dL =
L
M
2
2EI
2
A
y
2
dA dL
Since
...
david roylance mechanics of materials Part 8 doc
... -0. 122 8D-15
-0.1639E-16 -0 .21 50E-15 0 .20 83E-09 -0.6 022 D-16 -0. 122 8D-15 0 .22 28D-19
0. 721 8E-10 0.1084E-18 -0.6 022 E-16 0.3058D-09 -0. 426 5D-11 -0.1967D-15
0. 621 4E -22 -0. 721 8E-10 -0. 122 8E-15 -0. 426 5D-11 ... −
a
2
r
2
+
σ
2
1+
3a
4
r
4
−
4a
2
r
2
cos 2
σ
θ
=
σ
2
1+
a
2
r
2
−
σ
2
1+
3a
4
r
4
cos 2 (19)
τ
rθ
= −
σ
2
1 −
3a
4
r
4
+
2a...
david roylance mechanics of materials Part 9 pot
... DOF 1 DOF 2 DOF 3 DOF 4 DOF 5 DOF 6
1 000000
2 0.013333 -0.0 321 9 0000
3 0. 02 -0.084379 0000
4 000000
5 -0.0066667 -0.038856 0000
Element Stresses
1: 4000
2: 20 00
3: -28 28.4
4: 20 00
5: -28 28.4
6: ... k
(2)
21
k
(1)
44
+ k
(2)
22
k
(2)
23
k
(2)
24
00 k
(2)
31
k
(2)
32
k
(2)
33
k
(2)
34
00 k
(2)
41
k
(2)
42
k
(2)
43
k
(2)
44
...
david roylance mechanics of materials Part 10 ppt
... and divide by the complex conjugate of the
denominator) to yield:
E
∗
=
kω
2
τ
2
1+ω
2
τ
2
+ i
kωτ
1+ω
2
τ
2
(25 )
In Eq. 25 , the real and imaginary components of the complex modulus are given explicitly; ... (3,1)
13
ENGINEERING VISCOELASTICITY
David Roylance
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 021 39...
david roylance mechanics of materials Part 11 ppsx
... differential equation
a
2
¨σ + a
1
˙σ + a
0
σ = b
2
¨ + b
1
˙ + b
0
where
a
2
= τ
1
τ
2
,a
1
= τ
1
+ τ
2
,a
0
=1
b
2
= τ
1
τ
2
(k
e
+ k
1
+ k
2
) ,b
1
= k
e
(τ
1
+ τ
2
)+k
1
τ
1
+ k
2
τ
2
,b
0
= k
e
14. ... of
C(t)atthattime.
26
Using the given shift factor, we can adjust the time of the second temperature at 50
◦
Ctoanequivalent
time t
2
at 20
◦
C as foll...
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