1. CE 418
INTRODUCTION TO FINITE ELEMENT METHODS
Yogesh M. Desai
Department of Civil Engineering
Indian Institute of Technology Bombay
Powai, Mumbai - 400076
3. Introduction
Many problems in engineering and
applied science are governed by differential
or integral equations.
Due to complexities in geometry,
properties and boundary conditions in
most real-world problems, an exact
solution cannot be obtained.
4. Finite element method is an
approximate numerical method for
solving problems of engineering and
mathematical sciences.
Useful for problems with complicated
geometries, external influences and
properties for which analytical
solutions are not available.
Introduction
5. OBJECTIVES
•To introduce the basic concepts involved in the method
•To understand advantages and disadvantages of the method
•To apply method to a variety of 1-D and 2-D problems
•To expose students to computer implementation of the method
6. Course Contents
Introduction
Basics of Finite Element Methods
Matrix algebra
Solution of system of linear equations
Static condensation
3 – 4 Lectures
One Dimensional Finite Element Analysis
Linear Spring
Axial Bar / Truss
1-D Torsion
1-D steady state heat conduction
1-D flow through porous media
1-D ideal fluid flow
Beam
Plane frame and grid
10–13 Lectures
7. Conditions of symmetry / anti-symmetry
Computer Implementation of Finite
Element Method
3 – 5 Lectures
Two Dimensional Finite Element Analysis
2-D flow through porous media
Plane stress / Plane strain / Axi-
symmetric
Iso-parametric formulation
Numerical integration
10 – 12 Lectures
Total Lectures
~ 30
(~ 45 Hrs)
Course Contents
8.
9. Assignments and Term Projects :10 %
Quiz-1 :10% (August 22)
Mid - Term Exam :20 % (as per time table)
Quiz-2 :10% (October 17)
End - Term Exam :50 % (as per time table)
Assessment Scheme
Notes: (1) Bring calculator to all the lecture sessions.
(2) 80% Attendance is required.
10. Brief History
It is difficult to document the exact origin of the
FEM, because the basic concepts have evolved
over a period of 150 or more years.
Hrennikoff [1941] – Framework method for
elasticity problems
Courant [1943] - Variational form
Levy [1947, 1953] - Flexibility and Stiffness
Argyris [1955] - Energy Theorems and Structural
Analysis
Turner, Clough, Martin and Topp [1956] -
Stiffness Method
Clough [1960] - Termed “Finite Elements”
11. In early 1960s, engineers used the method
for approximate solution of problems in stress
analysis, fluid flow, heat transfer, and other
areas.
The first book on the FEM by Zienkiewicz and
Chung was published in 1967.
Brief History
12. • Can be applied to a variety of fields like
structural mechanics, aerospace engineering,
geotechnical engineering, fluid mechanics,
hydraulic and water resource engineering,
mechanical engineering, nuclear engineering,
electrical and electronics engineering,
metallurgical, chemical and environmental
engineering, meteorology and bioengineering,
etc.
How can FEM Help ?
13. •Easily applied to complex, irregular-shaped
objects composed of several different
properties and having complex boundary
conditions and external influences.
• Applicable to steady-state (static), time
dependent as well as characteristic value
problems.
• Applicable to linear as well as nonlinear
problems.
14. Finite Element Method is an Approximate Numerical
Method to Solve Problems of Engineering and
Mathematical Sciences.
Any given problem reduces to
