The finite element method is used to solve engineering problems involving stress analysis, heat transfer, and other fields. It involves dividing a structure into small pieces called finite elements and deriving the governing equations for each element. The element equations are assembled into a global stiffness matrix and force vector. Boundary conditions are applied and the system is solved for the unknown displacements at nodes. Results like stresses, strains, and temperatures are then determined. Key steps are discretization, deriving the element stiffness matrix, assembling the global matrix, applying boundary conditions, and solving for nodal displacements.
A short introduction presentation about the Basics of Finite Element Analysis. This presentation mainly represents the applications of FEA in the real time world.
A short introduction presentation about the Basics of Finite Element Analysis. This presentation mainly represents the applications of FEA in the real time world.
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.
Introduction to CAE & CFD
It contains brief introduction to various types of numerical methods its advantages and disadvantages .steps involved in performing any CAE OR CFD related projects
FEM: Introduction and Weighted Residual MethodsMohammad Tawfik
What are weighted residual methods?
How to apply Galerkin Method to the finite element model?
#WikiCourses #Num001
https://wikicourses.wikispaces.com/TopicX+Approximate+Methods+-+Weighted+Residual+Methods
Analysis of Cross-ply Laminate composite under UD load based on CLPT by Ansys...IJERA Editor
In current study the strength of composite material configuration is obtained from the properties of constituent
laminate by using classical laminate plate theory. For the purpose of analysis various configurations of 2 layered
and 4 layered cross ply laminates are used. The material of laminate is supposed to be boron/epoxy having
orthotropic properties. The loading in current study is supposed to be of uniformly distributed load type. For the
analysis purpose software working on finite element analysis logics i.e. Ansys mechanical APDL is used. By the
help of Ansys mechanical APDL the deflection and stress intensity is found out. The effect of variation of
laminate layers is also studied in current study along with the effect of variation of stacking patterns. The current
study will also help to conclude which stacking pattern is best in 2 layered and 4 layered cross ply laminate.
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.
Introduction to CAE & CFD
It contains brief introduction to various types of numerical methods its advantages and disadvantages .steps involved in performing any CAE OR CFD related projects
FEM: Introduction and Weighted Residual MethodsMohammad Tawfik
What are weighted residual methods?
How to apply Galerkin Method to the finite element model?
#WikiCourses #Num001
https://wikicourses.wikispaces.com/TopicX+Approximate+Methods+-+Weighted+Residual+Methods
Analysis of Cross-ply Laminate composite under UD load based on CLPT by Ansys...IJERA Editor
In current study the strength of composite material configuration is obtained from the properties of constituent
laminate by using classical laminate plate theory. For the purpose of analysis various configurations of 2 layered
and 4 layered cross ply laminates are used. The material of laminate is supposed to be boron/epoxy having
orthotropic properties. The loading in current study is supposed to be of uniformly distributed load type. For the
analysis purpose software working on finite element analysis logics i.e. Ansys mechanical APDL is used. By the
help of Ansys mechanical APDL the deflection and stress intensity is found out. The effect of variation of
laminate layers is also studied in current study along with the effect of variation of stacking patterns. The current
study will also help to conclude which stacking pattern is best in 2 layered and 4 layered cross ply laminate.
Improvement of the Shell Element Implemented in FEASTSMTiosrjce
The paper deals with shear locking problem in shell element. Shear locking does not mean complete
rigidity, it refers to unwanted high-stiffness behavior that influences the solution but does not over whelm it, so
that convergence with mesh refinement is slowed but not prevented. In the present study the Bilinear
Degenerated Shell (BDS) element model is improved based on the bubble function for membrane strain energy
and selective integration for the shear energy. After formulation of the shell element, implementation is carried
out in FEASTSMT (FINITE ELEMENT ANALYSIS OF STRUCTURES). Result of the shell element without any
bubble function terms showed sensitivity to shear locking problem. Use of bubble functions and selective
integration greatly improves the element performance. The results were compared with those available in
literatures.
First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of
laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the
governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for
various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency
parameters are evaluated and compared with previous work available in the literature. The good agreement with
other available data demonstrates the capability and reliability of the finite element method and the adopted beam
model used.
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.
Analysis of Stress Concentration of Laminated Composite Plate With Circular Holeijiert bestjournal
Composite materials are finding a wide range of applications in structural design,especially for lightweight structure that have stringent stiffness and strength requirements. They are attractive replacement for metallic materials for many structural applications. By finding efficient composite str ucture design that meets all requirements of specific application. This is achieved by tailoring of material properties through selective choice of orientation,no. of stacking sequence of layers that make up composite material. Composites are used more and more often for load carrying and safety structures in all kind of applications foe aviation and space technology,for vehicles etc. Composite materials have been introduced progressively in automobiles,followingpolymer materials,a few of which have be en used as matrices. It is interestingto examine the relative masses of different materials which are used in theconstruction of automobiles. Even thoughthe relative mass of polymer - based materials appears low,one needs to take intoaccount that the specif ic mass of steel is about 4 times greater than that of polymers.This explains the higher percentage in terms of volume for the polymers.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
2. Definition
The finite element method is a computational scheme to solve field problems in
engineering and science. The technique has very wide application, and has been
used on problems involving stress analysis, fluid mechanics, heat transfer,
diffusion, vibrations, electrical and magnetic fields, etc. The fundamental concept
involves dividing the body under study into a finite number of pieces (subdomains)
called elements.
3. Static vs. Dynamic FEM
Static analysis is good for engineering, to find just the end result.
Dynamic analysis is good for simulation, to find all intermediate steps.
4. Phases in FEA
Preprocessing
o Understanding the Problem (Thermal , Structural, Dynamic etc)
o Element Selection (Solid i.e 3D , Shell i.e 2D , Beams i.e 1D etc)
o Deciding the Boundary Conditions (Constraints , Connections etc..)
o Load Application (Point , Surface , Body loads etc..)
Solution
o Program derives the governing matrix equations from the model &
solves for the primary quantities.
Post processing of Results (Deflection , Stress , Strain etc..)
o Validity check of the solution.
o Report Preparation.
o Observation and Conclusion from the Analysis. (MS Calcs, Design ok)
o Suggestion and Recommendation for Design Changes, if required.
5. 5
Idealization of
geometry (if necessary)
CAD geometry Simplified
geometry
CAD FEA Pre-
processing
Basic Steps In The Finite Element Analysis
Restraints
Material
properties
Type of
analysis Loads
MATHEMATICAL
MODEL
6. 6
FEA model FEA results
Discretization Numerical solver
FEA Pre-
processing
FEA
Solution
FEA Post-
processing
MATHEMATICAL
MODEL
Basic Steps In The Finite Element Analysis
9. Types of Materials
• Isotropic Materials- A material having identical values of a property
in all directions. Ex: Glass and metals.
• Anisotropic Materials- Properties such as Young's Modulus, change
with direction along the object. Ex: wood and composites.
• Orthotropic Materials- They have material properties that differ
along three mutually-orthogonal twofold axes of rotational symmetry.
They are a subset of anisotropic materials, because their properties
change when measured from different directions. Ex: wood.
• Homogeneous Material- A material of uniform composition
throughout that cannot be mechanically separated into
different materials. Ex: Certain types of plastics, ceramics, glass,
metals, alloys, paper, board, resins, and coatings.
10. Common Alloys used in Aircrafts
Aluminium Alloys
1. Al 2024 Composition-
Due to its high strength and fatigue resistance, 2024 is widely used in aircraft structures,
especially wing and fuselage structures under tension. Al 2024 is known as the “aircraft
alloy” in machining rod.
a. Al 2024-T351 –
T351 temper 2024 plate has an ultimate tensile strength of 470 MPa (68 ksi) and yield
strength of 280 MPa (41 ksi). It has elongation of 20%.
b. Al 2024-T3 –
T3 temper 2024 sheet has an ultimate tensile strength of 400–430 MPa (58–62 ksi) and yield
strength of at least 270–280 MPa (39–40 ksi). It has an elongation of 10-15%.
Element Content (%)
Aluminium / Aluminum, Al 93.50
Copper, Cu 4.4
Magnesium, Mg 1.5
Manganese, Mn 0.6
11. 2. Al 5052 Composition-
Al 5052 is an aluminium alloy, primarily alloyed with magnesium and chromium.
Aluminium / Aluminum 5052 alloy is used in the manufacture of Milk crates, Hydraulic
tubes, Appliances, Kitchen cabinets, Small boats, home freezers, Aircraft tube, Fencing etc.
This alloy is also used widely in sheet metal work and in sheet metal parts.
3. Al 7050 Composition-
Element Content (%)
Aluminum, Al 89
Copper, Cu 2.3
Magnesium, Mg 2.3
Zinc, Zn 6.2
Zirconium, Zr 0.12
12. Aluminium / Aluminum 7050 alloy is a heat treatable alloy. It has high toughness, strong
mechanical strength, and good stress corrosion cracking resistance.
Aluminium / Aluminum 7050 alloy is mainly used in manufacturing aircraft and other
structures.
a. Al 7050-T76511 -
Solution heat-treated, stress-relieved by controlled stretching and then artificially overaged
in order to achieve a good exfoliation corrosion resistance. The products receive no further
straightening after stretching, except that minor straightening is allowed after stretching to
comply with standard tolerances.
4. Al 7075 Composition-
Element Content (%)
Aluminum, Al 90
Zinc, Zn 5.6
Magnesium, Mg 2.5
Copper, Cu 1.6
Chromium, Cr 0.23
13. Aluminum alloy 7075 is an aluminum alloy, with zinc as the primary alloying element. It is
strong, with a strength comparable to many steels, and has good fatigue strength and
average machinability, but has less resistance to corrosion than many other Al alloys.
Aluminum 7075 alloy is mainly used in manufacturing aircraft and other aerospace
applications.
a. Al 7075-T6 -
T6 temper 7075 has an ultimate tensile strength of 510–540 MPa (74,000–78,000 psi) and
yield strength of at least 430–480 MPa (63,000–69,000 psi). It has a failure elongation of 5–
11%.
b. Al 7075-T 6511 –
Solution heat-treated, stress-relieved by controlled stretching (permanent set 1% to 3% for
extruded rod, bar, shapes and tube, 0.5% to 3% for drawn tube) and then artificially aged.
Minor straightening is allowed after stretching to comply with standard tolerances
14. Meshing( Discretization )
Discretization is the method of approximating the differential equations
by a system of algebraic equations for the variables at some set of discrete
locations in space and time.
Continuous domain Discretized domain
15. Concept of Discretization (Meshing)
Concept of FEM is all about Discretization (Meshing) i.e. Dividing a big
structure/component into small discrete Blocks (Nodes and Element concept)
But why we do Meshing ???
Ans: Ex: (1) No. of Points =∞
DoF per point = 6
Total No of Equations to be solved=∞ * 6 = ∞
(2) No. of Points =8
DoF per point = 6
Total No of Equations to be solved=8 * 6 = 48
*From Infinite to Finite…Hence the Term “Finite Element Method”*
16. Basic Steps in the Finite Element Method
Time Independent Problems
Domain Discretization
Select Element Type (Shape and Approximation)
Derive Element Equations.
Assemble Element Equations to Form Global System.
[K]{U} = {F}
where, [K] = Stiffness or Property Matrix
{U} = Nodal Displacement Vector
{F} = Nodal Force Vector
Incorporate Boundary and Initial Conditions.
Solve Assembled System of Equations for Unknown Nodal
Displacements and Secondary Unknowns of Stress and Strain Values.
20. In general, we will have a stiffness matrix
of the form (assume for now that we do
not know k11, k12, etc)
333231
232221
131211
kkk
kkk
kkk
K
The finite element force-
displacement relations:
3
2
1
3
2
1
333231
232221
131211
F
F
F
d
d
d
kkk
kkk
kkk
k1
k2F1x F2x F3x
x
1 2 3
Element 1 Element 2
d1x d2x
d3x
Physical Significance of Stiffness Matrix
21. The first equation is,
1313212111 Fdkdkdk
Force equilibrium
equation at node 1
What if d1=1, d2=0, d3=0 ?
313
212
111
kF
kF
kF
Force along node 1 due to unit displacement at node 1
Force along node 2 due to unit displacement at node 1
Force along node 3 due to unit displacement at node 1
While nodes 2 and 3 are held fixed
Similarly we obtain the physical significance of the other entries of the
global stiffness matrix.
Columns of the global stiffness matrix
22. Steps in solving a problem
Step 1: Write down the node-element connectivity table linking local and
global displacements
Step 2: Write down the stiffness matrix of each element
Step 3: Assemble the element stiffness matrices to form the global stiffness
matrix for the entire structure using the node element connectivity table
Step 4: Incorporate appropriate boundary conditions
Step 5: Solve resulting set of reduced equations for the unknown
displacements
Step 6: Compute the unknown nodal forces
23. MNTamin, CSMLab
ke
Ae Ee
1 1
le 1 1
3. Element force vector
due to body force, fb
1
2
e e b
f e A l f
1
4. Element force vector
due to traction force, T
1e
Te Tl
2 1
1q
le
E
1 1
q2
Some formulas used in 1-D problems
1. Stress-strain relation
2. Element stiffness matrix
25. Solution
1. Transform the given plate into 2 sections, each
having uniform cross-sectional area.
Note:
Area at midpoint is
Amid = 4.5 in2.
Average area of section 1 is
A1 = (6 + 4.5)/2 = 5.25 in2.
Average area of section 2 is
A2 = (4.5 + 3)/2 = 3.75 in2.
2. Model each section using 1-D
(line) element.
26. element 2:
6
12
k(2) 3.753010 1
1
1 1
4. Assemble global stiffnessmatrix,
6
12
5.25
K
3010 5.25 3.75
5.25 0
9.00
0 3.75 3.75
3. Write the element stiffness matrix for each element
element 1:
6
12
1
k(1)
5.253010 1
1 1
Note: The main diagonal must contain positive numbersonly!
27. 5. Write the element force vector for each element
a) Due to body force, fb = 0.2836lb/in3
element 1 (1)
12
fb
5.25120.2836 1
element 2 (2)
12
fb
3.75120.2836 1
Assemble global force vector due to body force,
15.3
2
bF
5.25 8.9
120.2836
9.00
3.75 6.4
28. b) Due to traction force, T = 36 lb/ft
element 1
1
2
3612
T(1)
12
1
18
1 1
element 2
1
2
3612
T(2)
12
1
18
1 1
Assemble global force vector due to traction force,
1 18
FT 182 36
1 18
29. c) Due to concentrated load, P = 100 lb at node 2
0
FP 100
0
6. Assemble all element force vectors to form the globalforce
vector for the entire structure.
lb
8.918 0 26.9
F 15.336100 151.3
24.46.4180
30. 12
0 3.75
Q1 26.9
30106
5.25
5.25 3.75 Q2 151.3
Q 24.4
5.25 0
9.00
3.75 3
7. Write system of linear equations (SLEs) for entire model
The SLEs can be written in condensed matrix form as
KQF
Expanding all terms and substituting values, we get
Note:
1. The global force term includes the unknown reaction force R1 at
the support. But it is ignored for now.
2. The SLEs have no solutions since the determinant of [K] = 0;
Physically, the structure moves around as a rigid body.
31. 8. Impose boundary conditions (BCs) on the global SLEs
There are 2 types of BCs:
a) Homogeneous = specified zero displacement;
b) Non-homogeneous = specified non-zero displacement.
In this example, homogeneous BC exists at node 1.
How to impose this BC on the global SLEs?
DELETE ROW AND COLUMN #1 OF THE SLEs!
12
0 3.75
5.25 5.25 0 Q1 26.9
30106
5.25 3.75Q2 151.3
Q 24.4
9.00
3.75 3
32. 30106
2
9.00 3.75 Q 151.3
12 3.75 3.75 Q3 24.4
Solve using Gaussian elimination method, yields
2
in
5
Q 1.33910
5
Q3 1.59910
9. Solve the reduced SLEs for the unknown nodal
displacements
The reduced SLEs are,
Quiz: Does the answers make sense? Explain…
33. 10. Estimate stresses in each elements
1q
le
(e)
EBq E
1
1 1
q2
element 1
0
12
1
1 30106
1
1
33.48 psi
1.339105
element 2
12
5
11.33910
2
30106
1
1
6.5psi
1.599105
Recall,
34. 12
0
5
5.25 26.9 R1
30106
5.25 3.75 1.33910 151.3
24.4
5.25 0 0
9.00
3.75
3.75 1.599 105
6
1
0
12
R
3010
5.25 5.25 01.339105
26.9334
1.599105
R1 202.68lb
11. Compute the reaction force R1 at node1
We now include the reaction force term in the global SLEs.
From the 1st. equation we get,
We have,