Introduction to Continuum Mechanics 3 Episode 6 docx
Introduction to Continuum Mechanics 3 Episode 6 docx
... 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
divergence with respect
to ... normal stress acting.
4 .6.
For the
following state
of
stress
findTn'
and
T
1
^'
where
e
x
'
is
in
the
direction
of
ej
+
2e
2
+
3e
3
and
63 & apos;is
in...
Introduction to Continuum Mechanics 3 Episode 4 docx
... single-valued continuous solutions
#1, #2
an
^
U
3
°f
the
six
equation
Eq.
(3. 16. 1)
to Eq.
(3. 16. 6)
are
118
Kinematics
of a
Continuum
and
Thus,
the
equation
is
satisfied,
and ... 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...
Introduction to Continuum Mechanics 3 Episode 5 docx
... 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. 30.13d).
Ki...
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
... 2B3.1
Given that
a
tensor
T
which
transforms
the
base vectors
as
follows:
Tej
=
2e
1
-6e
2
+4e
3
T02
=
3ej+ 462 - 63
Te
3
=
-26J +62 +2 63
How
does this te...
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 ...
j2
11
=cos(e
1
,ei)=cos30°=—,
(2i2
=cos
(
e
i»
e
2)
=cosl2
0
0
= ,
(2i3
=
cos(e
1
,e
3
)=cos90
0
=G
^2i=cos(e2,ei)=cos60
0
=-,j322
==
cos(e
2
,ei)=cos30
0
=—,j2 23
==c
os(...
Introduction to Continuum Mechanics 3 Episode 3 ppsx
... of Eq.
(3. 6 .3) ,
we
obtain
Now,
from
Eq.
(3. 6 .3) ,
we
have
Thus
Since
RR
= I, RR
+RR
= 0, so
that
RR is
antisymmetric
which
is
equivalent
to a
dual
(or
axial) vector
<o
... 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...
Introduction to Continuum Mechanics 3 Episode 7 potx
... 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
will
... 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...
Introduction to Continuum Mechanics 3 Episode 8 pps
... Elastic
Solid
279
From
the
compatibility equations, Eqs. (3. 16. 8), (3. 16. 9)
and
(3. 16. 7),
we
have
Thus,
G(XI
£1)
= a
K\
+
J3x2
+
y.
In the
absence
of
body
forces,
the
equations
... 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...
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)
... 7\i>0.
5 .65 .
Verify
that
if
<p
(x\,
X2)
satisfy
Eq.
(5. 16. 7),
than
it
does correspond
to a
compatible
strain
field.
5 .66 . Show that
if the
bending moment...
Introduction to Continuum Mechanics 3 Episode 10 pptx
... have
Thus,
i.e.,
36 0
Navier-Stokes
Equation
For
Incompressible
Fluids
6. 7
Navier-Stokes Equation
For
Incompressible Fluids
Substituting
the
constitutive equation [Eq.
(6. 6.4)]
into
the
... given
by Eq.
(6. 13. 3),
however,
the
driving force
now is
Newtonian
Viscous
Fluid
36 1
These
are
known
as the
Navier-Stokcs
Equations
of
motion
for
incompressible
Ne...
Từ khóa:
- j n reddy introduction to continuum mechanics
- introduction to fluid mechanics
- an introduction to the mechanics of tensegrity structures
- introduction to biofluid mechanics
- introduction to dislocation mechanics
- 6 00x introduction to computer science and programming mit
- an introduction to computer science using python 3 download
- introduction to computer science using python 3
- mit 6 00 introduction to computer science and programming download