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A
Presentation on
Computer Aided Engineering (302050)
Department of Mechanical Engineering
Pimpri Chinchwad Education Trust’s
Pimpri Chinchwad College of Engineering & Research
Ravet
Presented by:
Prof. Pradeep Gaikwad
Academic Year 2022-23
SEM - II
Pre-requisites
05/17/2023 ©PCCOE&R, Ravet, Pune 2
FE SE TE BE
Subject
Name
Basic Physics /
Engineering
mechanics
Basic
Mechanical
Engineering
FPL
Mathematics
Thermo
Fluid
Mechanics
Power Plant
Engineering
Finite
Elements
Analysis
CAD CAM
Automation
Heat Transfer
Design of
Machine
Elements
Numerical
Methods
CAE
Solid
Mechanics
Teaching and Examination Scheme
B. E. Mechanical Engineering
Teaching Faculties (2021-22):
• Prof. Pradeep Gaikwad (8hr Th + 12hr Pr)
• Mrs. Bhagyashree Bhosale (Lab Assistant )
Examination Scheme:
• Theory Paper(IN-SEM) : 30 Marks
• Theory Paper(END-SEM) : 70 Marks
• Practical: 50 Marks
5/17/2023 ©PCCOE&R, Ravet, Pune 3
Syllabus
5/17/2023 ©PCCOE&R, Ravet, Pune 4
Sr.No Contents
01
Elemental Properties
C302050.1- DEFINE the use of CAE tools and DESCRIBE the
significance of shape functions in finite element formulations.
(BT-1,2)
02 Meshing Techniques
03 1D Finite Element Analysis
04 2D Finite Element Analysis
05 Non-Linear and Dynamic Analysis
06 Applications of Computer Aided Engineering
Linear, Non-linear Analysis
5/17/2023 ©PCCOE&R, Ravet, Pune 5
Linear, Non-linear Analysis
5/17/2023 ©PCCOE&R, Ravet, Pune 6
Newton Raphson Method
5/17/2023 ©PCCOE&R, Ravet, Pune 7
Newton Raphson Method
5/17/2023 ©PCCOE&R, Ravet, Pune 8
Newton Raphson Method
5/17/2023 ©PCCOE&R, Ravet, Pune 9
Newton Raphson Method
5/17/2023 ©PCCOE&R, Ravet, Pune 10
Newton Raphson Method
5/17/2023 ©PCCOE&R, Ravet, Pune 11
Newton Raphson Method
5/17/2023 ©PCCOE&R, Ravet, Pune 12
Dynamic Analysis Process
5/17/2023 ©PCCOE&R, Ravet, Pune 13
Static and Dynamic Analysis
5/17/2023 ©PCCOE&R, Ravet, Pune 14
Static and Dynamic Analysis
5/17/2023 ©PCCOE&R, Ravet, Pune 15
Time Domain and Frequency Domain
5/17/2023 ©PCCOE&R, Ravet, Pune 16
Types of Loading
5/17/2023 ©PCCOE&R, Ravet, Pune 17
Types of Loading
5/17/2023 ©PCCOE&R, Ravet, Pune 18
Numerical Methods
5/17/2023 ©PCCOE&R, Ravet, Pune 19
Finite Elements Method:
 Finite
 Elements
 Methods
Difference between Continuum Method
and FEM
5/17/2023 ©PCCOE&R, Ravet, Pune 20
No Continuum Method FEM
01 Analytical Method Numerical Method
02 Simple Problems Complex Problems
03 Linear Problems Non-linear Problems
04 Solution for entire body Solution for each node and element
05
Anisotropy and non-
homogeneity can not be handled
Anisotropy and non-homogeneity can
be handled
06 Method is complex Simple as software package is used
Difference between FDM and FEM
5/17/2023 ©PCCOE&R, Ravet, Pune 21
No FDM FEM
01
Point wise approximation.
Ensures continuity at only nodes
Piece wise approximation. Ensures
continuity at nodes elements
02
Solution can be obtained only at
the nodes
Solution can be obtained at the nodes
as well as at any point within the field
using shape function
03
Need more number of nodes to
get good results
Need lesser number of nodes to get
good results
04 Simple Problems Complex Problems
05
Stair case approximation for
boundary slopes
Considers boundary as it is
Finite Element Terminology
5/17/2023 ©PCCOE&R, Ravet, Pune 22
Terminolgy:
 Continuum or Domain
 Nodes
 Element
 Degree of Freedom
 Load or Forces
Point Load
Body Force
Surface / traction Force
 Constraints
Finite Element Terminology
5/17/2023 ©PCCOE&R, Ravet, Pune 23
Terminolgy:
 Constraints
(1) Homogeneous Boundary Conditions:
Finite Element Terminology
5/17/2023 ©PCCOE&R, Ravet, Pune 24
(2) Non-homogeneous Boundary Conditions:
General FEM Procedure
5/17/2023 ©PCCOE&R, Ravet, Pune 25
Step I : Discretization of the given continuum
General FEM Procedure
5/17/2023 ©PCCOE&R, Ravet, Pune 26
Step II : Selection of Displacement model
Polynomial Displacement Function
Trigonometric Displacement Function
Governing Conditions of Displacement Model
(1) Type and order of function
(2) Specific magnitude of displacement at nodes
(3) Convergence
General FEM Procedure
5/17/2023 ©PCCOE&R, Ravet, Pune 27
Step III : Derivation of Elemental Stiffness matrices and
load Vectors
[Ke] {qe} = {fe}
Where, [Ke] = Elemental Stiffness Matrix,
{qe} = Elemental Displacement Vector,
{fe} = Elemental Force or Load Vector
General FEM Procedure
5/17/2023 ©PCCOE&R, Ravet, Pune 28
Step IV : Assemblage of Elemental Equations to Obtain
Global Equilibrium Equations
[K] {Q} = {F}
Where, [K] = Global Stiffness Matrix,
{Q} = Global Displacement Vector,
{F} = Global Force or Load Vector
General FEM Procedure
5/17/2023 ©PCCOE&R, Ravet, Pune 29
Step V : Application of Boundary Conditions
Elimination Method
Penalty Method
Multipoint Constraint Method
General FEM Procedure
5/17/2023 ©PCCOE&R, Ravet, Pune 30
Step VI : To Determine the Unknown Parameters
Nodal Displacement
Elemental Strains
Elemental Stresses
Temperature
Preprocessor, Processor & Postprocessor
5/17/2023 ©PCCOE&R, Ravet, Pune 31
Preprocessor involves following Steps :
Choose discipline
eg. Structural, Thermal, Fluid, Electromagnetics etc.
Choose suitable element from library (NAFEMS)
Assign material & geometric properties
Construction of geometric model and importing
Discretization or meshing and mesh refinement
Application of boundary condition and loading
Preprocessor, Processor & Postprocessor
5/17/2023 ©PCCOE&R, Ravet, Pune 32
Processor solver involves following Steps :
Program calls governing equations from model and solves for
primary quantities.
Governing equations are assembled into matrix form and
solved numerically.
Type of process depends upon type of analysis eg. Static or
dynamic, element type, material properties and boundary
conditions.
Preprocessor, Processor & Postprocessor
5/17/2023 ©PCCOE&R, Ravet, Pune 33
Postprocessor involves following Steps :
Reading results in tabular or graphical form.
Judge whether FEM result makes any sense of physical
meaning.
Comparison of results.
Error estimation and authenticity.
Applications
5/17/2023 ©PCCOE&R, Ravet, Pune 34
Equilibrium Problems and Propagation Problems
 Aerospace Engineering
 Automotive Engineering
 Biomedical Engineering
 Civil Engineering
 Electrical Engineering
 Hydraulic Engineering
 Mechanical Engineering
 Nuclear Engineering
Error Analysis
5/17/2023 ©PCCOE&R, Ravet, Pune 35
 Domain Approximation Error
 Quadrature and Finite Arithmetic Errors
 Solution Approximation Error
Types of Error Estimation
5/17/2023 ©PCCOE&R, Ravet, Pune 36
 A Priori Error Estimates
 A Posteriori Error Estimates
Meshing Techniques
5/17/2023 ©PCCOE&R, Ravet, Pune 37
 Structured Mesh
 Unstructured Mesh
Criteria for Good Meshing
5/17/2023 ©PCCOE&R, Ravet, Pune 38
 Shape of Element
 Number of Elements
 Topological Consistency
 Automatic and adaptable
Mesh Generation Methods
5/17/2023 ©PCCOE&R, Ravet, Pune 39
 Mapped Mesh Generation
 Free Mesh Generation
Mesh Refinement Methods
5/17/2023 ©PCCOE&R, Ravet, Pune 40
 h - Refinement
 P – Refinement
 hP – Refinement
 r - Refinement
Advantages of FEA
5/17/2023 ©PCCOE&R, Ravet, Pune 41
Can handle complex geometry and contours.
Can handle complex analysis type. eg. Vibration, non-linear,
transient etc.
Can handle complex loading conditions. eg. Nodal based,
element based, volume based, time and frequency based etc.
Can handle complex constraints eg. Fixed, simply supported, roller
supported, symmetric and unsymmetrical boundary conditions.
Can handle bodies of homogenous and non-homogenous materials.
Can handle special material effects such as temperature, moisture,
electricity etc.
Disadvantages of FEA
5/17/2023 ©PCCOE&R, Ravet, Pune 42
Specific numerical solution is required for specific problem.
Obtained solution is approximate for higher order problem.
Experience and judgment is required to construct good FEA model.
Powerful and reliable FEA software is essential.
A digital computer with large memory is required to store the data.
Force Distribution
5/17/2023 ©PCCOE&R, Ravet, Pune 43
Internal Forces
External Forces
Point Load
Body Force
Surface Forces
Sectioned Axially Loaded Beam
Surface Forces: T(x)
S
Cantilever Beam Under Self-Weight Loading
Body Forces: F(x)
Force Distribution
5/17/2023 ©PCCOE&R, Ravet, Pune 44
Internal Forces
External Forces
Force Distribution
5/17/2023 ©PCCOE&R, Ravet, Pune 45
Different forces having components along x, y and z
direction are shown below:
T =
Tx
Ty
Tz
= [Tx Ty Tz]T
P =
Px
Py
Pz
= [Px Py Pz]T
U =
u
v
w
= [u v w]T
Force Distribution
5/17/2023 ©PCCOE&R, Ravet, Pune 46
x
z
y
y
x
yx
z
xy
xz
zy
yz
zx





















z
zy
zx
yz
y
yx
xz
xy
x
]
[

2D Stress Equilibrium Equations
5/17/2023 ©PCCOE&R, Ravet, Pune 47
x

y

dx
x
x
x





xy

yx

dy
y
y
y





dx
x
xy
xy





dy
y
yx
yx





x
F
y
F
Body Forces
Equilibrium Equation Example
5/17/2023 ©PCCOE&R, Ravet, Pune 48
0
0
0
0
0
2
3
2
3
0
_________
__________
__________
__________
)
1
(
4
3
,
0
,
2
2
3
equations
m
equilibriu
e
satisfy th
stresses
following
that the
show
forces,
body
no
Assuming
3
3
2
2
3

































y
x
c
Py
c
Py
y
x
c
y
c
P
c
N
c
Pxy
y
xy
yx
x
xy
y
x
a
a
3D Stress Equilibrium Equations
5/17/2023 ©PCCOE&R, Ravet, Pune 49
3D Stress Equilibrium Equations
5/17/2023 ©PCCOE&R, Ravet, Pune 50
0





































dxdydz
F
dxdy
dz
z
dxdy
dxdz
dy
y
dxdz
dydz
dx
x
dydz
x
xz
xz
xz
xy
xy
xy
x
x
x











 

 0
;
0
;
0 Fz
F
F y
x
0










 x
xz
xy
x
F
z
y
x



0
0
,




















z
z
yz
xz
y
yz
y
xy
F
z
y
x
F
z
y
x
Similarly






Stress Equilibrium Equations
5/17/2023 ©PCCOE&R, Ravet, Pune 51
Stain Displacement Relations
5/17/2023 ©PCCOE&R, Ravet, Pune 52
u(x,y)
u(x+dx,y)
v(x,y)
v(x,y+dy)
dx
dy
A B
C D
A'
B'
C'
D'
dy
y
u


dx
x
v




x
y












z
zy
zx
yz
y
yx
xz
xy
x










 ]
[
Three-Dimensional Theory
z
u
x
w
y
w
z
v
x
v
y
u
z
w
y
v
x
u
xz
yz
xy
z
y
x
































 ;
;
Deformation and Strain Example
5/17/2023 ©PCCOE&R, Ravet, Pune 53
 
 
 
Ax
Cy
z
u
x
w
Cx
Cx
y
w
z
v
Bx
Bx
x
v
y
u
z
w
By
y
v
Az
x
u
C
B
A
Cxy
w
y
x
B
v
Axz
u
zx
yz
xy
z
y
x
































































2
1
2
1
2
1
0
2
1
2
1
2
0
2
1
2
1
0
2
_
__________
__________
__________
__________
constants
are
,
,
where
,
,
)
(
,
field
nt
displaceme
following
for the
strain
of
components
the
Determine
2
2






Strain-Stress Relationships in 3D
5/17/2023 ©PCCOE&R, Ravet, Pune 54
 The stress transformations equations were derived solely from
equilibrium conditions and they are material independent.
 Here the material properties will be considered (strain) taking into
account the following:
(a)The material is uniform throughout the body (homogeneous)
(b)The material has the same properties in all directions (isotropic)
(c)The material follows Hooke’s law (linearly elastic material)
Hooke’s law: Linear relationship between stress and strain.
For uniaxial stress: (E = modulus of elasticity or Young’s modulus)
σ = Eε
For pure shear : (G = Shear modulus of elasticity) ; τ = Gγ
al
longitudin
transverse
Strain
Axial
Strain
lateral
Ratio
s
Poisson


 



:
'
Strain-Stress Relationships in 3D
5/17/2023 ©PCCOE&R, Ravet, Pune 55
From Generalized Hooke’s law
as
defined
is
G
Rigidity
of
Modulus
and
Ratio
s
Poisson
Modulus
s
Young
or
Elasticity
of
Modulus
E
where
E
E
E
E
E
E
E
E
E
y
x
z
z
z
x
y
y
z
y
x
x
)
(
'
'
,
























xy
xy
Srain
Shear
Stress
Shear
G




Strain-Stress Relationships in 3D
5/17/2023 ©PCCOE&R, Ravet, Pune 56
xy
xy
xy
xy
xy
xy
xy
E
e
i
E
E
becomes
G
Therefore
E
G
G
E












)
1
(
2
.
.
).
1
(
2
1
)
1
(
2
,
)
1
(
2
)
1
(
2
is
(G)
rigidity
of
modulus
and
(E)
elasticity
of
modulus
between
relation
the
that,
know
We












Strain-Stress Relationships in 3D
5/17/2023 ©PCCOE&R, Ravet, Pune 57
components
Stress
components
Strain
matrix
Dynamic
D
where
D
E
form
matrix
in
writing
E
E
Also
xz
yz
xy
z
y
x
xz
yz
xy
z
y
x
xz
xz
yz
yz













































































































,
;
)
1
(
2
0
0
0
0
0
0
)
1
(
2
0
0
0
0
0
0
)
1
(
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
,
)
1
(
2
;
)
1
(
2
,
Stress-Strain Relationships in 3D
5/17/2023 ©PCCOE&R, Ravet, Pune 58
)
2
1
)(
(
1
2
2
2
)
(
1
,
law
s
Hooke’
d
Generalize
From












































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equations
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E
E
Stress-Strain Relationships in 3D
5/17/2023 ©PCCOE&R, Ravet, Pune 59
)
(
)
1
(
equation,
previous
g
rearrangin
Now
system.
coordinate
the
changing
after
even
value
its
change
not
does
hich
quantity w
a
is
invarient
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invarient
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1st
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1st
,
)
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1
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)
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1
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1
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where
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I
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or
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Stress-Strain Relationships in 3D
5/17/2023 ©PCCOE&R, Ravet, Pune 60
)
1
)(
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x
Stress-Strain Relationships in 3D
5/17/2023 ©PCCOE&R, Ravet, Pune 61
xy
xy
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xy
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x
z
z
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z
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y
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Stress-Strain Relationships in 3D
5/17/2023 ©PCCOE&R, Ravet, Pune 62
components
Stress
components
Strain
matrix
Dynamic
D
where
D
E
form
matrix
in
writing
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E
Similarly
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xz
yz
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2
Plane Stress Problem
5/17/2023 ©PCCOE&R, Ravet, Pune 63
figure)
in
(Shown
shaft
a
on to
fitted
ring
A
:
Example
problem.
stress
plane
as
treated
is
direction
in this
applied
loading
and
ss)
or thickne
direction
-
(z
direction
normal
along
dimensions
has
body
a
If
equation
previous
from
Therefore
0
;
0
;
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:
case
Problem
Stress
Plane
For

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0
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1
Plane Strain Problem
5/17/2023 ©PCCOE&R, Ravet, Pune 64
pressure
fluid
internal
to
subjected
cylinder
A thick
:
Example
problem.
strain
plane
as
treated
is
problem
then
axis
al
longitudin
lar to
perpendicu
applied
is
loading
and
length)
(i.e.
long
very
is
direction
al
longitudin
along
dimension
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equation
previous
from
Therefore
0
;
0
;
0
:
case
Problem
Strain
Plane
For

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z 
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)
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)(
1
(
Stress-Strain Temperature Relations
5/17/2023 ©PCCOE&R, Ravet, Pune 65
have;
we
materials,
isotropic
and
elastic
For
deform.
to
free
is
body
when the
stresses
any
cause
not
does
strain
this
Also,
material.
the
of
expansion
linear
of
t
coefficien
on the
depends
which
strain,
uniform
a
in
results
z)
y,
T(x,
change
re
temperatu
the
materials,
isotropic
For
strain.
thermal
be
to
said
is
ture
in tempera
change
to
due
length
original
unit
per
length
in
change
The


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Initial
where
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or
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xy
y
x
xy
y
x
xy
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
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

Stress-Strain Temperature Relations
5/17/2023 ©PCCOE&R, Ravet, Pune 66
:
equation
above
the
solving
by
strains
of
in terms
stresses
express
also
can
We
Stress
Initial
E
where
E
or
E
xy
y
x
xy
y
x
xy
y
x

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0
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,
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)
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(
0
0
0
1
0
1
)
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
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










Stress-Strain Temperature Relations
5/17/2023 ©PCCOE&R, Ravet, Pune 67
:
by
strain
to
related
is
stress
the
example,
For
expansion
thermal
of
t
coefficien
,
;
0
:
by
given
is
loading)
(thermal
change
re
temperatu
to
due
strains
initial
case,
strain
plane
In the
2
)
2
1
(
0
0
0
)
1
(
0
)
1
(
)
2
1
)(
1
(
0
0
0
0
0
0

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
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

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
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
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

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





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






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
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
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
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
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
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




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












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
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
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





















where
T
T
E
xy
y
x
xy
y
x
xy
y
x
xy
y
x
Strain Energy
5/17/2023 ©PCCOE&R, Ravet, Pune 68
Total Potential Energy
5/17/2023 ©PCCOE&R, Ravet, Pune 69
Essential and Forced (Natural)
Boundary Condtions
5/17/2023 ©PCCOE&R, Ravet, Pune 70
Essential and Forced (Natural)
Boundary Condtions
5/17/2023 ©PCCOE&R, Ravet, Pune 71
Numericals
5/17/2023 ©PCCOE&R, Ravet, Pune 72
Numericals
5/17/2023 ©PCCOE&R, Ravet, Pune 73
Banded Skyline Solutions (Method of Minimizing
Bandwidth)
Symmetric Banded Matrix
5/17/2023 ©PCCOE&R, Ravet, Pune 74
Examples
5/17/2023 ©PCCOE&R, Ravet, Pune 75
Examples
5/17/2023 ©PCCOE&R, Ravet, Pune 76
Skyline Storage
5/17/2023 ©PCCOE&R, Ravet, Pune 77
Derivation of Stiffness Matrix of Bar
Element by Direct Approach
5/17/2023 ©PCCOE&R, Ravet, Pune 78
Derivation of Stiffness Matrix of Bar
Element by Direct Approach
5/17/2023 ©PCCOE&R, Ravet, Pune 79
Derivation of Stiffness Matrix of Bar
Element by Direct Approach
5/17/2023 ©PCCOE&R, Ravet, Pune 80
Derivation of Stiffness Matrix of Bar
Element by Direct Approach
5/17/2023 ©PCCOE&R, Ravet, Pune 81
Derivation of Stiffness Matrix of Bar
Element by Potential Energy Method
5/17/2023 ©PCCOE&R, Ravet, Pune 82
Derivation of Stiffness Matrix of Bar
Element by Potential Energy Method
5/17/2023 ©PCCOE&R, Ravet, Pune 83
Derivation of Stiffness Matrix of Bar
Element by Potential Energy Method
5/17/2023 ©PCCOE&R, Ravet, Pune 84
Derivation of Stiffness Matrix of Bar
Element by Potential Energy Method
5/17/2023 ©PCCOE&R, Ravet, Pune 85
Derivation of Stiffness Matrix of Bar
Element by Potential Energy Method
5/17/2023 ©PCCOE&R, Ravet, Pune 86
Derivation of Stiffness Matrix of Bar
Element by Potential Energy Method
5/17/2023 ©PCCOE&R, Ravet, Pune 87
Derivation of Stiffness Matrix of Bar
Element by Potential Energy Method
5/17/2023 ©PCCOE&R, Ravet, Pune 88
Pre-requisites
6/12/2019 ©PCCOE&R, Ravet, Pune 89
FE SE TE BE
Subject
Name
Basic Physics /
Engineering
mechanics
Basic
Mechanical
Engineering
FPL
Mathematics
Thermo
Fluid
Mechanics
Power Plant
Engineering
Finite
Elements
Analysis
CAD CAM
Automation
Heat Transfer
Design of
Machine
Elements
Numerical
Methods
Program Outcomes (POs)
5/17/2023 ©PCCOE&R, Ravet, Pune 90
No Program Outcomes No Program Outcomes
01 Engineering knowledge 07 Environment and sustainability
02 Problem analysis 08 Ethics
03
Design/development of
solutions
09 Individual and team work
04
Conduct investigations of
complex problems
10 Communication
05 Modern tool usage 11 Project management and finance
06 The engineer and society 12 Life-long learning
Engineering Graduates will be able to: (For Details see NBA Guideline manual)
Course Objectives
 To understand the philosophy and general procedure of Finite Element
Method as applied to solid mechanics and thermal analysis problems.
 To familiarize students with the displacement-based finite element
method for displacement and stress analysis and to introduce related
analytical and computer tools.
 It provides a bridge between hand calculations based on mechanics of
materials and machine design and numerical solutions for more complex
geometries and loading states.
 To study approximate nature of the finite element method and
convergence of results are examined.
 It provides some experience with a commercial FEM code and some
practical modeling exercises
5/17/2023 ©PCCOE&R, Ravet, Pune 91
Course Outcomes (COs)
 Recognize theoretical background of FEM, matrix algebra and solid mechanics
for simple structural elements
 Determine Stiffness matrix, Load vector, displacement matrix for 1D and 2D
elements under mechanical and thermal loading conditions
 Compute FE Discretisation with coordinate mapping and formulation of
element equations.
 Solve steady state heat conduction and convection problems
 Construct a model of bar, truss, beam, CST, axisymmetric triangular and
quadrilateral elements under dynamic considerations
 Understand basic steps of FEM as Pre processing, meshing and post processing
for 1D and 2D elements
5/17/2023 ©PCCOE&R, Ravet, Pune 92
CO-PO Mapping
5/17/2023 ©PCCOE&R, Ravet, Pune 93
Program Outcomes
(Course
Outcomes)
PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12
CO1 3 1 2
CO2 3 3 3 2 2
CO3 2 3 3 2 3 1 3
CO4 2 3 2 2 3 1 2
CO5 2 3 2 2 3 1 1 3
CO6 2 3 2 2 3 1 1 3
Target 2.33 2.66 2.4 2.00 3.00 1.00 1.00 2.5
CO Assessment Plan
5/17/2023 ©PCCOE&R, Ravet, Pune 94
Direct Method
Indirect Methods
(Course
Outcomes)
Internal Assessment External Assessment
CO1
 Assignment on
each unit
 Unit Tests
 Preliminary
Examination
 Mock oral
 In-semester
Examination
 End Semester
Examination
 Course End
Survey
CO2
CO3
CO4
CO5
CO6
Criterio <40% =40% ; <60% =60% ; <75% =75% ; <
Attainment
level
0 1 2 3
Gap Identified in Curriculum
5/17/2023 ©PCCOE&R, Ravet, Pune 95
PO PO Description Activity Planned
PO6 The Engineer and Society Industrial and Field Visits
PO7 Environment and sustainability
Industrial and Field Visits
PO8 Ethics Copyrights and Patents
PO9 Individual and team work Individual and Group Projects
PO10 Communication Presentation based on Project Work
PO11
Project management and
finance
Individual and Group Projects with
detailed report
Instructional Methods
5/17/2023 ©PCCOE&R, Ravet, Pune 96
Unit / Content Methods Practical / Hands-on
Unit I : Fundamental
Concepts of FEA
(6 Hours)
 Online Lectures
using Google Meet
 Video Lectures
 Power point
presentations
 Tests on each unit
 Quizzes on each
unit
 Animations &
Videos
 NPTEL notes
 Group Activities
 Classroom
teaching (After
Lockdown)
 Static stress concentration factor
calculation for a plate with center hole
subjected to axial loading in tension
 Modal analysis of any machine
component
 Stress and deflection analysis of any
machine component consisting of 3-D
elements
 Elasto-plastic stress analysis
 Coupled Thermal-Structural Analysis
using FEA software
 Computer program for stress analysis
of 1D bar
 Computer program for stress analysis
of 2-D truss
 Computer programs for (i) modal
analysis and, (ii) stress analysis for 1-D
beam
 Computer program for 1-D
temperature analysis
Unit II : 1D Elements
(6 Hours)
Unit III : 2D Elements
(6 Hours)
Unit IV : Isoparametric
Elements and Numerical
Integration
(6 Hours)
Unit V : 1D Steady State
Heat Transfer Problems
(6 Hrs)
Unit VI : Dynamic
Analysis (6 Hours)
Videos Lectures Prepared (Unit-I)
5/17/2023 ©PCCOE&R, Ravet, Pune 97
Sr.
No.
Title of Video Description Link
01
Unit I : Fundamental
Concepts of FEA
Solution methodologies
to solve engineering
problems
Teaching Plan - Theory
5/17/2023 ©PCCOE&R, Ravet, Pune 98
Teaching Plan – Theory (FEA)
Teaching Plan - Practical
5/17/2023 ©PCCOE&R, Ravet, Pune 99
Teaching Plan – Practical (FEA)
Slow and Advanced Learners
Procedure - Identifying Slow Learners and Fast Learners
 Updation of Mentor form carried out and based on the report of
individual mentors, Slow Learners and Fast Learners will be
identified.
 Slow learners and fast learners identify on the basis of previous
semester marks.
Supporting activities for Slow Learners
 To conduct extra classes.
 To assign the home work and ensure that it gets completed duly.
 Personal Counseling through fast learners.
5/17/2023 ©PCCOE&R, Ravet, Pune 100
Slow and Advanced Learners
Encouraging activities for Advanced learners
 To conduct extra tutorials, assignment and experts lectures.
 To give case study on real life problem of relevant subject to
enhance subject knowledge.
 To explore their potential through activities like BAJA, Go-Kart,
TIFAN, ROBOCON etc.
 Participating at national/International events like Paper
Presentation, Technical Competition etc.
5/17/2023 ©PCCOE&R, Ravet, Pune 101
Result Analysis
5/17/2023 ©PCCOE&R, Ravet, Pune 102
AY 2017-18 AY 2018-19 AY 2019-20
AY 2020-21
(Target)
Percentage 93.42 97.72 98.42 100
0
25
50
75
100
Result
(%)
Content Beyond Syllabus
 Assignment on Ansys Workbench
 Introduction to CFD and assignment on Ansys Fluent
 Assignment on Topology Optimization
 Guest lecture by Mr. K.K. Mate on ‘Recent Trends in
CAE’
5/17/2023 ©PCCOE&R, Ravet, Pune 103
Feedback
5/17/2023 ©PCCOE&R, Ravet, Pune 104
AY 2017-18 AY 2018-19 AY 2019-20
AY 2020-21
(Target)
Percentage 86.65 89.78 97.42 98
0
25
50
75
100
Feedback
(%)
Research & Innovations &
Co-curricular Activities
5/17/2023 ©PCCOE&R, Ravet, Pune 105
Sr.
No.
Description Total Remark
01
Coursera Certificate
courses
10
Completed with score
more than 90%
02
Faculty Development
Programs
05
Based on advanced
trends
03 Copyrights 02 Filed
04
Paper Publications /
Conferences
02 Accepted
05 Patent 01 Drafted
06 Industrial training 01 Sandvik Asia (I) Ltd.
Portfolios & Responsibilities
5/17/2023 ©PCCOE&R, Ravet, Pune 106
 Departmental Academic Coordinator
 NBA Criteria II coordinator
 Higher Studies Cell Member
 Lab Incharge (Turbomachines)
 Mentor
Plan for Current Semester
5/17/2023 ©PCCOE&R, Ravet, Pune 107
 Two NPLEL Courses
 Conduction of Two FDP & Two Guest Lectures
 Two Patents & Five Copyrights
 Ten Coursers Courses
 Preparation of Video Lectures for FEA & MSD
 Documentation of Critera II
 Group wise project for FEA Subject
Reference Books
 Daryl L, A First Course in the Finite Element Method,. Logan, 2007.
 G Lakshmi Narasaiah, Finite Element Analysis, B S Publications,
2008.
 Y.M.Desai, T.I.Eldho and A.H.Shah, Finite Element Method with
Applications in Engineering, Pearson Education, 2011
 Chandrupatla T. R. and Belegunda A. D., Introduction to Finite
Elements in Engineering, Prentice Hall India, 2002.
 P., Seshu, Text book of Finite Element Analysis, PHI Learning Private
Ltd. , New Delhi, 2010.
5/17/2023 ©PCCOE&R, Ravet, Pune 108
5/17/2023 ©PCCOE&R, Ravet, Pune 109

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CAE Session.pptx

  • 1. A Presentation on Computer Aided Engineering (302050) Department of Mechanical Engineering Pimpri Chinchwad Education Trust’s Pimpri Chinchwad College of Engineering & Research Ravet Presented by: Prof. Pradeep Gaikwad Academic Year 2022-23 SEM - II
  • 2. Pre-requisites 05/17/2023 ©PCCOE&R, Ravet, Pune 2 FE SE TE BE Subject Name Basic Physics / Engineering mechanics Basic Mechanical Engineering FPL Mathematics Thermo Fluid Mechanics Power Plant Engineering Finite Elements Analysis CAD CAM Automation Heat Transfer Design of Machine Elements Numerical Methods CAE Solid Mechanics
  • 3. Teaching and Examination Scheme B. E. Mechanical Engineering Teaching Faculties (2021-22): • Prof. Pradeep Gaikwad (8hr Th + 12hr Pr) • Mrs. Bhagyashree Bhosale (Lab Assistant ) Examination Scheme: • Theory Paper(IN-SEM) : 30 Marks • Theory Paper(END-SEM) : 70 Marks • Practical: 50 Marks 5/17/2023 ©PCCOE&R, Ravet, Pune 3
  • 4. Syllabus 5/17/2023 ©PCCOE&R, Ravet, Pune 4 Sr.No Contents 01 Elemental Properties C302050.1- DEFINE the use of CAE tools and DESCRIBE the significance of shape functions in finite element formulations. (BT-1,2) 02 Meshing Techniques 03 1D Finite Element Analysis 04 2D Finite Element Analysis 05 Non-Linear and Dynamic Analysis 06 Applications of Computer Aided Engineering
  • 5. Linear, Non-linear Analysis 5/17/2023 ©PCCOE&R, Ravet, Pune 5
  • 6. Linear, Non-linear Analysis 5/17/2023 ©PCCOE&R, Ravet, Pune 6
  • 7. Newton Raphson Method 5/17/2023 ©PCCOE&R, Ravet, Pune 7
  • 8. Newton Raphson Method 5/17/2023 ©PCCOE&R, Ravet, Pune 8
  • 9. Newton Raphson Method 5/17/2023 ©PCCOE&R, Ravet, Pune 9
  • 10. Newton Raphson Method 5/17/2023 ©PCCOE&R, Ravet, Pune 10
  • 11. Newton Raphson Method 5/17/2023 ©PCCOE&R, Ravet, Pune 11
  • 12. Newton Raphson Method 5/17/2023 ©PCCOE&R, Ravet, Pune 12
  • 13. Dynamic Analysis Process 5/17/2023 ©PCCOE&R, Ravet, Pune 13
  • 14. Static and Dynamic Analysis 5/17/2023 ©PCCOE&R, Ravet, Pune 14
  • 15. Static and Dynamic Analysis 5/17/2023 ©PCCOE&R, Ravet, Pune 15
  • 16. Time Domain and Frequency Domain 5/17/2023 ©PCCOE&R, Ravet, Pune 16
  • 17. Types of Loading 5/17/2023 ©PCCOE&R, Ravet, Pune 17
  • 18. Types of Loading 5/17/2023 ©PCCOE&R, Ravet, Pune 18
  • 19. Numerical Methods 5/17/2023 ©PCCOE&R, Ravet, Pune 19 Finite Elements Method:  Finite  Elements  Methods
  • 20. Difference between Continuum Method and FEM 5/17/2023 ©PCCOE&R, Ravet, Pune 20 No Continuum Method FEM 01 Analytical Method Numerical Method 02 Simple Problems Complex Problems 03 Linear Problems Non-linear Problems 04 Solution for entire body Solution for each node and element 05 Anisotropy and non- homogeneity can not be handled Anisotropy and non-homogeneity can be handled 06 Method is complex Simple as software package is used
  • 21. Difference between FDM and FEM 5/17/2023 ©PCCOE&R, Ravet, Pune 21 No FDM FEM 01 Point wise approximation. Ensures continuity at only nodes Piece wise approximation. Ensures continuity at nodes elements 02 Solution can be obtained only at the nodes Solution can be obtained at the nodes as well as at any point within the field using shape function 03 Need more number of nodes to get good results Need lesser number of nodes to get good results 04 Simple Problems Complex Problems 05 Stair case approximation for boundary slopes Considers boundary as it is
  • 22. Finite Element Terminology 5/17/2023 ©PCCOE&R, Ravet, Pune 22 Terminolgy:  Continuum or Domain  Nodes  Element  Degree of Freedom  Load or Forces Point Load Body Force Surface / traction Force  Constraints
  • 23. Finite Element Terminology 5/17/2023 ©PCCOE&R, Ravet, Pune 23 Terminolgy:  Constraints (1) Homogeneous Boundary Conditions:
  • 24. Finite Element Terminology 5/17/2023 ©PCCOE&R, Ravet, Pune 24 (2) Non-homogeneous Boundary Conditions:
  • 25. General FEM Procedure 5/17/2023 ©PCCOE&R, Ravet, Pune 25 Step I : Discretization of the given continuum
  • 26. General FEM Procedure 5/17/2023 ©PCCOE&R, Ravet, Pune 26 Step II : Selection of Displacement model Polynomial Displacement Function Trigonometric Displacement Function Governing Conditions of Displacement Model (1) Type and order of function (2) Specific magnitude of displacement at nodes (3) Convergence
  • 27. General FEM Procedure 5/17/2023 ©PCCOE&R, Ravet, Pune 27 Step III : Derivation of Elemental Stiffness matrices and load Vectors [Ke] {qe} = {fe} Where, [Ke] = Elemental Stiffness Matrix, {qe} = Elemental Displacement Vector, {fe} = Elemental Force or Load Vector
  • 28. General FEM Procedure 5/17/2023 ©PCCOE&R, Ravet, Pune 28 Step IV : Assemblage of Elemental Equations to Obtain Global Equilibrium Equations [K] {Q} = {F} Where, [K] = Global Stiffness Matrix, {Q} = Global Displacement Vector, {F} = Global Force or Load Vector
  • 29. General FEM Procedure 5/17/2023 ©PCCOE&R, Ravet, Pune 29 Step V : Application of Boundary Conditions Elimination Method Penalty Method Multipoint Constraint Method
  • 30. General FEM Procedure 5/17/2023 ©PCCOE&R, Ravet, Pune 30 Step VI : To Determine the Unknown Parameters Nodal Displacement Elemental Strains Elemental Stresses Temperature
  • 31. Preprocessor, Processor & Postprocessor 5/17/2023 ©PCCOE&R, Ravet, Pune 31 Preprocessor involves following Steps : Choose discipline eg. Structural, Thermal, Fluid, Electromagnetics etc. Choose suitable element from library (NAFEMS) Assign material & geometric properties Construction of geometric model and importing Discretization or meshing and mesh refinement Application of boundary condition and loading
  • 32. Preprocessor, Processor & Postprocessor 5/17/2023 ©PCCOE&R, Ravet, Pune 32 Processor solver involves following Steps : Program calls governing equations from model and solves for primary quantities. Governing equations are assembled into matrix form and solved numerically. Type of process depends upon type of analysis eg. Static or dynamic, element type, material properties and boundary conditions.
  • 33. Preprocessor, Processor & Postprocessor 5/17/2023 ©PCCOE&R, Ravet, Pune 33 Postprocessor involves following Steps : Reading results in tabular or graphical form. Judge whether FEM result makes any sense of physical meaning. Comparison of results. Error estimation and authenticity.
  • 34. Applications 5/17/2023 ©PCCOE&R, Ravet, Pune 34 Equilibrium Problems and Propagation Problems  Aerospace Engineering  Automotive Engineering  Biomedical Engineering  Civil Engineering  Electrical Engineering  Hydraulic Engineering  Mechanical Engineering  Nuclear Engineering
  • 35. Error Analysis 5/17/2023 ©PCCOE&R, Ravet, Pune 35  Domain Approximation Error  Quadrature and Finite Arithmetic Errors  Solution Approximation Error
  • 36. Types of Error Estimation 5/17/2023 ©PCCOE&R, Ravet, Pune 36  A Priori Error Estimates  A Posteriori Error Estimates
  • 37. Meshing Techniques 5/17/2023 ©PCCOE&R, Ravet, Pune 37  Structured Mesh  Unstructured Mesh
  • 38. Criteria for Good Meshing 5/17/2023 ©PCCOE&R, Ravet, Pune 38  Shape of Element  Number of Elements  Topological Consistency  Automatic and adaptable
  • 39. Mesh Generation Methods 5/17/2023 ©PCCOE&R, Ravet, Pune 39  Mapped Mesh Generation  Free Mesh Generation
  • 40. Mesh Refinement Methods 5/17/2023 ©PCCOE&R, Ravet, Pune 40  h - Refinement  P – Refinement  hP – Refinement  r - Refinement
  • 41. Advantages of FEA 5/17/2023 ©PCCOE&R, Ravet, Pune 41 Can handle complex geometry and contours. Can handle complex analysis type. eg. Vibration, non-linear, transient etc. Can handle complex loading conditions. eg. Nodal based, element based, volume based, time and frequency based etc. Can handle complex constraints eg. Fixed, simply supported, roller supported, symmetric and unsymmetrical boundary conditions. Can handle bodies of homogenous and non-homogenous materials. Can handle special material effects such as temperature, moisture, electricity etc.
  • 42. Disadvantages of FEA 5/17/2023 ©PCCOE&R, Ravet, Pune 42 Specific numerical solution is required for specific problem. Obtained solution is approximate for higher order problem. Experience and judgment is required to construct good FEA model. Powerful and reliable FEA software is essential. A digital computer with large memory is required to store the data.
  • 43. Force Distribution 5/17/2023 ©PCCOE&R, Ravet, Pune 43 Internal Forces External Forces Point Load Body Force Surface Forces Sectioned Axially Loaded Beam Surface Forces: T(x) S Cantilever Beam Under Self-Weight Loading Body Forces: F(x)
  • 44. Force Distribution 5/17/2023 ©PCCOE&R, Ravet, Pune 44 Internal Forces External Forces
  • 45. Force Distribution 5/17/2023 ©PCCOE&R, Ravet, Pune 45 Different forces having components along x, y and z direction are shown below: T = Tx Ty Tz = [Tx Ty Tz]T P = Px Py Pz = [Px Py Pz]T U = u v w = [u v w]T
  • 46. Force Distribution 5/17/2023 ©PCCOE&R, Ravet, Pune 46 x z y y x yx z xy xz zy yz zx                      z zy zx yz y yx xz xy x ] [ 
  • 47. 2D Stress Equilibrium Equations 5/17/2023 ©PCCOE&R, Ravet, Pune 47 x  y  dx x x x      xy  yx  dy y y y      dx x xy xy      dy y yx yx      x F y F Body Forces
  • 48. Equilibrium Equation Example 5/17/2023 ©PCCOE&R, Ravet, Pune 48 0 0 0 0 0 2 3 2 3 0 _________ __________ __________ __________ ) 1 ( 4 3 , 0 , 2 2 3 equations m equilibriu e satisfy th stresses following that the show forces, body no Assuming 3 3 2 2 3                                  y x c Py c Py y x c y c P c N c Pxy y xy yx x xy y x a a
  • 49. 3D Stress Equilibrium Equations 5/17/2023 ©PCCOE&R, Ravet, Pune 49
  • 50. 3D Stress Equilibrium Equations 5/17/2023 ©PCCOE&R, Ravet, Pune 50 0                                      dxdydz F dxdy dz z dxdy dxdz dy y dxdz dydz dx x dydz x xz xz xz xy xy xy x x x                0 ; 0 ; 0 Fz F F y x 0            x xz xy x F z y x    0 0 ,                     z z yz xz y yz y xy F z y x F z y x Similarly      
  • 51. Stress Equilibrium Equations 5/17/2023 ©PCCOE&R, Ravet, Pune 51
  • 52. Stain Displacement Relations 5/17/2023 ©PCCOE&R, Ravet, Pune 52 u(x,y) u(x+dx,y) v(x,y) v(x,y+dy) dx dy A B C D A' B' C' D' dy y u   dx x v     x y             z zy zx yz y yx xz xy x            ] [ Three-Dimensional Theory z u x w y w z v x v y u z w y v x u xz yz xy z y x                                  ; ;
  • 53. Deformation and Strain Example 5/17/2023 ©PCCOE&R, Ravet, Pune 53       Ax Cy z u x w Cx Cx y w z v Bx Bx x v y u z w By y v Az x u C B A Cxy w y x B v Axz u zx yz xy z y x                                                                 2 1 2 1 2 1 0 2 1 2 1 2 0 2 1 2 1 0 2 _ __________ __________ __________ __________ constants are , , where , , ) ( , field nt displaceme following for the strain of components the Determine 2 2      
  • 54. Strain-Stress Relationships in 3D 5/17/2023 ©PCCOE&R, Ravet, Pune 54  The stress transformations equations were derived solely from equilibrium conditions and they are material independent.  Here the material properties will be considered (strain) taking into account the following: (a)The material is uniform throughout the body (homogeneous) (b)The material has the same properties in all directions (isotropic) (c)The material follows Hooke’s law (linearly elastic material) Hooke’s law: Linear relationship between stress and strain. For uniaxial stress: (E = modulus of elasticity or Young’s modulus) σ = Eε For pure shear : (G = Shear modulus of elasticity) ; τ = Gγ al longitudin transverse Strain Axial Strain lateral Ratio s Poisson        : '
  • 55. Strain-Stress Relationships in 3D 5/17/2023 ©PCCOE&R, Ravet, Pune 55 From Generalized Hooke’s law as defined is G Rigidity of Modulus and Ratio s Poisson Modulus s Young or Elasticity of Modulus E where E E E E E E E E E y x z z z x y y z y x x ) ( ' ' ,                         xy xy Srain Shear Stress Shear G    
  • 56. Strain-Stress Relationships in 3D 5/17/2023 ©PCCOE&R, Ravet, Pune 56 xy xy xy xy xy xy xy E e i E E becomes G Therefore E G G E             ) 1 ( 2 . . ). 1 ( 2 1 ) 1 ( 2 , ) 1 ( 2 ) 1 ( 2 is (G) rigidity of modulus and (E) elasticity of modulus between relation the that, know We            
  • 57. Strain-Stress Relationships in 3D 5/17/2023 ©PCCOE&R, Ravet, Pune 57 components Stress components Strain matrix Dynamic D where D E form matrix in writing E E Also xz yz xy z y x xz yz xy z y x xz xz yz yz                                                                                                              , ; ) 1 ( 2 0 0 0 0 0 0 ) 1 ( 2 0 0 0 0 0 0 ) 1 ( 2 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 , ) 1 ( 2 ; ) 1 ( 2 ,
  • 58. Stress-Strain Relationships in 3D 5/17/2023 ©PCCOE&R, Ravet, Pune 58 ) 2 1 )( ( 1 2 2 2 ) ( 1 , law s Hooke’ d Generalize From                                                    z y x z y x z y x z y x z y x y x z z z x y y z y x x E E E E E equations above the Adding E E E E E E E E E
  • 59. Stress-Strain Relationships in 3D 5/17/2023 ©PCCOE&R, Ravet, Pune 59 ) ( ) 1 ( equation, previous g rearrangin Now system. coordinate the changing after even value its change not does hich quantity w a is invarient An invarient Strain 1st invarient Stress 1st , ) 2 1 ( ) 2 1 ( 1 1 1 1 1 1 1 z y x x x x x z y x x z y x z y x E E E E E E E J I where J E I I E J or                                           
  • 60. Stress-Strain Relationships in 3D 5/17/2023 ©PCCOE&R, Ravet, Pune 60 ) 1 )( 2 1 ( ) 1 )( 2 1 ( ) 1 )( 2 1 ( ) 1 ( ) ( ) 1 )( 2 1 ( ) 1 ( ) 1 )( 2 1 ( ) 1 ( ) 2 1 ( . ) 1 ( ) 2 1 ( . ) 1 ( ) 1 ( 1 1 1 1                                                                              E E E E E E J E E J E J E E I E z y x x x z y x x x x x x x x x x x
  • 61. Stress-Strain Relationships in 3D 5/17/2023 ©PCCOE&R, Ravet, Pune 61 xy xy xy xy y x z z x z y y z y x x z y x x G G Also E E E E E E Similarly E E E E E E                                                       . , . ) 2 1 )( 1 ( . ) 2 1 )( 1 ( . ) 2 1 )( 1 ( ) 1 ( . ) 2 1 )( 1 ( . ) 2 1 )( 1 ( . ) 2 1 )( 1 ( ) 1 ( , . ) 2 1 )( 1 ( . ) 2 1 )( 1 ( . ) 2 1 )( 1 ( ) 1 ( ) 1 )( 2 1 ( ) 1 )( 2 1 ( ) 2 1 ( 1 ) 1 (                                                 
  • 62. Stress-Strain Relationships in 3D 5/17/2023 ©PCCOE&R, Ravet, Pune 62 components Stress components Strain matrix Dynamic D where D E form matrix in writing E E Similarly E xz yz xy z y x xz yz xy z y x xz xz yz yz xy xy                                                                                                                            , ; 2 ) 2 1 ( 0 0 0 0 0 0 2 ) 2 1 ( 0 0 0 0 0 0 2 ) 2 1 ( 0 0 0 0 0 0 ) 1 ( 0 0 0 ) 1 ( 0 0 0 ) 1 ( ) 2 1 )( 1 ( . ) 1 ( 2 ; . ) 1 ( 2 , . ) 1 ( 2
  • 63. Plane Stress Problem 5/17/2023 ©PCCOE&R, Ravet, Pune 63 figure) in (Shown shaft a on to fitted ring A : Example problem. stress plane as treated is direction in this applied loading and ss) or thickne direction - (z direction normal along dimensions has body a If equation previous from Therefore 0 ; 0 ; 0 : case Problem Stress Plane For    yz xz z                                      xy y x xy y x E          ) 1 ( 2 0 0 0 1 0 1 1
  • 64. Plane Strain Problem 5/17/2023 ©PCCOE&R, Ravet, Pune 64 pressure fluid internal to subjected cylinder A thick : Example problem. strain plane as treated is problem then axis al longitudin lar to perpendicu applied is loading and length) (i.e. long very is direction al longitudin along dimension If equation previous from Therefore 0 ; 0 ; 0 : case Problem Strain Plane For    yz xz z                                          xy y x xy y x E              2 ) 2 1 ( 0 0 0 ) 1 ( 0 ) 1 ( ) 2 1 )( 1 (
  • 65. Stress-Strain Temperature Relations 5/17/2023 ©PCCOE&R, Ravet, Pune 65 have; we materials, isotropic and elastic For deform. to free is body when the stresses any cause not does strain this Also, material. the of expansion linear of t coefficien on the depends which strain, uniform a in results z) y, T(x, change re temperatu the materials, isotropic For strain. thermal be to said is ture in tempera change to due length original unit per length in change The   Strain Initial where E or E xy y x xy y x xy y x                                                  0 0 1 0 0 0 , ) 1 ( 2 0 0 0 1 0 1 1                
  • 66. Stress-Strain Temperature Relations 5/17/2023 ©PCCOE&R, Ravet, Pune 66 : equation above the solving by strains of in terms stresses express also can We Stress Initial E where E or E xy y x xy y x xy y x                                                                0 0 0 0 0 0 2 , 2 ) 1 ( 0 0 0 1 0 1 ) 1 (                  
  • 67. Stress-Strain Temperature Relations 5/17/2023 ©PCCOE&R, Ravet, Pune 67 : by strain to related is stress the example, For expansion thermal of t coefficien , ; 0 : by given is loading) (thermal change re temperatu to due strains initial case, strain plane In the 2 ) 2 1 ( 0 0 0 ) 1 ( 0 ) 1 ( ) 2 1 )( 1 ( 0 0 0 0 0 0                                                                                                            where T T E xy y x xy y x xy y x xy y x
  • 69. Total Potential Energy 5/17/2023 ©PCCOE&R, Ravet, Pune 69
  • 70. Essential and Forced (Natural) Boundary Condtions 5/17/2023 ©PCCOE&R, Ravet, Pune 70
  • 71. Essential and Forced (Natural) Boundary Condtions 5/17/2023 ©PCCOE&R, Ravet, Pune 71
  • 74. Banded Skyline Solutions (Method of Minimizing Bandwidth) Symmetric Banded Matrix 5/17/2023 ©PCCOE&R, Ravet, Pune 74
  • 78. Derivation of Stiffness Matrix of Bar Element by Direct Approach 5/17/2023 ©PCCOE&R, Ravet, Pune 78
  • 79. Derivation of Stiffness Matrix of Bar Element by Direct Approach 5/17/2023 ©PCCOE&R, Ravet, Pune 79
  • 80. Derivation of Stiffness Matrix of Bar Element by Direct Approach 5/17/2023 ©PCCOE&R, Ravet, Pune 80
  • 81. Derivation of Stiffness Matrix of Bar Element by Direct Approach 5/17/2023 ©PCCOE&R, Ravet, Pune 81
  • 82. Derivation of Stiffness Matrix of Bar Element by Potential Energy Method 5/17/2023 ©PCCOE&R, Ravet, Pune 82
  • 83. Derivation of Stiffness Matrix of Bar Element by Potential Energy Method 5/17/2023 ©PCCOE&R, Ravet, Pune 83
  • 84. Derivation of Stiffness Matrix of Bar Element by Potential Energy Method 5/17/2023 ©PCCOE&R, Ravet, Pune 84
  • 85. Derivation of Stiffness Matrix of Bar Element by Potential Energy Method 5/17/2023 ©PCCOE&R, Ravet, Pune 85
  • 86. Derivation of Stiffness Matrix of Bar Element by Potential Energy Method 5/17/2023 ©PCCOE&R, Ravet, Pune 86
  • 87. Derivation of Stiffness Matrix of Bar Element by Potential Energy Method 5/17/2023 ©PCCOE&R, Ravet, Pune 87
  • 88. Derivation of Stiffness Matrix of Bar Element by Potential Energy Method 5/17/2023 ©PCCOE&R, Ravet, Pune 88
  • 89. Pre-requisites 6/12/2019 ©PCCOE&R, Ravet, Pune 89 FE SE TE BE Subject Name Basic Physics / Engineering mechanics Basic Mechanical Engineering FPL Mathematics Thermo Fluid Mechanics Power Plant Engineering Finite Elements Analysis CAD CAM Automation Heat Transfer Design of Machine Elements Numerical Methods
  • 90. Program Outcomes (POs) 5/17/2023 ©PCCOE&R, Ravet, Pune 90 No Program Outcomes No Program Outcomes 01 Engineering knowledge 07 Environment and sustainability 02 Problem analysis 08 Ethics 03 Design/development of solutions 09 Individual and team work 04 Conduct investigations of complex problems 10 Communication 05 Modern tool usage 11 Project management and finance 06 The engineer and society 12 Life-long learning Engineering Graduates will be able to: (For Details see NBA Guideline manual)
  • 91. Course Objectives  To understand the philosophy and general procedure of Finite Element Method as applied to solid mechanics and thermal analysis problems.  To familiarize students with the displacement-based finite element method for displacement and stress analysis and to introduce related analytical and computer tools.  It provides a bridge between hand calculations based on mechanics of materials and machine design and numerical solutions for more complex geometries and loading states.  To study approximate nature of the finite element method and convergence of results are examined.  It provides some experience with a commercial FEM code and some practical modeling exercises 5/17/2023 ©PCCOE&R, Ravet, Pune 91
  • 92. Course Outcomes (COs)  Recognize theoretical background of FEM, matrix algebra and solid mechanics for simple structural elements  Determine Stiffness matrix, Load vector, displacement matrix for 1D and 2D elements under mechanical and thermal loading conditions  Compute FE Discretisation with coordinate mapping and formulation of element equations.  Solve steady state heat conduction and convection problems  Construct a model of bar, truss, beam, CST, axisymmetric triangular and quadrilateral elements under dynamic considerations  Understand basic steps of FEM as Pre processing, meshing and post processing for 1D and 2D elements 5/17/2023 ©PCCOE&R, Ravet, Pune 92
  • 93. CO-PO Mapping 5/17/2023 ©PCCOE&R, Ravet, Pune 93 Program Outcomes (Course Outcomes) PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 CO1 3 1 2 CO2 3 3 3 2 2 CO3 2 3 3 2 3 1 3 CO4 2 3 2 2 3 1 2 CO5 2 3 2 2 3 1 1 3 CO6 2 3 2 2 3 1 1 3 Target 2.33 2.66 2.4 2.00 3.00 1.00 1.00 2.5
  • 94. CO Assessment Plan 5/17/2023 ©PCCOE&R, Ravet, Pune 94 Direct Method Indirect Methods (Course Outcomes) Internal Assessment External Assessment CO1  Assignment on each unit  Unit Tests  Preliminary Examination  Mock oral  In-semester Examination  End Semester Examination  Course End Survey CO2 CO3 CO4 CO5 CO6 Criterio <40% =40% ; <60% =60% ; <75% =75% ; < Attainment level 0 1 2 3
  • 95. Gap Identified in Curriculum 5/17/2023 ©PCCOE&R, Ravet, Pune 95 PO PO Description Activity Planned PO6 The Engineer and Society Industrial and Field Visits PO7 Environment and sustainability Industrial and Field Visits PO8 Ethics Copyrights and Patents PO9 Individual and team work Individual and Group Projects PO10 Communication Presentation based on Project Work PO11 Project management and finance Individual and Group Projects with detailed report
  • 96. Instructional Methods 5/17/2023 ©PCCOE&R, Ravet, Pune 96 Unit / Content Methods Practical / Hands-on Unit I : Fundamental Concepts of FEA (6 Hours)  Online Lectures using Google Meet  Video Lectures  Power point presentations  Tests on each unit  Quizzes on each unit  Animations & Videos  NPTEL notes  Group Activities  Classroom teaching (After Lockdown)  Static stress concentration factor calculation for a plate with center hole subjected to axial loading in tension  Modal analysis of any machine component  Stress and deflection analysis of any machine component consisting of 3-D elements  Elasto-plastic stress analysis  Coupled Thermal-Structural Analysis using FEA software  Computer program for stress analysis of 1D bar  Computer program for stress analysis of 2-D truss  Computer programs for (i) modal analysis and, (ii) stress analysis for 1-D beam  Computer program for 1-D temperature analysis Unit II : 1D Elements (6 Hours) Unit III : 2D Elements (6 Hours) Unit IV : Isoparametric Elements and Numerical Integration (6 Hours) Unit V : 1D Steady State Heat Transfer Problems (6 Hrs) Unit VI : Dynamic Analysis (6 Hours)
  • 97. Videos Lectures Prepared (Unit-I) 5/17/2023 ©PCCOE&R, Ravet, Pune 97 Sr. No. Title of Video Description Link 01 Unit I : Fundamental Concepts of FEA Solution methodologies to solve engineering problems
  • 98. Teaching Plan - Theory 5/17/2023 ©PCCOE&R, Ravet, Pune 98 Teaching Plan – Theory (FEA)
  • 99. Teaching Plan - Practical 5/17/2023 ©PCCOE&R, Ravet, Pune 99 Teaching Plan – Practical (FEA)
  • 100. Slow and Advanced Learners Procedure - Identifying Slow Learners and Fast Learners  Updation of Mentor form carried out and based on the report of individual mentors, Slow Learners and Fast Learners will be identified.  Slow learners and fast learners identify on the basis of previous semester marks. Supporting activities for Slow Learners  To conduct extra classes.  To assign the home work and ensure that it gets completed duly.  Personal Counseling through fast learners. 5/17/2023 ©PCCOE&R, Ravet, Pune 100
  • 101. Slow and Advanced Learners Encouraging activities for Advanced learners  To conduct extra tutorials, assignment and experts lectures.  To give case study on real life problem of relevant subject to enhance subject knowledge.  To explore their potential through activities like BAJA, Go-Kart, TIFAN, ROBOCON etc.  Participating at national/International events like Paper Presentation, Technical Competition etc. 5/17/2023 ©PCCOE&R, Ravet, Pune 101
  • 102. Result Analysis 5/17/2023 ©PCCOE&R, Ravet, Pune 102 AY 2017-18 AY 2018-19 AY 2019-20 AY 2020-21 (Target) Percentage 93.42 97.72 98.42 100 0 25 50 75 100 Result (%)
  • 103. Content Beyond Syllabus  Assignment on Ansys Workbench  Introduction to CFD and assignment on Ansys Fluent  Assignment on Topology Optimization  Guest lecture by Mr. K.K. Mate on ‘Recent Trends in CAE’ 5/17/2023 ©PCCOE&R, Ravet, Pune 103
  • 104. Feedback 5/17/2023 ©PCCOE&R, Ravet, Pune 104 AY 2017-18 AY 2018-19 AY 2019-20 AY 2020-21 (Target) Percentage 86.65 89.78 97.42 98 0 25 50 75 100 Feedback (%)
  • 105. Research & Innovations & Co-curricular Activities 5/17/2023 ©PCCOE&R, Ravet, Pune 105 Sr. No. Description Total Remark 01 Coursera Certificate courses 10 Completed with score more than 90% 02 Faculty Development Programs 05 Based on advanced trends 03 Copyrights 02 Filed 04 Paper Publications / Conferences 02 Accepted 05 Patent 01 Drafted 06 Industrial training 01 Sandvik Asia (I) Ltd.
  • 106. Portfolios & Responsibilities 5/17/2023 ©PCCOE&R, Ravet, Pune 106  Departmental Academic Coordinator  NBA Criteria II coordinator  Higher Studies Cell Member  Lab Incharge (Turbomachines)  Mentor
  • 107. Plan for Current Semester 5/17/2023 ©PCCOE&R, Ravet, Pune 107  Two NPLEL Courses  Conduction of Two FDP & Two Guest Lectures  Two Patents & Five Copyrights  Ten Coursers Courses  Preparation of Video Lectures for FEA & MSD  Documentation of Critera II  Group wise project for FEA Subject
  • 108. Reference Books  Daryl L, A First Course in the Finite Element Method,. Logan, 2007.  G Lakshmi Narasaiah, Finite Element Analysis, B S Publications, 2008.  Y.M.Desai, T.I.Eldho and A.H.Shah, Finite Element Method with Applications in Engineering, Pearson Education, 2011  Chandrupatla T. R. and Belegunda A. D., Introduction to Finite Elements in Engineering, Prentice Hall India, 2002.  P., Seshu, Text book of Finite Element Analysis, PHI Learning Private Ltd. , New Delhi, 2010. 5/17/2023 ©PCCOE&R, Ravet, Pune 108