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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 Winkler’s 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 selected—there 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 for—and 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 introduced—as 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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Ajay Harish 2020.What is finite element method. Simscale Blog.

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Jim Butterworth Finite Element Analysis of Structural Steelwork Beam to

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T. Ananda Babu et al. 2012 Crash Analysis Of Car Chassis Frame Using

Finite Element Method International Journal of Engineering Research &

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