The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to find approximate solutions to partial differential equations. It involves dividing a complex structure into smaller, simpler parts called finite elements and solving sets of algebraic equations. Commercial FEM software programs allow users to analyze complex engineering problems without an in-depth knowledge of mathematics. The document gives examples of how FEM can be used to model different structures and its applications in fields like mechanics, thermal analysis, and biomechanics.

1. INTRODUCTION TO FINITE
ELEMENT METHOD
Dr. MOHD ZAMEERUDDIN
MOHD SALEEMUDDIN
ASSISTANT PROFESSOR
DEPARTMENT OF CIVIL ENGINEERING
MGM’s COLLEGE OF ENGINEERING,
NANDED (m. s)
Email: zameerstd1@hotmail.com
Mobile: +919822913231

2. Introduction
The Finite Element Method (FEM) is a numerical
technique to find approximate solutions of partial differential
equations. It was originated from the need of solving complex
elasticity and structural analysis problems in Civil, Mechanical
and Aerospace engineering.
Finite element analysis (FEA) involves solution of
engineering problems using computers. Engineering structures
that have complex geometry and loads, are either very difficult to
analyze or have no theoretical solution. However, in FEA, a
structure of this type can be easily analyzed..
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Commercial FEA programs, written so that a user can solve a
complex engineering problems without knowing the governing
equations or the mathematics; the user is required only to know
the geometry of the structure and its boundary conditions. FEA
software provides a complete solution including deflections,
stresses, reactions, etc.
Introduction
The fast improvements in computer hardware
technology and slashing of cost of computers have boosted this
method, since the computer is the basic need for the application
of this method. A number of popular brand of finite element
analysis packages are now available commercially. Some of the
popular packages are STAAD-PRO, GT-STRUDEL,
NASTRAN, NISA, ANSYS and ABAQUS. Using these
packages one can analyse several complex structures.
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The basic idea in the finite element method is to find the
solution of a complicated problem by replacing it by a simpler
one. Since the actual problem is replaced by a simpler one in
finding the solution,
Basic Concepts
In the finite element method, the solution region is
considered as built up of many small, interconnected sub
regions called finite elements. As an example of how a finite
element model might be used to represent a complex
geometrical shape are;
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Basic Concepts
EXAMPLES
LEGO (Kid’s Play) Buildings

6. 6Finite Element Mesh of a Fighter Aircraft
Basic Concepts
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Why Finite Element Method ???????????????
• Design Analysis:
Hand calculations, experiments and computer
simulations.
•FEM/FEA is the most widely applied computer
simulation method in engineering.
•Closely integrated with CAD/ CAM applications
•………

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Application of Finite Element Method
• Mechanical/ Aerospace/ Civil/ Automobile Engineering.
•Structure analysis (static/ dynamic, Linear/nonlinear).
•Thermal / fluid flows
•Electromagnetic
•Geomechanics
•Biomechanics
Modeling of concrete beam © MZS Engineering Technologies

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Application of Finite Element Method
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Application of Finite Element Method
Modeling of nuclear power plant
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Historical Background
Although the name of the finite element method was given recently,
the concept dates back for several centuries. For example, ancient
mathematicians found the circumference of a circle by
approximating it by the perimeter of a polygon as shown in Figure
In terms of the present-day notation,
each side of the polygon can be
called a "finite element." By
considering the approximating
polygon inscribed or circumscribed,
one can obtain a lower bound S(i) or
an upper bound S(u) for the true
circumference S. Furthermore, as the
number of sides of the polygon is
increased, the approximate values
converge to the true value. © MZS Engineering Technologies

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The finite element analysis can be traced back to the work by
Alexander Hrennikoff (1941) and Richard Courant (1942).
Hrenikoff introduced the framework method, in which a plane
elastic medium was represented as collections of bars and beams.
These pioneers share one essential characteristic: mesh
discretization of a continuous domain into a set of discrete sub-
domains, usually called elements.
Historical Background
In 1950s, solution of large number of simultaneous
equations became possible because of the digital computer.
In 1960, Ray W. Clough first published a paper using term
“Finite Element Method”.
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Historical Background
In 1965, First conference on “finite elements” was held.
In 1967, the first book on the “Finite Element Method” was
published by Zienkiewicz and Chung.
In the late 1960s and early 1970s, the FEM was applied to a wide
variety of engineering problems.
In the 1970s, most commercial FEM software packages
(ABAQUS, NASTRAN, ANSYS, etc.) originated. Interactive FE
programs on supercomputer lead to rapid growth of CAD
systems.
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Historical Background
In the 1980s, algorithm on electromagnetic applications, fluid
flow and thermal analysis were developed with the use of FE
program.
Engineers can evaluate ways to control the vibrations and extend
the use of flexible, deployable structures in space using FE and
other methods in the 1990s. Trends to solve fully coupled
solution of fluid flows with structural interactions, bio-
mechanics related problems with a higher level of accuracy were
observed in this decade.
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