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"Application of Finite Element Analysis"

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The finite element analysis (FEA) also known as finite element method (FEM) is a numerical analysis technique for obtaining approximate solutions to a wide variety of engineering problems. A finite element model of a problem gives a piecewise approximation to the governing equations. The basic premise of the FEM is that a solution region can be analytically modelled or approximated by replacing it with an assemblage of discrete elements (discretization). Since these elements can be put together in a variety of ways, they can be used to represent exceedingly complex shape. With the advancement in the computational power of modern computers, this field is gaining more and more recognition. Specific attention is devoted to its application in the field of Civil Engineering, Aeronautical Engineering, Mechanical engineering and other related fields. Furthermore, the related works in Bio-Mechanics is also included with special attention on Dental Implants. In addition, its application in other wide range of problem is described briefly which will lead to a better understanding of the applications of this potentially high impact field of engineering.
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A | Department of Civil Engineering
SEMINAR REPORT
Application of Finite Element Analysis
A SEMINAR REPORT
submitted to
SSM COLLEGE OF ENGINEERING
By
Farhaan Zaidi Bhat
In Partial Fulfilment for The Award of The Degree of
BACHELOR OF ENGINEERING
In
CIVIL ENGINEERING
Department of Civil Engineering
SSM COLLEGE OF ENGINEERING
DIVAR, PARIHASPORA, PATTAN
January 2021
B | Department of Civil Engineering
SEMINAR REPORT
SSM COLLEGE OF ENGINEERING
DIVAR, PARIHASPORA, PATTAN
CERTIFICATE
This is to certify that the seminar report entitles "Application of Finite
Element Analysis" submitted to Department of Civil Engineering, SSM
College of Engineering, Divar, Parihaspora, Baramulla, in partial fulfilment for
the award of Bachelor’s Degree in Civil Engineering is a Bonafide record of
student namely Farhaan Zaidi Bhat bearing college En. No. 6807 &
University En. No. 17201135002 of BTech Civil 7th Semester (Batch 2017).
Er. Syed Tahir
Seminar Guide/Coordinator
Er Shabina Masoodi
H.O.D (Department of Civil Engineering)
Department Seal: Dated:
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SEMINAR REPORT
DECLARATION
I declare that the work which is being presented in the Seminar Report titled
“Application of Finite Element Analysis” submitted to the Department of Civil
Engineering, SSM College of Engineering, Parihaspora, Pattan is an authentic
record of my work carried out during 7th Semester.
I further declare that we have not submitted the matter presented in this seminar
anywhere for the award of any other Degree.
FARHAAN ZAIDI BHAT
Enroll: - 6807
D | Department of Civil Engineering
SEMINAR REPORT
ACKNOWLEDGEMENT
I take this opportunity to express my gratitude and thanks to the respected
Er Shabina Masoodi, H.O.D, Department of Civil Engineering. SSM College of
Engineering for her valuable technical suggestions and constant encouragement
without which this paper would not have come into existence. I'm thankful for
her time, support and mentorship which has shaped my abilities as an engineer
and a researcher.
I am especially thankful to Er. Syed Tahir, Department of Civil Engineering
SSM College of Engineering, Parihaspora, Pattan for his time to train, much
remarks valuable guidance.
All of this would have not been possible without the constant support and
encouragement of my family and friends.
FARHAAN ZAIDI BHAT
Enroll: - 6807
E | Department of Civil Engineering
SEMINAR REPORT
Contents
Abstract……………………………………………………………… 01
Introduction…………………………………………………………. 01
Partial Differential Equations
FEM Principle of Energy Minimization
History………………………………………………………………...04
Technical Overview of FEM…………………………………………05
Weak Form
Discretization
Solvers
FEA in Civil Engineering…………………………………………....08
Structural Engineering
Geotechnical Engineering
FEA in Mechanical Engineering…………………………………....18
Design Analysis
Structural Analysis
FEA in Aerospace Engineering……………………………………..23
Design Optimization
FEA in Bio-Mechanics……………………………………………....30
Dental Implants
Other Areas………………………………………………………….34
Bridge Design Optimization
Groundwater Hydrology
Manufacturing Design of Sports Equipment
Design of Musical Instruments
Conclusion………………………………………………………… ..37
Reference…………………………………………………………....38
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SEMINAR REPORT
ABSTRACT
The finite element analysis (FEA) also known as finite element method (FEM) is
a numerical analysis technique for obtaining approximate solutions to a wide
variety of engineering problems. A finite element model of a problem gives a
piecewise approximation to the governing equations. The basic premise of the
FEM is that a solution region can be analytically modelled or approximated by
replacing it with an assemblage of discrete elements (discretization). Since these
elements can be put together in a variety of ways, they can be used to represent
exceedingly complex shape.
With the advancement in the computational power of modern computers, this
field is gaining more and more recognition. Specific attention is devoted to its
application in the field of Civil Engineering, Aeronautical Engineering,
Mechanical engineering and other related fields. Furthermore, the related works
in Bio-Mechanics is also included with special attention on Dental Implants. In
addition, its application in other wide range of problem is described briefly which
will lead to a better understanding of the applications of this potentially high
impact field of engineering.
INTRODUCTION
The finite element method (FEM) is a numerical technique used to perform finite
element analysis (FEA) of any given physical phenomenon.
It is necessary to use mathematics to comprehensively understand and quantify
any physical phenomena, such as structural or fluid behaviour, thermal transport,
wave propagation, and the growth of biological cells. Most of these processes are
described using partial differential equations (PDEs). However, for a computer
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to solve these PDEs, numerical techniques have been developed over the last few
decades and one of the most prominent today is the finite element method.
The finite element method started with significant promise in the modelling of
several mechanical applications related to aerospace and civil engineering. The
applications of the finite element method are only now starting to reach their
potential. One of the most exciting prospects is its application in coupled
problems such as fluid-structure interaction, thermomechanical, thermochemical,
thermo-chemo-mechanical problems, biomechanics, biomedical engineering,
piezoelectric, ferroelectric, and electromagnetics.
There have been many alternative methods proposed in recent decades, but their
commercial applicability is yet to be proved.
Partial Differential Equations:
Firstly, it is important to understand the different genre of PDEs and their
suitability for use with FEM. Understanding this is particularly important to
everyone, irrespective of the motivation for using finite element analysis. It is
critical to remember that FEM is a tool and any tool is only as good as its user.
Fig. 01: Laplace equation on an annulus. Image by Fourtytwo [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], via
Wikimedia Commons.
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PDEs can be categorized as elliptic, hyperbolic, and parabolic. When solving
these differential equations, boundary and/or initial conditions need to be
provided. Based on the type of PDE, the necessary inputs can be evaluated.
Examples for PDEs in each category include the Poisson equation (elliptic),
Wave equation (hyperbolic), and Fourier law (parabolic).
There are two main approaches to solving elliptic PDEs, namely the finite
difference methods (FDM) and variational (or energy) methods. FEM falls into
the second category. Variational approaches are primarily based on the
philosophy of energy minimization.
Hyperbolic PDEs are commonly associated with jumps in solutions. For example,
the wave equation is a hyperbolic PDE. Owing to the existence of discontinuities
(or jumps) in solutions, the original FEM technology (or Bubnov-Galerkin
Method) was believed to be unsuitable for solving hyperbolic PDEs. However,
over the years, modifications have been developed to extend the applicability of
FEM technology.
Before concluding this discussion, it is necessary to consider the consequence of
using a numerical framework that is unsuitable for the type of PDE. Such usage
leads to solutions that are known as “improperly posed.” This could mean that
small changes in the domain parameters lead to large oscillations in the solutions,
or that the solutions exist only in a certain part of the domain or time, which are
not reliable. Well-posed explications are defined as those where a unique solution
exists continuously for the defined data. Hence, considering reliability, it is
extremely important to obtain well-posed solution.
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FEM Principle of Energy Minimization:
How does FEM work? What is the primary driving force? The principle of
minimization of energy forms the primary backbone of the finite element method.
In other words, when a particular boundary condition is applied to a body, this
can lead to several configurations but yet only one particular configuration is
realistically possible or achieved. Even when the simulation is performed
multiple times, same results prevail. Why is this so?
Fig. 02: Depiction of the principle of virtual work
This is governed by the principle of minimization of energy. It states that when a
boundary condition (like displacement or force) is applied, of the numerous
possible configurations that the body can take, only that configuration where the
total energy is minimum is the one that is chosen.
HISTORY
Technically, depending on one’s perspective, FEM can be said to have had its
origins in the work of Euler, as early as in the 16th century. The first efforts to use
piecewise continuous functions defined over triangular domains appear in the
applied mathematics literature with the work of Schellback [1851] and Courant
[1943]. Courant developed the idea of the minimization of a functional using linear
approximation over sub-regions, with the values being specified at discrete points
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which in essence become the node points of a mesh of elements. FEM was
independently developed by engineers to address structural mechanics problems
related to aerospace and civil engineering. The developments began in the mid-
1950s with the papers of Turner, Clough, Martin, and Topp [1956] (in a paper on
plane elasticity problems), Argyris [1957], and Babuska and Aziz [1972]. The
books by Zienkiewicz [1971] and Strang, and Fix [1973] also laid the foundations
for future development in FEM.
Technical Overview of Finite Element Method
Weak Form:
One of the first steps in FEM is to identify the PDE associated with the physical
phenomenon. The PDE (or differential form) is known as the strong form and
the integral form is known as the weak form. Consider the simple PDE as
shown below. The equation is multiplied by a trial function v(x) on both sides
and integrated with the domain [0,1].
Now, using integration of parts, the LHS of the above equation can be reduced
to
As it can be seen, the order of continuity required for the unknown function u(x)
is reduced by one. The earlier differential equation required u(x) to be
differentiable at least twice while the integral equation requires it to be
differentiable only once. The same is true for multi-dimensional functions, but
the derivatives are replaced by gradients and divergence.
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Without going into the mathematics, the Riesz representation theorem can prove
that there is a unique solution for u(x) for the integral and hence the differential
form. In addition, if f(x) is smooth, it also ensures that u(x) is smooth.
Discretization:
Once the integral or weak form has been set up, the next step is the
discretization of the weak form. The integral form needs to be solved
numerically and hence the integration is converted to a summation that can be
calculated numerically. In addition, one of the primary goals of discretization is
also to convert the integral form to a set of matrix equations that can be
solved using well-known theories of matrix algebra.
Fig 03: Meshing of a simple beam
As shown in Fig. 03, the domain is divided into small pieces known as
“elements” and the corner point of each element is known as a “node”
The unknown functional u(x) are calculated at the nodal points. Interpolation
functions are defined for each element to interpolate, for values inside the
element, using nodal values. These interpolation functions are also often
referred to as shape or ansatz functions. Thus the unknown functional u(x) can
be reduced to
where nen is the number of nodes in the element, Ni and ui are the interpolation
function and unknowns associated with node i, respectively. Similarly,
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interpolation can be used for the other functions v(x) and f(x) present in the
weak form, so that the weak form can be rewritten as
The summation schemes can be transformed into matrix products and can be
rewritten as:-
The weak form can now be reduced to a matrix form [K]{u} = {f}
Note above that the earlier trial function v(x) that had been multiplied does not
exist anymore in the resulting matrix equation. Also here [K] is known as the
stiffness matrix, {u} is the vector of nodal unknowns, and {R} is the residual
vector. Further on, using numerical integration schemes, like Gauss or Newton-
Cotes quadrature, the integrations in the weak form that forms the tangent
stiffness and residual vector are also handled easily.
A lot of mathematics is involved in the decision of choosing interpolation
functions, which requires knowledge of functional spaces (such as Hilbert and
Sobolev.
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Solvers:
Once the matrix equations have been established, the equations are passed on to
a solver to solve the system of equations. Depending on the type of problem,
direct or iterative solvers are generally used.
FEA in Civil Engineering
Finite element analysis (FEA) is an extremely useful tool in the field of civil
engineering for numerically approximating physical structures that are too
complex for regular analytical solutions. Within the fields of structural and civil
engineering, there are several such problems where FEA can be used to simplify
a structure and understand its overall behaviour. As the field of computer-aided-
engineering (CAE) has advanced, so have FEA tools, with tremendous benefit to
the civil engineering sector. The use of advanced FEA tools has not only led to
more innovative and efficient products but also furthered the development of
accurate design methods and determining material properties and behaviour.
Structural Engineering:
Structural analysis involves determining the behaviour of a structure when it is
subjected to loads, such as those resulting from gravity, wind, or even in extreme
cases natural disasters (e.g., earthquakes). Using basic concepts of applied
mathematics, any built structure can be analysed buildings, bridges, dams or
even foundations.
Originally, civil engineers used laboratory experiments to solve these design
problems, especially in regards to the behaviour of the steel structures when
subjected to high wind loads and earthquakes. However, such reliance on
laboratory testing was costly and not immediately accessible. Thus, structural
codes were developed. These codes made it easier for engineers to define what
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sort of behaviour was acceptable and safe for standard structures. However, with
the recent advent of accessible CAE tools, designing, testing and guaranteeing
the safety of an innovative building project and its materials has become easier,
faster, and significantly cheaper.
Consider the example of steel structure as follows:
Fig 4: Steel Structure
FEA is super useful in case of designing beam steel structures. Every now and
then, there is a joint which is difficult to be calculated by hand. Moreover,
Accurate analysis of the connection is difficult due to the number of connection
components and their inherit non-linear behaviour. The bolts, welds, beam and
column sections, connection geometry and the end plate itself can all have a
significant effect on connection performance. Any one of these can cause
connection failure. The most accurate method of analysis is of course to fabricate
full scale connections and test these to destruction. Unfortunately, this is time
consuming, expensive to undertake and has the disadvantage of only recording
strain readings at pre-defined gauge locations on the test connection. A three
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dimensional materially non-linear finite element analysis approach has therefore
been developed as an alternative method of connection appraisal.
The test performed in the laboratory are simulated in any FEA software. Based
on the test conditions, the results obtained through the finite element analysis
yield similar results wrt Actual test in terms of material properties, behaviour and
test results.
Fig 5: Actual Testing Frame Fig 6: Steel Joint Representation
ABAQUS, ANSYS, SIMSCALE and other similar FEA software can be used for
the finite element analysis. The FEA models can be created using command files
but the CAD interface tools are preferred. FEA models can often be a black box
that provides answers without the user being fully aware of what the model
exactly entails. Therefore, the user must be knowledgeable in the domain. The
technique of FEA lies in the development of a suitable mesh arrangement. The
mesh discretisation must balance the need for a fine mesh to give an accurate
stress distribution and reasonable analysis time. The optimal solution is to use a
fine mesh in areas of high stress and a coarser mesh in the remaining areas. To
further reduce the size of the model file and the subsequent processing time
symmetry can be employed.
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Figure 7 shows a FEA model with the final arrangement of mesh discretisation.
Figure 8 shows the FEA supports and loading.
Fig 9: FEA Model
Figure 9 shows the FEA Model of the Beam. It can be seen that the beam
experiences greater stress near the joint due to application of load that the rest of
the structure. Finite element analysis is even helpful in predicting the deformation
of the structure. In the following figure, the deformation of the structure can be
seen at the bolt prior to its failure and the corresponding FEA Mesh Model which
predicts the deformation quite accurately.
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Fig 10: FEA deformed Mesh Model Fig 11: Test Structure prior to Bolt Failure
The results are observed to be consistent with the actual results obtained and
hence the finite element analysis can be used to simulate the loading condition
and obtain test result which makes this method of analysis easier, faster, and
significantly cheaper.
Geotechnical Engineering:
1) Soil Structure Interaction: - The soil-structure interaction can be defined
as the process in which the response from the soil influences the motion of the
structure and the motion of the given structure affects the response from the
soil. This is a phenomenon in which the structural displacements and the
ground displacements are interdependent on each other. The study of soil-
structure interaction (SSI) is related to the field of earthquake engineering. It
is very important to note that the structural response is mainly due to the soil-
structure interaction forces that brings an impact on the structure. This is a
form of seismic excitation. SSI is a function of following: -
· Stiffness of the structure relative to the stiffness of the soil.
· Height or slenderness of the structure relative to footing width.
· Mass of the structure relative to the mass of the soil supporting the footing.
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Soil-structure interaction is useful in case of stiff structures on soft soil. Soft
soil sediments can significantly elongate the period of seismic waves and the
increase in natural period of structure may lead to the resonance with the long
period ground vibration. Additionally, the ductility demand can significantly
increase with the increase in the natural period of the structure due to SSI
effect. The permanent deformation and failure of soil may further aggravate
the seismic response of the structure. The impact of SSI can be evaluated by
the Traditional Methods (Winkler Model) as well as the numerical model but
results show that traditional methods significantly underestimate the soil
rigidity, producing almost half of the differential settlement elements that are
obtained by modelling the soil as 3D solid elements.
Fig 12: Comparison between Traditional and Finite Element Analysis
The picture on the left describes the SSI using Winklers Model done in Midas
Civil and the right picture describes the SSI using Finite Element Analysis
using GTS NX. The corresponding value of the displacements have a large
variation with FEA Model being more accurate.
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2) Stability of Slopes:-Slope stability analysis is an important area in
geotechnical engineering. There are several methods of slope stability
analysis. A detailed review of equilibrium methods of slope stability analysis
is presented by Duncan (Duncan, 1996). These methods include the ordinary
method of slices, Bishop’s modified method, force equilibrium methods,
Janbu’s generalized procedure of Slices, Morgenstern and Price’s method and
Spencer’s method. These methods, in general, require the soil mass to be
divided into slices. The directions of the forces acting on each slice in the slope
are assumed. This assumption is a key role in distinguishing one limit
equilibrium method from another. Limit equilibrium methods require a
continuous surface passes the soil mass. This surface is essential in calculating
the minimum factor of safety (FOS) against sliding or shear failure. Before the
calculation of slope stability in these methods, some assumptions, for example,
the side forces and their directions, have to be given out artificially in order to
build the equations of equilibrium. With the development of cheaper personal
computer, finite element method has been increasingly used in slope stability
analysis. The advantage of a finite element approach in the analysis of slope
stability problems over traditional limit equilibrium methods is that no
assumption needs to be made in advance about the shape or location of the
failure surface, slice side forces and their directions. The method can be
applied with complex slope configurations and soil deposits in two or three
dimensions to model virtually all types of mechanisms. General soil material
models that include Mohr-Coulomb and numerous others can be employed.
The equilibrium stresses, strains, and the associated shear strengths in the soil
mass can be computed very accurately. The critical failure mechanism
developed can be extremely general and need not be simple circular or
logarithmic spiral arcs. The method can be extended to account for seepage
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induced failures, brittle soil behaviours, random field soil properties, and
engineering interventions such as geo-textiles, soil nailing, drains and
retaining walls (Swan et al, 1999). This method can give information about
the deformations at working stress levels and is able to monitor progressive
failure including overall shear failure (Griffiths, 1999). Generally, there are
two approaches to analyse slope stability using finite element method. One
approach is to increase the gravity load and the second approach is to reduce
the strength characteristics of the soil mass.
The following Model was analysed using Phase2 software and the
corresponding Meshed and FEA analysed modelled are shown.
Fig 12 d shows the variation in Factor of safety results between the limit
equilibrium methods and FEA Model analysed using Phase2 software. It is
seen that the variation in results is less than 5%.
a) Model to be analysed b) Meshed Model (using T6 Mesh)
c) FEA Model d) Results
Fig 12: FEA of Slope for Stability
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Design of Pile Foundation: -Pile foundations are used as medium between
unstable soil and solid ground in order to initiate construction of solid structures
like building, pillar, etc. These pile foundations exhibit different behaviour in
different physical conditions and external factors. Hence, the pile foundation
behaviour has been a subject of research for a long time. Many researchers have
tested and used different research techniques for understanding the nature and
behaviour of pile foundation according to different external characteristics.
Different researchers used different external factors to analyse the change in the
behaviour of pile foundation with the change in the effect of external factors.
Again, different researchers used different techniques and methods for the
research purposes that have given different and nearly accurate results on the
behaviour of pile foundations. Gerolymos et al. used beam on Winkler foundation
model (BWF) for the analysis of pile foundations against static and dynamic
loading. They mainly based their research on the soil behaviour against deflecting
pile. They also analysed soil and interface non-linearities (slippage and separation
of the pile from the soil), frequency-dependent visco-plastic response (radiation
damping) and cyclic hysteretic soil behaviour during a dynamic pile-soil
interaction. Similar studies can be done using finite element analysis in order to
calculate the response of pile foundation upon application of different loads and
help in design optimization.
Fig 13: Design optimization of Pile Foundation
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Consolidation of Soil: -The compression of saturated soil under steady static
pressure is termed as consolidation which is completely due to expulsion of water
from the voids. Consolidation is generally related to fine-grained soils such as
silts and clays. Coarse-grained soils, such as sands and gravels, also undergo
consolidation but at a much faster rate due to their high permeability. Saturated
clays consolidate at a much slower rate due to their low permeability.
Consolidation is a time-related process of increasing the density of a saturated
soil by draining some of the water out of the voids. Consolidation theory is
required for the prediction of both the magnitude and the rate of consolidation
settlements to ensure the serviceability of structures founded on a compressible
soil layer. The effects of consolidation are most conspicuous where a building sits
over a layer of soil with low stiffness and low permeability, such as marine clay,
leading to large settlement over many years. Consolidation analysis using
nonlinear finite element method is performed to study the behaviour of a footing
resting on soil mass. Noded isoparametric plane strain element with translational
degrees of freedom can be used to model the soil deformation. Pore pressure can
be modelled using noded isoparametric element. Behaviour of soil maybe
considered as nonlinear and can be modelled using the hyperbolic relationship
proposed by Duncan and Chang. The displacement of footing and pore pressure
in soil are coupled and the resulting equations are solved to obtain the
displacement of soil and footing and pore pressure in soil at various time interval.
The analysis is used to model the laboratory consolidation test with double
drainage. The displacement obtained from the analysis are compared with the
displacement obtained from the laboratory consolidation test. The applicability
of the analysis is also demonstrated to study the behaviour of a strip footing
resting on soil mass.
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Fig 14: Consolidation analysis using FEA
FEA in Mechanical Engineering
Perhaps, the field in which Finite element analysis is most widely used is the
Mechanical and Aerospace engineering. From Crash analysis to thermal analysis,
Mechanical engineering exploits all the aspects of Finite element analysis. The
Finite Element Analysis (FEA) has been widely implemented by automotive
companies and is used by design engineers as a tool during the product
development process. Design engineers analyse their own designs while they are
still in the form of easily modifiable CAD models to allow for quick turnaround
times and to ensure prompt implementation of analysis results in the design
process. While FEA software is readily available, successful use of FEA as a
design tool still requires an understanding of FEA basics, familiarity with FEA
process and commonly used modeling techniques, as well as an appreciation of
inherent errors and their effect on the quality of results. When used properly, the
FEA becomes a tremendous productivity tool, helping design engineers reduce
product development time and cost. Misapplication of FEA however, may lead
to erroneous design decisions, which are very expensive to correct later in the
design process.
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Design:
Finite element analysis can generate realistic results that help scientists and
engineers understand the way that cars are affected by different crash scenarios
and help them optimise the design the cars. Instead of running real life situations,
it is much more cost effective to simulate car crash using a commercial software.
With the development of commercial software, engineers can use computer to
simulate real life scenarios, estimate the outcomes, and develop new design
technology to help save lives in the events of car crashes or similar situations.
Safety is one of the design considerations in automobile community. Therefore,
crash test is an important step to validate the novel car design. However, high cost
in experimental testing limits the number of crash tests, and adequate data might
not be obtained consequently. Alternatively, numerical modelling and simulation
have been widely used to study car crash in addition to experimental testing. As
a powerful numerical tool, finite element method (FEM) plays an vital role in
crash test simulations. Scientists have developed a numerical model for the
computer simulation of car crash analysis. They can analyse crash situations at
different speeds and different scenario. A high-speed vehicle crashing into a wall
and a high-speed test vehicle crashing into a static vehicle.
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The research objective is to identify the sources of harm to driver and passengers
when car crashes occur. On the other hand, the major concern in design of bumper
is its potentiality to bear impact loads. Numerical simulations are also normally
used to assure a bumper design to meet the safety requirements. Scientists have
also employed an explicit FEM to investigate stress and effective plastic strain of
bumper at impact. They recommended modifications in bumper design to
improve its impact performance based on the simulation results. In addition,
analysis can be carried out using CAE simulation with high performance
computing techniques.
Suppose for a full-scale testing we require 1000 cars. Instead of crashing 1000
cars, Finite element analysis allows us to test a lot less no. of cars obtaining
similar results as would have been obtained with full-scale testing. The test cars
used may now reduce to only 100 or few thus helping in cost reduction. The test
data that is required for the design improvement can be obtained using reduced
full-scale test performed and the same data is fed to the computer. The data
obtained helps in simulating the test virtually and helps in reducing cost, the time
required for full-scale testing and provides more versatility overall.
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The crash analysis is performed for following scenarios:
Frontal Rear
Side Rollover crashes
In automobile design, apart from crash analysis, structural analysis is the other
most important engineering processes in developing a high quality vehicle. Safety
engineers design and manufacture vehicle body structures to withstand static and
dynamic service loads encountered during the vehicle life cycle. The vehicle body
provides most of the vehicle rigidity in bending and in torsion. In addition, it
provides a specifically designed occupant cell to minimize injury in the event of
crash. The vehicle body together with the suspension is designed to minimize
road vibrations and aerodynamic noise transfer to the occupants. In addition, the
vehicle structure is designed to maintain its integrity and provide adequate
protection in survivable crashes. The automobile structure has evolved over the
last ten decades to satisfy consumer needs and demands subject to many
constraints. Among these constraints are materials and energy availability, safety
regulations, economics, competition, engineering technology and manufacturing
capabilities. Current car body structures and light trucks include two categories:
body-over-frame structure or unit-body structure. The latter designation includes
space-frame structures.
Unibody Construction: Most vehicles today are manufactured with a Unitized
Body/Frame (Unibody) construction. This is a manufacturing process where
sheet metal is bent and formed then spot welded together to create a box which
makes up the structural frame and functional body of the car. These vehicles have
"crumple Zones" to protect the passengers in case of a collision.
Body-on-Frame Construction: Most heavy-duty trucks and a few premium full-
size cars are still manufactured with a body-on-frame construction. This is a
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manufacturing process which a weight-bearing frame is welded together and then
the, engine, driveline, suspension, and body is bolted to the frame. In an accident,
the Unibody frame is designed to "crumple" and absorb the energy of an impact
better than a Body-on-Frame construction. The chassis frame supports the engine,
transmission, power train, suspension and accessories. In frontal impact, the
frame and front sheet metal absorb most of the crash energy by plastic
deformation. The three structural modules are bolted together to form the vehicle
structure. The vehicle body is attached to the frame by shock absorbing body
mounts, designed to isolate from high frequency vibrations. Unibody vehicles
combine the body, frame, and front sheet metal into a single unit constructed from
stamped sheet metal and assembled by spot welding or other fastening methods.
The construction of the unit body structure, also known as unit-frame-and-body
or frame-less body, is claimed to enhance whole vehicle rigidity and provide for
weight reduction.
Fig 15: Fluid flow over bike
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FEA in Aerospace Engineering
The concept of Finite Element Analysis was actually first developed for
Aerospace Engineering and then subsequently applied to other fields. Around
1950’s, the Aerospace companies began solving structural problem and since
then, with the advancement in computational power, been extensively used in
design optimization in Aerospace industry.
Aerospace parts must withstand extreme stress from a variety of forces, including
air pressure, inertia forces, or impact stresses during take-offs and landings.
Known as loads, these forces and moments can apply extreme stress to an
aircraft’s structural integrity. Aerospace parts must be able to continuously
withstand these stresses to keep the aircraft intact and their passengers safe
It’s not surprising then that aerospace manufacturing must abide to the strictest
of manufacturing requirements. One way that aerospace manufacturers ensure
their aircraft parts can stand these tests is through Finite Element Analysis (FEA)-
tested custom wire baskets. Following are some of the fields within aerospace
engineering where FEA is utilized:
Composite Structures FEA
Shock and Vibration FEA calculations
Durability and Fatigue Life Estimation
Modal Analysis and Frequency response calculations
Weight Reduction and Shape Optimization
Force estimations in Actuators, Mechanisms and Complex Mechanical
Devices
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Cooling and Thermal Management of Avionics, Electronic Cooling
Systems
Structural Strength and Buckling calculations
Non-Linear FEA of Elastomers and Composites
Stress calculations on components and sub-system.
Kinematic Analysis using Cosmos Motion for mechanisms such as landing
gear, door-closure, actuating levers, remotely controlled devices
Non-linear Simulation of Elastomers, Seals, Gaskets, re-inforced rubber
components for strains, performance, durability, sealing effectiveness,
pressure foot-print, deflections
Stiffness, Durability, Tri-axial / Random Vibration and Life estimation for
aerospace components such as mounts
Stiffness and strain calculations for Composite Panels
Life Calculations of safety systems
Fluid Flow calculations for valves, pumps, pressure-regulating devices
Fig 16: FEA simulation of Aircraft parts
Fatigue and Damage Tolerance:
Fatigue failure is a result of repeated stress application under cyclic loading
often way below yield stress levels. Conventional fatigue analysis identifies stress
concentration sites throughout the aircraft using linear static FEA analysis. This
can be done with detail models or downstream assessment of a loads model.
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The loading mechanism and history applied at the sites are critical, and require
careful identification of how compressive, tensile or shear stress states combine.
Vibration fatigue analysis may be required on components that see significant
dynamic response, such as engine pylons and skins near jet efflux.
Fatigue analysis identifies sites in a structure where crack initiation is likely to
occur. The estimate of the fatigue life is based on empirical methods fitted to test
data. Fatigue analysis does not, by itself, predict any form of crack growth.
Damage tolerance assessment, on the other hand, can predict crack growth.
Potential crack initiation sites are identified, and various crack shapes and sizes
are assumed. Linear elastic fracture mechanics coupled with FEA solutions are
used to estimate crack growth. The principle is straightforward; however, the
challenge is in meshing a crack in a 2D shell or 3D solid model and then allowing
automatic re-meshing of the growing crack.
Damage tolerance assessment requires a high level of mesh refinement in a local
detail model. Specific sites of interest have to be selectedthere is no overall
process to sweep through a complete aerospace model.
Loads Derivation:
Loading environments vary considerably across aerospace applications. Military
aircraft sustain high G maneuvers across all corners of the flight envelope. Also,
there may be many variations in external payload and fuel state that have to be
assessed, with particular dynamic environments from gunfire or store ejection.
The critical cases for civil aircraft include gust response and dynamic landing.
Variations of payload and fuel state must be accounted forand each possible
phasing and positioning of the aircraft in the gust and landing conditions has to
be assessed. There may be hundreds of thousands of load cases to be used in
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assessment of the structural integrity of all components of aircraft. The sheer
quantity of load cases demands specific processes to handle this volume of data
and stress analysis.
Launcher and satellite structures see high inertial loading during the launch. This
occurs together with a harsh dynamic environment, with random vibration
loading forces being transmitted from the rocket motors up through the structure.
A great deal of effort is spent on ensuring strength and fatigue life.
Aerospace vehicles are subject to aerodynamic loading. Until fairly recently,
most of the loading data was calculated from wind tunnel results or well proven
classical solutions. As structural configurations have become more complex and
performance requirements more demanding, however, a need for greater fidelity
in aerodynamic calculations has evolved: Computational fluid dynamics (CFD)
now plays a vital role in modern aerodynamic simulation and loads derivation.
For initial calculations, a wing or control surface is assumed to be rigid under
aerodynamic loading. However, the wing is flexible and will change its
configuration with resultant perturbation of aerodynamic loading until a balanced
state is reached. Steady aeroelastic FEA calculates this interaction, and allows a
modified aerodynamic loading distribution to be used.
Unsteady aeroelastic analysis calculates the dynamic interaction between an
oscillating airflow and a vibrating control surface. A search is carried out for
critical flutter modes across the aircraft flight envelope. (Flutter is an extremely
dangerous phenomenon, and is usually catastrophic.)
Both steady and unsteady aeroelastic analysis traditionally used linear structural
analysis, basic aerodynamic panel methods and simple load models to develop
the required dynamic interaction. However, these methods cannot deal well with
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structural non-linearity, complex 3D vehicle shapes, transonic flow or highly
localized flow.
There is now a move to couple more accurate CFD calculations with structural
calculations using fluid structure interaction (FSI) methods. UAVs can have
highly flexible wings and FSI permits coupling non-linear structural analysis with
CFD. The main issue here, however, is that the CFD calculations are expensive
compared to structural calculations.
Thermal loading and analysis are required for structures near engines, rocket
motors, etc., as well as kinetic heating of the airframe from high-speed flight.
This may be done fully within an FEA solution, or an independent thermal
solution may be mapped or coupled to the structural FEA.
Composites:
The biggest change in aircraft design over the past 20 years has been the dramatic
increase in the use of composites for primary structures. Test programs and
techniques have developed to provide the supporting evidence for strength and
stiffness assessment. Similarly, simulation methods have evolved to handle a new
type of structure (see Fig. 3). This has been a steady evolution from classical
laminate theory mapped into thin shell applications.
This works well for continuous structures such as wing and fuselage skins.
However, for joints and more complex (and typically, heavier) fittings, local
effects become important in a composite layup. In this case, 3D solid elements
are used that allow full interlaminar and through-thickness effects to be
simulated. Failure modes such as delamination and interlaminar shear would
otherwise be missed.
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Fig. 17: A 3D solid composite.
The actual failure mode of a composite structure can be a challenge to assess.
Even a simple coupon test, subject to compression and shear, results in complex
microlevel failure that is not well represented by traditional failure theories. If the
real structure is a skin-to-stringer joint at the edge of a panel, it can be difficult to
predict failure. FEA techniques are evolving along several fronts to try and deal
with these situations.
Phenomenological failure criteria attempt to predict distinct failure modes that
are strongly dependent on loading action. These replace the more traditional
failure criteria. For example:
Progressive ply failure degrades the stiffness properties of plies within a layup to
allow a more gradual loss of strength as load is increased.
Cohesive zone elements attempt to model the bond line failure between plies,
using local bond separation forces and displacements.
Virtual crack closure technique (VCCT) methods model bond line and possibly
ply matrix failure using a fracture mechanics approach, to assess crack
propagation under loading history.
Micromechanics analysis of failure modes in localized regions is mapped to the
global FEA model to improve the fidelity of the failure modeling.
New Analysis Areas:
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Fig. 18: Management-based Design for Environment (MbDfE) co-simulation of a wing flap mechanism.
In addition, there are structural analysis techniques becoming increasingly
important within the aerospace industry, including:
Multi-body dynamics analysis (MBDA) deals with mechanisms made up of
rigid components. The technology has been extended so that flexible bodies
created from FEA can be coupled into the MBDA. In the past, structures such as
flaps were analysed in separate configurations. With MBDA, multiple
configurations can be introducedas well as the dynamic interaction with the
surrounding structure. Whole vehicle applications in gust or dynamic landing
scenarios look promising.
Non-linear analysis has not traditionally been used, as structures are expected to
show adequate margin over limit conditions. However, in the drive for ever-
lighter structures combined with the strength-to-weight ratio of composites, post-
buckling analysis of structures that are allowed to develop wrinkles or moderate
buckling below limit load is being explored. Some radical designs of UAV, space
sails, etc., require large deformation analysis, for example.
The biggest changes in aerospace analysis are linked to the growth of composites.
However, the tremendous growth in computing speed and power is allowing a
steady increase in the number of highly detailed local models of aircraft
structures.
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One of the biggest challenges is to be able to harness this level of model fidelity,
and use it effectively within the traditional strength assessment requirement for
the whole vehicle structure. At some point in the future, there will be a migration
to solid-element, full-vehicle modeling that will require a rethink of the whole
process.
FEA in Bio-Mechanics
Since the discovery of dental implants by Brainmark 1969 it has become a ground
breaking reality, of the use of dental implants for replacing a missing tooth.
Dental implants have become an inseparable part of dental practice and its use in
recent years has increased in leaps and bounds. Clinical success of dental implant
mainly depends on its biomechanical behaviour as the pattern of stress
distribution in dental implants is completely different from that of a natural tooth.
Since the later has periodontal ligament which acts as a shock absorber to occlusal
forces. Success or failure of dental implant mainly depends on a key feature i.e
the manner in which stress is transferred from dental implant to the adjoining
alveolar bone. If the occlusal forces around a dental implant are distributed
homogenously then the bone is maintained well. When we look into the literature
several attempts to preserve the marginal bone around dental implants has been
done. Contributing factors for marginal bone loss that have been accepted to some
degree are biological, clinical and mechanical factors. It is vital to understand the
biomechanical behaviour of bony tissues and dental implants in order to prevent
marginal bone loss and implant failure. In order to prevent implant failures and
complications due to mechanical and technical factors, these factors have to be
evaluated in advance. As a result use of these essential steps could increase the
survival rate of implant supported restorations. Hence, there has been a dramatic
increase in the number of biomechanical studies in the field of implant dentistry
in an effort to decrease dental implant failure rates.
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Fig a. Missing molar in the mandible Fig b. After flap elevation, the cortical bone is visible Fig c. Dental implant with an abutment
Fig d. Implant is placed in the ridge Fig e. Implant after 2 months of healing Fig f. Abutment is attached to the implant
Fig g. Porcelain-fused metal implant Fig h. Intraoral picture of a broken implant Fig I. Severe bone resorption
Figure j. Severe bone defect is seen after implant removal; advanced bone regeneration techniques are
needed to replace the implant
Research in different fields of Dentistry needs a methodology that is cost effective
and reproducible. Such an approach may perhaps be situated to guide researchers
in biomechanics structure in healthy and pathologic conditions. In bioengineering
field, the application of simulations introduced in recent years, certainly is a vital
instrument to measure the best clinical option, only if that it is precisely sufficient
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in investigation particular physiological conditions. Oral environment in
biomechanical research such as restorative dentistry, endodontics, orthodontics,
prosthodontics, periodontics, and Implantology has been performed in vitro since
the oral cavity is an intricate biomechanical system due to this complexity and
limited access. A non-invasive way to predict in vivo contact mechanics is done
mainly by using computerized modeling. To investigate stress distribution around
peri-implant bone various methods have been current explored. To name a few
we have photo elastic model, strain gauge analysis, and 3-dimensional finite
element model analysis (FEA). Due to availability of software and the ability to
determine 3D stresses and strains Finite Element Modeling (FEM) is considered
the most commonly used method. Initially, FEM was technologically innovated
which aimed at answering structural analysis difficulties involving Mechanics,
Civil and Aeronautical Engineering. FEM basically stands for a numerical model
of analysing stresses as well as distortions in the form of any agreed geometry.
Therefore, the shape is discretized into the so-called “finite elements‟ coupled
through nodes. Accuracy of the results is determined by type, planning and total
number of elements used for a particular study model.
Fig a. Implants are modeled with threads and abutments
Fig b. Mandible is modeled and region of interest is selected
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Fig c. Region of interest is extracted
Fig d. Part of the mandible modeled with superstructure, implant, and surrounding bone
Fig e. Implant, abutment, abutment screw, framework, and porcelain structure are modeled as 1
unit
Fig f. Static forces were applied at 30 degrees obliquely and separately to the lingual inclination
of the buccal cusps of the crown
Fig g. Force application to the region of restoration
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Historical Perspective R. Courant was a first researcher who developed this
technique. His main goal was to minimize the various calculative procedures to
gain absolute solution to bio-mechanical system. He used ritz method to solve
such numeric equations. Later in Turner et al. attempted to describe this method
by developing broader definition of these numeric analyses. Weinstein in 1976
used this technique in implant dentistry to evaluate various loads of occlusion on
implant and adjacent bone. Since then, evolution of this technique has been
observed in a very rapid and sophisticated scale in micro-computer as well as
analysis of large-scale structural system. Application of finite element analysis in
dentistry Meticulous quantifiable information on any place inside a mathematical
model can be provided by Finite element analysis (FEA). As a result, FEA has to
turn out to be a valued analytical instrument in the estimation of stress and strain
in implant systems. One of the salient characteristics of FEM rests in its near
physical similarity amongst the real structure as well as its FEM. However
unnecessary simplification in geometry shall invariably lead to inconsistent
results.
Other Areas
a) Bridge Design Optimization: The aims of structural analysis for bridges lie
at the optimization of design from engineering and sustainability perspectives and
visual appearance. Through consideration of location and number of support
midway between the bridge span, thickness of the span, quantity of concrete and
steel and other necessary elements for extreme loading condition, structural
engineers build structures of immense strength.
Validating of designs includes numerous calculations when done manually, but
with FEA behaviours of each layer of the structure is studied when subjected to
various physical phenomena in virtual environment. Say for instance upper layer
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of the span is under compression and lower layers undergo tensile stresses when
bridge is in sagging condition would include computing moments, stress and
various types of loads.
Though the same phenomena occurs in a beam of building, the analysis method
will differ, since the bridge components are subjected to outdoor extreme
conditions of temperature variation, reverse cycles of live loading and more
chances of corrosion. Thus, bridge structure requires an approach that addresses
adequate services and additional fatigue limits.
When this entire process is compared with traditional approach, one realizes how
sophisticated and detailed model based FEA approach is. Most of the challenges
and considerations during construction work are eliminated in initial stages
leaving engineers a better scope for design optimization.
b) Groundwater Hydrology:
Since its introduction into the groundwater literature during the mid-1960’s, the
finite element method has developed into a very powerful numerical tool for
analysing a variety of groundwater flow problems. Applications of the method
cover flow in multi-aquifer systems, flow with a free surface, saturated-
unsaturated flow, land subsidence, fractured-porous systems, and large
groundwater basins under steady or non-steady conditions. The method derives
its power from the fact that it uses a very general technique for the evaluation
of spatial gradients in any direction at any point within the flow domain. This
advantage is complemented in the method by an integral statement of the
conservation equation at the point of interest. The algorithms stemming from
this approach permit relatively simple geometric inputs, even when the problem
of interest has complex geometries. From a conceptual perspective there is
reason to suspect that alternate formulations of the finite element method may
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be possible in which the weighted integration technique is dispensed with in
favour of an explicit definition of the subdomains of integration. The flexibility
of existing finite element algorithms may be enhanced by having options for
inputting pre-processed geometric inputs in addition to nodal point coordinates
and element lists. Direct formulation of the finite element equations from
conservation integrals may provide an alternative that deserves attention. With
the advent of mini computers, the finite element method promises to become an
every day tool for the practising engineer during the 1980’s.
c) Manufacturing and Design of Sports Equipment:
The implementation of composite materials in the manufacturing of sporting
equipment has made participating in sports safer and the equipment associated
with them more durable. FEM can be used in designing of sports equipment like,
tennis racket, ice hockey stick, golf ball etc, and also building golf clubs and
stadiums. It plays a vital role in construction and design of equipment for sports
injuries such as nose protector, sports shoes and many others.
d) Design of Musical Instruments:
FEM is specifically powerful for dynamic and vibration analysis of musical
instruments like guitar design process, carving process of xylophone. It helps in
adjusting frequencies of modes when assembling and fine tuning stringed musical
instruments and hence developing the improved musical instruments. A FE model
can be used to design of a guitar neck system to address the problems like bending
and twisting of the neck due to string forces, moisture content expansion forces,
cylindrical orthotropic nature of wood and several other problems.
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CONCLUSION
Finite element analysis continues to grow each day with the advancement in the
computational power of modern computers. Since its usefulness from mid 1900’s,
it has shown enormous potential and promises to be employed in numerous more
fields in near future due to its high accuracy power, ease of application, economic
concept and versatility in analysis.
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  • Jagota Vishal
 Vishal Jagota, Amanpreet Singh Sethi, Dr. Khushmeet Kumar 2013.Finite