The document discusses finite element analysis (FEA) and its applications. It provides an overview of FEA, including the basic theory and principles. It explains that FEA is a numerical method for solving engineering problems by dividing a complex system into smaller pieces called finite elements. The document lists various element types and common applications of FEA, such as thermal, modal, buckling, and non-linear analyses. It also provides resources on FEA tutorials and examples involving different problem types.
A Presentation About The Introduction Of Finite Element Analysis (With Example Problem) ... (Download It To Get More Out Of It: Animations Don't Work In Preview) ... !
A Presentation About The Introduction Of Finite Element Analysis (With Example Problem) ... (Download It To Get More Out Of It: Animations Don't Work In Preview) ... !
General steps of the finite element methodmahesh gaikwad
General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.
General steps of the finite element methodmahesh gaikwad
General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Topics to be discussed-
Introduction
How Does FEM Works?
Types Of Engineering Analysis
Uses of FEM in different fields
How can the FEM Help the Design Engineer?
How can the FEM Help the Design Organization?
Basic Steps & Phases Involved In FEM
Advantages and disadvantages
The Future Scope
References.
A short introduction presentation about the Basics of Finite Element Analysis. This presentation mainly represents the applications of FEA in the real time world.
*Discretization of a Structure, 1D, 2D and 3D element Meshing, * Element selection criteria, *Refining Mesh,
*Effect of mesh density in critical region,
*Use of Symmetry.
*Element Quality Criterion:-Jacobian, Aspect ratio, Warpage, Minimum and Maximum angles, Average element size, Minimum Length, skewness, Tetra Collapse etc., *Higher Order Element vs Mesh Refinement,
*Geometry Associate Mesh, *Mesh quality,
*Bolted and welded joints representation,
*Mesh independent test.
Introduction to CAE and Element Properties.pptxDrDineshDhande
INTRODUCTION
USE OF CAE IN PRODUCT DEVELOPMENT
CONTENTS:
(1) DISCRETIZATION METHODS : FEM,FDM AND FVM
(2) CAE TOOLS
(3) ELEMET SHAPES
(4) SHAPE FUNCTIONS
Explore our comprehensive data analysis project presentation on predicting product ad campaign performance. Learn how data-driven insights can optimize your marketing strategies and enhance campaign effectiveness. Perfect for professionals and students looking to understand the power of data analysis in advertising. for more details visit: https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/
Adjusting primitives for graph : SHORT REPORT / NOTESSubhajit Sahu
Graph algorithms, like PageRank Compressed Sparse Row (CSR) is an adjacency-list based graph representation that is
Multiply with different modes (map)
1. Performance of sequential execution based vs OpenMP based vector multiply.
2. Comparing various launch configs for CUDA based vector multiply.
Sum with different storage types (reduce)
1. Performance of vector element sum using float vs bfloat16 as the storage type.
Sum with different modes (reduce)
1. Performance of sequential execution based vs OpenMP based vector element sum.
2. Performance of memcpy vs in-place based CUDA based vector element sum.
3. Comparing various launch configs for CUDA based vector element sum (memcpy).
4. Comparing various launch configs for CUDA based vector element sum (in-place).
Sum with in-place strategies of CUDA mode (reduce)
1. Comparing various launch configs for CUDA based vector element sum (in-place).
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Empowering the Data Analytics Ecosystem: A Laser Focus on Value
The data analytics ecosystem thrives when every component functions at its peak, unlocking the true potential of data. Here's a laser focus on key areas for an empowered ecosystem:
1. Democratize Access, Not Data:
Granular Access Controls: Provide users with self-service tools tailored to their specific needs, preventing data overload and misuse.
Data Catalogs: Implement robust data catalogs for easy discovery and understanding of available data sources.
2. Foster Collaboration with Clear Roles:
Data Mesh Architecture: Break down data silos by creating a distributed data ownership model with clear ownership and responsibilities.
Collaborative Workspaces: Utilize interactive platforms where data scientists, analysts, and domain experts can work seamlessly together.
3. Leverage Advanced Analytics Strategically:
AI-powered Automation: Automate repetitive tasks like data cleaning and feature engineering, freeing up data talent for higher-level analysis.
Right-Tool Selection: Strategically choose the most effective advanced analytics techniques (e.g., AI, ML) based on specific business problems.
4. Prioritize Data Quality with Automation:
Automated Data Validation: Implement automated data quality checks to identify and rectify errors at the source, minimizing downstream issues.
Data Lineage Tracking: Track the flow of data throughout the ecosystem, ensuring transparency and facilitating root cause analysis for errors.
5. Cultivate a Data-Driven Mindset:
Metrics-Driven Performance Management: Align KPIs and performance metrics with data-driven insights to ensure actionable decision making.
Data Storytelling Workshops: Equip stakeholders with the skills to translate complex data findings into compelling narratives that drive action.
Benefits of a Precise Ecosystem:
Sharpened Focus: Precise access and clear roles ensure everyone works with the most relevant data, maximizing efficiency.
Actionable Insights: Strategic analytics and automated quality checks lead to more reliable and actionable data insights.
Continuous Improvement: Data-driven performance management fosters a culture of learning and continuous improvement.
Sustainable Growth: Empowered by data, organizations can make informed decisions to drive sustainable growth and innovation.
By focusing on these precise actions, organizations can create an empowered data analytics ecosystem that delivers real value by driving data-driven decisions and maximizing the return on their data investment.
Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...Subhajit Sahu
Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.
Opendatabay - Open Data Marketplace.pptxOpendatabay
Opendatabay.com unlocks the power of data for everyone. Open Data Marketplace fosters a collaborative hub for data enthusiasts to explore, share, and contribute to a vast collection of datasets.
First ever open hub for data enthusiasts to collaborate and innovate. A platform to explore, share, and contribute to a vast collection of datasets. Through robust quality control and innovative technologies like blockchain verification, opendatabay ensures the authenticity and reliability of datasets, empowering users to make data-driven decisions with confidence. Leverage cutting-edge AI technologies to enhance the data exploration, analysis, and discovery experience.
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Leverage these privacy-preserving datasets for training and testing AI models without compromising sensitive information. Opendatabay prioritizes transparency by providing detailed metadata, provenance information, and usage guidelines for each dataset, ensuring users have a comprehensive understanding of the data they're working with. By leveraging a powerful combination of distributed ledger technology and rigorous third-party audits Opendatabay ensures the authenticity and reliability of every dataset. Security is at the core of Opendatabay. Marketplace implements stringent security measures, including encryption, access controls, and regular vulnerability assessments, to safeguard your data and protect your privacy.
5. An innovative way to solve
engineering problems
FEA: A matrix method
through use of computer
6. Any Engineering Problem
Analytical Methods Experimental Methods Numerical Methods
• Classical method
• Infinite elements
• Assumptions
• Solution of
differential equations
• Exact solution
• Simple linear
problems
• Matrix method
• Finite elements (no
Assumptions considered)
• Real life situation
• Solution of algebraic
equations
• Approximate solution
• Real life complicated
problems
• Actual Measurements
• Time Consuming &
need Exp. Set up
• Results can not be
believed blindly &
requires verification
1
7. CLASSICAL METHOD vs. FEM
FEM
1. Exact equations but
approximate solutions
2. Solutions for all problems
3. Linear algebraic equations
4. Finite degrees of freedom
5. Can handle all types of
material properties.
6. Can handle all types of
Nonlinearities
CLASSICAL
1. Exact equations and exact
solutions
2. Solutions for few standard
cases only
3. Partial differential
equations
4. Infinite degrees of freedom
5. Good for homogeneous and
isotropic materials
6. Cannot handle nonlinear
problems
8. FEM is superior to the classical methods only
for the problems involving a number of
complexities which cannot be handled by
classical methods without making drastic
assumptions.
However for all regular, standard and simple
problems, the solutions by classical methods
are the best solutions.
The finite element knowledge makes a
good engineer better
9. Need for Studying FEM?
•Any FEM software tool used as a black box
•Any input to the black box results in an output.
•Garbage in and garbage out
•Interpretation of results
•Debugging the errors during the analysis
•No knowledge of FEA may produce more
dangerous results.
10. Why it is called Finite elements ?
• The domain or region is discretized into finite
number of elements.
11. Simple Approach of FEM Concept
•Basic concept of discretization of a Domain by Finite
elements.
•Assume that you don’t know how to calculate area of the
circle but knew the formula for the area of the Triangle.
Area ‘unknown’ )
h
b
(
2
1
Area
b
h
15. Various Element Types
• Divide the body into a systems of finite
elements with nodes and the appropriate
element type
• Element Types:
– One-dimensional Element
(Bar/Spring/Truss/Beam)
– Two-dimensional Element
(Plates/Shells)
– Three-dimensional Element
16.
17.
18. Common Types of Elements
One-Dimensional Elements
Line
Rods, Beams, Trusses,
Frames
Two-Dimensional Elements
Triangular, Quadrilateral
Plates, Shells
Three-Dimensional Elements
Tetrahedral, Rectangular Prism
(Brick)
33. Discontinuity of Load
• Concentrated loads and sudden
change in the intensity of
uniformly distributed loads are
the sources of discontinuity of
loads.
• A node or a line of nodes should
be there to model the structure.
34.
35.
36. Discontinuity of Boundary Conditions
• If the boundary condition for a structure
suddenly change we have to discretize such
that there is node or a line of nodes.
38. Refining Mesh
• To get better results, the finite element mesh should
be refined in the following situations
(a) To approximate curved boundary of the structure
(b) At the places of high stress gradients.
39. Use of Symmetry
• Wherever there is symmetry in the problem,
it should be made use.
• By doing so lot of computer memory
requirement is reduced.
40.
41. Element Aspect Ratio
• The shape of the element also affects the
accuracy of analysis.
• It is defined as the ratio of largest to smallest
size in an element.
• It is applied to 2D and 3D elements.
• For good accuracy or better results, the aspect
ratio should be as close to unity as possible.
ension
Smaller
ensio
er
L
Ratio
Apspect
dim
dim
arg
45. General Procedure for FEA
Select a suitable field variable.
Discretization or meshing into a number of
elements.
Selection of shape/interpolation functions.
Development of element equations.
e e e
k q f
F = kq for a spring
This is a matrix
equation
This is a
algebraic
equation
46. Assembly of the element equations to
produce a global system of equations.
Imposition of the boundary conditions. (In
this step, the assembled system of equations
is modified by applying the prescribed
boundary conditions)
K Q F
47. Solution of equations. (In this step, modified
global system of equations is solved and
primary variables at the nodes are obtained)
Additional computations (if desired). (In
this step, various secondary quantities are
computed from the obtained solution. For
example, stresses and strains are computed
from the obtained nodal displacements)
1
Q K F
49. What is Finite Element Analysis ?
•Finite Element Analysis is
a computer simulation
technique used in
engineering analysis.
•It is a way to simulate
loading conditions on a
design and determine its
response to those loading
conditions.
51. General Steps of Any FEA Software
• Set the type of analysis
• Create CAD model
• Assign the material
• Define the element type
• Divide the geometry into nodes and elements (meshing)
• Element equations created in the background
• Assemble equations created in the background
• Apply loads and boundary conditions
• Modified equations are framed
• Solution and Interpretation of results
52.
53. Stages of Any FEA Software
..General scenario..
Preprocessing
Analysis/Solution
Postprocessing
Step 1
Step 2
Step 3
57. Preprocessing
• Define the geometric domain of the problem.
• Define the element type(s) to be used.
• Define the material properties of the elements.
• Define the geometric properties of the
elements (length, area, and the like).
• Define the element connectivity (meshing)
• Define the boundary conditions.
• Define the loadings.
58. Processing/Solution/Analysis
• The user asks the software to calculate
values of a set of parameters as per
requirement
• Assembles the governing algebraic
equations in matrix form and computes the
unknown values of the primary field
variable(s).
• The computed values are then used by back
substitution to compute reaction forces,
element stresses, and heat flow, etc.
59. Postprocessing
• Calculates stresses/strains
• Check equilibrium.
• Calculate factors of safety.
• Plot deformed structural shape.
• Animate dynamic model behavior.
• Produce color-coded temperature plots.
74. Shape/Interpolation Functions
In FEA, the main aim is to find the
field variables at nodal points. The
value of the field variable at any point
inside the element is a function of
values at nodal points of the element.
This function which relates the field
variable at any point within the
element to the field variables at nodal
points is called shape function.
75. Why Polynomial Shape Functions?
They are easy to handle
mathematically i.e. differentiation and
integration of polynomials is easy.
Using polynomial, any function can
be approximated reasonably well. If a
function is highly nonlinear we may
have to approximate with higher order
polynomial.
76. Important FE Equations
: e e e
Element Eqn K q F
:
T
e
v
Element Stiffness Matrix K B D B dv
Body force Surface force
:
T T
e
v s
Element LoadVector F N f dv N T ds P
Point load
1 1
:
n n
e e e
e e
Global Eqn K q F
1 1
n n
n n
K Q F
77. Prerequisites to Study FEA
Working knowledge on Matrix Algebra
Basic Elementary Knowledge on SOM
and HT
78. APPLICATIONS OF FEA
Analysis of Bar/Spring
Analysis of Beam
Analysis of Truss
Bar: Any structural member under axial load
Bar: Any member either under tension or compression
It means it may either elongate or contract
79. Beam: It is a structural member under transverse load
80. Shape Functions
2 1
1
1 2
1 1 2 2
1
1 2
2
1
q q
u x q x
l
x x
q q
l l
N q N q
q
N N
q
1 2
1
x x
N and N
l l
2 1
1 2
u x N q
Analysis of Bar
81. Properties of Shape Functions
At any point x,
At node 1, x = 0;
At node 2, x = l;
1 2 1
N N
1 2
1, 0
N N
1 2
0, 1
N N
82.
du d dN
Strain N q q B q
dx dx dx
1 2
, 1
1
1 1
dN dN d x d x
Where B
dx dx dx l dx l
Straindisplacement matrix
l
Stress E D B q
2 1
1 2
2 1
1 2
2 1
1 1 1 2
For one -dimensional problems
u x N q
B q
D B q
83. Element Stiffness Matrix of a Uniform Bar
0
0
2 1 2
0
2 1
2 2
1
1 1
1 1
1
1
1 1
1
1 1
1 1
l
T T
e
v
l
l
k B D B dv B E B Adx
AE dx
l l
AE
dx
l
AE
l
84. Element Stiffness Matrix of a Tapered Bar
1 1
1 1
e m
A E
K
l
1 2
, Mean or average area
2
m
A A
Where A
85. Element and Global Equations
2 2 2 1
2 1
1 1
2 2
:
1 1
1 1
e e e
Element Equation k q F
q F
AE
q F
l
1 1
:
n n n n
Global Equation K Q F
86. Example 1: Determine the nodal displacements at node 2,
stresses in each material and support reactions in the bar due to
applied force P = 400 kN. Given:
A1 = 2400 mm2, A2 = 1200 mm2, l1 = 300 mm, l 2 = 400 mm
E1 = 0.7 × 105 N/mm2, E2 = 2 × 105 N/mm2
87. Example 2: Determine the nodal displacement, element
stresses and support reactions of the axially loaded bar as
shown in Figure. Take
E = 200 GPa and P = 30 kN
88. ANALYSIS OF BEAMS
• Vertical displacement v (Translational degree of freedom)
• Slope, dv
dx
(Rotational degree of freedom)
1 1 2 2
T
q v v
1 2
1 2
and
dv dv
dx dx
89. Shape Functions
2 3 2 3
1 2
2 3 2
2 3 2 3
3 4
2 3 2
3 2 2
1 ,
3 2
,
x x x x
N N x
l l l l
x x x x
N N
l l l l
The displacement at any point within the element is
interpolated from the four nodal displacements .
1 1 2 1 3 2 4 2
v x N v N N v N
1
1
1 2 3 4
2
2
v
N N N N
v
4 1
1 4
N q
90. Element Stiffness Matrix
2 2
3
2 2
12 6 12 6
6 4 6 2
12 6 12 6
6 2 6 4
e
l l
l l l l
EI
k
l l
l
l l l l
91. Element Load Vector
1
1
1 1 2 2
2
2
1
2
3
4
T
e
F
M
F F M F M
F
M
92.
1
2
1
2
2
2
2
1
12
2
2
3
12
4
o
o
e
o
o
q l
F
q l
M
F
q l
F
q l
M
1
2
1
2
2
2
3
20
1
1
2
30
7 3
20 4
1
20
o
o
e
o
o
q l
F
q l
M
F
F
q l
M
q l
For a downward UDL, For a downward UVL,
93. Element and Global Equations
4 4 4 1
4 1
1 1
2 2
1 1
3
2 2
2 2
2 2
:
12 6 12 6
6 4 6 2
12 6 12 6
6 2 6 4
e e e
Element Equation k q F
v F
l l
M
l l l l
EI
v F
l l
l
M
l l l l
1 1
:
n n n n
Global Equation K Q F
94. Example 1:A beam of length 10 m, fixed at both ends carries
a 20 kN concentrated load at the centre of the span. By taking
the modulus of elasticity of material as 200 GPa and moment
of inertia as 24 × 10–6 m4, determine the slope and deflection
under load.
95. Example 2: Determine the rotations at the supports.
Given E = 200 GPa and I = 4 × 106 mm4.
96. Example 3: Find the slopes at nodes the beam shown in
Figure by finite element method and determine the end
reactions. Also determine the deflections at mid spans given
E = 2 × 105 N/mm2 and I = 5 × 106 mm4
97. Introduction to FEA
• A computing technique to obtain approximate solutions
to boundary value problems.
• Uses a numerical method called FEM
• Involves a CAD model design that is loaded and
analyzed for specific results
• Simulates the loading conditions of a design and
determines the design response in those conditions
• A better FEA knowledge helps in building more accurate
models