7/8/2012 Thermal Stresses 1
Thermal Stresses
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Thermal Stresses-Advanced Physics-Presentation, Slides of Physics
This presentation is for Physics subject project. It was task assigned by Prof. Adishree Yajnadhar at Central University of Kerala. It includes: Thermal, Stresses, Linear, Stress, Strain, Law, Thermal, Energy, Constant, Matrix
Typology: Slides
2011/2012
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7/8/2012 Thermal Stresses 1
Thermal Stresses
7/8/2012 Thermal Stresses 2
1
E
E T
0 T
Linear stress/strain law with initial thermal strain.
7/8/2012 Thermal Stresses 4
V
0
T
T 0 T
T
T 0
U u dV
D 2
1 u
2
1 u
Strain Energy
7/8/2012 Thermal Stresses 5
^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^
V
T
T T
T T
V
T
T T
V
T
T T
d B D B d dV 2
1 U
B d D B d dV 2
1 U
B d
D dV 2
1 U
Strain Energy
7/8/2012 Thermal Stresses 7
^ ^ ^ ^ ^
V
T
T T
V
T
T T T
V
T T L
D dV
U d B D dV
U d B D B d dV
Constant
Strain Energy
7/8/2012 Thermal Stresses 8
(^) T V
T
T T
V
L T
L T
B D dV f
d
U
B D B d dV
d
U
d
U
U U U
7/8/2012 Thermal Stresses 10
Thermal Strain Matrix
(one-dimensional bar):
T
E TA
E TA
f
f f
L
1
L
1 B
D E
T x T
T 2
T 1 T
7/8/2012 Thermal Stresses 11
Thermal Strain Matrix
(two-dimensional element):
0
T
T 1
PlaneS train
0
T
T
PlaneS tress
T
T
T
T
T
T
xy
y
x T
xy
y
x T
7/8/2012 Thermal Stresses 13
m
m
j
j
i
i
T
T
T
T
Et T
f
f
f
f
my
iy
ix
^21
Plane Stress :
7/8/2012 Thermal Stresses 14
Procedure
- Evaluate thermal force matrix and treat this as an equivalent nodal force matrix.
- Apply: {F}=[K]{d}-{F 0 }.
- If only thermal loads are present, then {F 0 }=[K]{d}.
- Back-substitute known {d} to obtain element nodal forces, stresses, and strains.
7/8/2012 Thermal Stresses 16
E TA
E TA f
1 1
1 1
L 2
AE k
T
For each element:
7/8/2012 Thermal Stresses 17
0 1 1
1 2 1
1 1 0
L 2
AE K
E TA
0
E TA
E TA
E TA E TA
E TA
fT
Assembling Global Matrices:
7/8/2012 Thermal Stresses 19
lb
42000
F
F
F
E TA
E TA
E TA
E TA
F
F
F
3 x
2 x
1 x
3 x
2 x
1 x
Reaction Forces:
7/8/2012 Thermal Stresses 20
10500 psi 4 in
42000 lb
2
Axial Stress: