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General description of Finite
Element Method, Application and limitations
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Node
numbering, Half band width
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Definition of FEA
The finite element method is a numerical technique for solving problems which are described
by partial differential equations
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Its
practical application is often known as finite element analysis (FEA)
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Basic principle of FEM
In FEM, actual component is replaced by a simplified model, identified by a finite number of
elements connected at common points called node’s with an assumed behaviour or response
of each element to the set of applied load’s and evaluating the unknown field variable
(displacement, temperature) at these finite number of points
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Steps in FEA
1
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3
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5
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Discretization of Continuum
Selection of Displacement of Interpolation polynomial
Derivation of Element Stiffness Matrix
Assembly of Elemental Equations to obtain overall equilibrium equations
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Bharat Vinjamuri, B
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Bangalore

2015-16
As Per sixth
semester VTU
syllabus

Ph: +91 9986579555
Email: bharat_v79@yahoo
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

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Bharat Vinjamuri, B
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Bangalore

2015-16
As Per sixth
semester VTU
syllabus

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

2015-16
As Per sixth
semester VTU
syllabus

4
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b) Axial strain or Linear Strain or Primary Strain
Axial strain is defined as the ratio of change in length due to deformation to the
original length of the specimen denoted by “∈”
c) Lateral strain
Lateral strain or secondary strain is defined as the ratio of change in Lateral
dimension to original dimension of the body
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Almost all engineering materials
possess a certain amount of elastic property
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Bharat Vinjamuri, B
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Bangalore

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

2015-16
As Per sixth
semester VTU
syllabus

5
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b) Traction (T):– is defined as the force per unit area acting at a given location on the body
surface
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c) Point Load (P):– Load acting at a point
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Equations of equilibrium

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Bharat Vinjamuri, B
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,M
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S
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E (Ph
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, B
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M
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T
Bangalore

2015-16
As Per sixth
semester VTU
syllabus

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

Prof
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tech
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Bharat Vinjamuri, B
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,M
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E (Ph
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, B
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M
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T
Bangalore

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

2015-16
As Per sixth
semester VTU
syllabus

7
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Bharat Vinjamuri, B
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,M
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M
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T
Bangalore

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

Prof
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Plane Stress:
A thin plate subjected to in-plane loading acting in its own plane, the state of stress and
deformation within the plate is called plane stress
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Bharat Vinjamuri, B
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T
Bangalore

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

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Plane Strain

If a long body is subjected to transverse loading and its cross section and loading do not
vary significantly in the longitudinal direction, a small thickness in the loaded area can be
treated as subjected to plane strain
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Bharat Vinjamuri, B
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Bangalore

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

2015-16
As Per sixth
semester VTU
syllabus

A long cylinder under internal pressure

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Types of Elements

1D Elements

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Bharat Vinjamuri, B
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T
Bangalore

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

2015-16
As Per sixth
semester VTU
syllabus

3D Elements

Special Type of Elements

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Size of Elements
The size of elements influences the convergence of the solution

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Aspect Ratio

13
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Bharat Vinjamuri, B
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Bangalore

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

2015-16
As Per sixth
semester VTU
syllabus

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Banded Matrix or Half Band width

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Bharat Vinjamuri, B
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,M
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, M
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S
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E (Ph
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, B
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M
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T
Bangalore

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

•
•
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2015-16
As Per sixth
semester VTU
syllabus

Node numbering along the smallest dimension yields lower band width
Node numbering along the Longest dimension yields higher band width
Continuous node numbering scheme will yield better results than random node
numbering scheme
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Bharat Vinjamuri, B
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E (Ph
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, B
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T
Bangalore

Ph: +91 9986579555
Email: bharat_v79@yahoo
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N
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Institute of Technology
Department of Mechanical Engineering

FINITE ELEMENT ANALYSIS – 10ME64

2015-16
As Per sixth
semester VTU
syllabus

16
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Advantages of FEM
Complex problems can be solved easily
FEM can model irregular shaped bodies quite easily
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Can handle different types of boundary condition
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Can be used to solve all types of Engineering Problems
FEA model can be modified easily
The analysis can be simulated

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Non structural Problems
• Heat transfer (Thermal analysis)
• Temperature distribution in solids & fluids
• Fluid flow analysis
• Distribution of electric or Magnetic Potential
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Nuclear Engineering
• Analysis of Nuclear pressure vessels and reactors
• Steady state temperature distribution in reactor components
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• Stress analysis in soils, dams layered piles and machine foundations
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Computer Packages for FEM
o MSC Nastran
COSMOS
o Ansys
NISA
o ALGOR
ADINA
o LS- Dyna
FLUENT
o RADIOSS
HYPERWORKS

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2015-16
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FEM Vs Classical Method
In FEM, we can obtain approximate solutions for the exact equations formed, whereas
in classical methods exact equations are formed and exact solutions are obtained
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If structure consists of more than one material, it is difficult to use classical method,
but finite element can be used without any difficulty
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Only few simple cases have been tried successfully by
researchers
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FEM is superior to the classical methods in the sense that the problems which cannot
be tackled by classical methods without making drastic assumptions
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Finite Difference Method (FDM)
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2
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The element for mutation is mathematically exact whereas the
finite difference technique involves the exact representation of the continuum in terms of
the differential equation and on this actual physical system, the mathematical model is
approximated
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FDM needs larger number of nodes to get good results while FEM needs fewer nodes
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FDM does not give the value at any point except at node points
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FEM can give the values at the point
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5
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Continuity along the sides of grid lines are not ensured
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2015-16
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semester VTU
syllabus

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What is FEM? What are the advantages and limitations of the method? (8 M— June 12)
2
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Also state the stress –
strain relations for both
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Explain plane stress and plane strain cases with examples
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Write the general description of the finite element method
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Explain Node numbering scheme for a finite element mesh
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Write the equilibrium equation for 3-D state of stress and state the terms involved
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Explain the discretization process of a given domain based on element shapes number and
size
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Explain the basic steps involved in FEM, with the help of an example involving a
structural member subjected to axial load’s
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Why FEA is widely accepted in engineering? List various applications of FEA in
engineering
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Explain the discretization process
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1D, 2D, 3D
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(6 M — May/June 2010)

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Bring out the differences between Continuum method and Finite element method
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What do you understand FEM
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(10 M — December 2010)
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Explain briefly about node location system
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Explain Pre Processing and Post Processing in FEM
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Explain the basic steps involved in FEM
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Write Stress - Strain & Strain - Stress relations for plane stress problems (2D - elastic
body)

(10 M — Dec 08/Jan 09)

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(10 M — Dec 08/Jan 09)
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Briefly explain the following stages of FEA
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Mention the different software packages used for FEA
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Define the following
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Derive Strain displacement relations in 2 - dimensional Cartesian co-ordinate system
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Bring out the differences between Continuum methods of FEM
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What is finite element method? List the advantages and disadvantages of FEM over the
numerical method FDM
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What is Symmetric banded Matrix? State its advantages in FEM
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Derive the equilibrium equations of 3D elastic body subjected to surface forces
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What are the advantages and disadvantages of finite element method?(6 M — May 2007)
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(i) its structure (ii) Typical elements available
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(15 M May 07)
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What are its Merits?

(10 M — Jan/Feb 2006)
(4 M — Jan/Feb 2005)

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(10 M — Jan/Feb 2005)

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(10 M — Aug/Sep 2000)
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