Introduction to Continuum Mechanics 3 Episode 8 pps
Introduction to Continuum Mechanics 3 Episode 8 pps
... respect
to
Si
and 52
planes
automatically ensures
the
symmetry
with
respect
to the
53
plane.
(c)
All
planes
that
are
perpendicular
to the
3
plane have their
normals
parallel
to ... — 0 is
automatically
satisfied
together with
On the
other
hand, since
Q&
= 1, we
have
This requirement leads
to
That
is,
Similarly,
the
equation
Ci 233
=
0
leads...
Introduction to Continuum Mechanics 3 Episode 1 ppsx
... (2A1.2)
3
etc.
x
Contents
6.17 Dissipation Functions
for
Newtonian Fluids
38 3
6. 18 Energy Equation
for a
Newtonian Fluid
38 4
6.19 Vorticity Vector
38 7
6.20 Irrotational Flow
39 0
6.21
... Block
32 5
5 .37 Bending
of a
Incompressible Rectangular Bar.
32 7
5 . 38 Torsion
and
Tension
of an
Incompressible Solid
Cylinder
33 1
Problems
33 5
Chapter
6
Newtonian...
Introduction to Continuum Mechanics 3 Episode 3 ppsx
... Eq.
(2C4 .3) , with
the
vector
a
equal
to
the
unit
base
vector
e
r
gives
To
evaluate
the
first
term
on the
right-hand side,
we
note that
so
that according
to Eq.
(2D3. 18) ,
with
... lines
of
every particle
in a
continuum
can be
described
by a
vector equation
of the
Fig.
3. 1
form
where
x =
x^i
+*2
e
2
+JC
3
e
3
*
s
tne
position vector
at
ti...
Introduction to Continuum Mechanics 3 Episode 2 doc
... Q 23
TII
T^
2
7 *33
^ 13
0 23
033
T
31
T
32
T
33
031 032 033
or
PartB
Symmetric
and
Antisymmetric
Tensors
35
This
is the
transformation
law for the
components
of a
vector. Thus,
fy ... Eq.
(2B 13. 1a)
reads
Tn
T'n
T^\
\Q
n
Q
2l
0
31
1
|"r
n
T
n
T
13
\
\Q
n
Q
n
Qi3\
<
2B 13
-
lb
)
T
2l
T
22
T
23
~
Ql2
Qn
032
T
21
T
22...
Introduction to Continuum Mechanics 3 Episode 4 docx
... from
Eq.
(3. 23. 4),
we
have
That
is
That
is
similarly,
Kinematics
of a
Continuum
133
thus,
for
this material element
(d)
For
dX
=
dS^
and
dX
=
dS
2
e
2
Example
3. 23. 3
Show
that
... single-valued continuous solutions
#1, #2
an
^
U
3
°f
the
six
equation
Eq.
(3. 16.1)
to Eq.
(3. 16.6)
are
1 18
Kinematics
of a
Continuum
and
Thus,
the
equation
is
s...
Introduction to Continuum Mechanics 3 Episode 5 docx
... respect
to the
basis
at the
reference configuration
3. 73. From
Eqs. (3. 30.4a),
obtain Eqs. (3. 30.5).
3. 74.
Verify
Eq. (3. 30.8b)
and
(3. 30.8d).
3. 75.
Verify
Eq.( 3. 30.9b)
and
(3. 30.9d).
3. 76. ... (3. 30.9d).
3. 76. Derive
Eqs. (3. 30.10).
3. 77. Using
Eqs. (3. 30.10)
derive Eqs. (3. 30.12a)
and
(3. 30.12d).
3. 78.
Verify
Eqs.
(3. 30. 13
a) and
(3. 3...
Introduction to Continuum Mechanics 3 Episode 6 docx
... cylindrical
wall
is
subjected
to
a
uniform
pressure
p
0
.
4 38 .
Verify
that
Eq.
(4 .8. 2b)
and
(4 .8. 2c)
are
satisfied
by the
stress
field
given
in
Example 4.9.2.
439 .
In
Example 4.9.2,
... vector
on
the
left
end
face
x\
~
0.
4.12.
For any
stress state
T., we
define
the
deviatoric
stress
S to be
Stress
Power
2 03
where
Div
denotes
the
dive...
Introduction to Continuum Mechanics 3 Episode 7 potx
... we
have
a
unit normal vector
n
=
(l/a)(x2*2
+
X
3* $)-
Therefore,
the
surface traction
on the
lateral surface
Substituting
from
Eqs.
(5. 13. 3)
and
(5. 13. 5),
we
have
Thus,
in
... the
lateral
surface
vanishes.
The
unit vector
on the
plane
*3
= a is
63,
so
that
the
surface traction
for the
stress tensor
of Eq.
(5. 13. 1)
is
given
by
Similarly, there...
Introduction to Continuum Mechanics 3 Episode 9 pptx
... (5 .33 .9)
and
(5 .33 .11),
as
those
cor-
responding
to a
change
of
rectangular Cartesian basis, then
we
come
to the
conclusion that
the
constitutive
equation
given
by Eq.
(5 .33 .6)
... Eqs.
(5 . 38 . 18)
and
(5 . 38 .19),
we can
obtain
Equation
(5 . 38 .20)
is
known
as
"Rivlin's
Universal
relation".
This equation gives,
for
small
twistin...
Introduction to Continuum Mechanics 3 Episode 10 pptx
... 100,000.
Newtonian
Viscous
Fluid
38 3
6.17
Dissipation Functions
for
Newtonian Fluids
The
rate
of
work done
P by the
stress vectors
and the
body forces
on a
material particle
of
a
continuum
... Eq.
(6 .3. 5),
we
have
Newtonian
Viscous
Fluid
37 1
In
the
following
sections,
we
restrict ourselves
to the
study
of
laminar
flows
only.
It is
therefore
to b...
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