Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 13
In this class let us review certain principles of calculus of variation.
(Refer Slide Time: 1:07)
As all of
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 3
In the last class we saw a number of applications of finite element analysis. We saw
really the breadth of ap
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 33
In this course, so far we have seen a number of elements which can be used in various
situations. We have ta
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 4
The last class we were looking at a very simple problem. We were trying to do this
problem by using the finit
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 26
We had a very detailed introduction for thermal problems yesterday. Now, I am sure all
of you are clear as t
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 2
In the last class we saw certain examples on the applications of finite element analysis
for real life proble
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 23
Before we proceed with our quadrilateral, quadratic elements, let us just go and look
at what we did before
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 18
By now we have understood that the crux of finite element analysis is interpolation. It
is that concept that
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 14
In the last class, we saw the potential energy theorem. We actually derived it by using
variation of princip
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 32
Yeah, let me summarize what all we did in the last class, I think that will give a good
picture of this whol
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 24
We have been talking about numerical integration in the last class and we saw that
there are very important
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 20
Before we go further, let us summarize what all we did in the last class about
isoparametric formulation. Re
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture 10
In the last class we started our discussion on strain energy density and strain energy
density function. We sa
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 28
Yesterday we were discussing a very interesting case study on pipe welding.
Remember that we said that this
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 17
We made some very important conclusions in the last class about how the
displacement results behave in a fin
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 5
In the last class we were enquiring about a quantity called stress.
(Refer Slide Time: 1:09)
We said that str
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 12
In the last class, we were looking at some examples and we derived the stress strain
relationship and so on.
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 7
In the last class we stopped at deriving the equilibrium equation. We said that the
equilibrium equations are
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 11
We saw in the last class, the derivation for what we call as the elastic moduli or the
matrix which relates
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 19
In this class, we are going to talk about isoparametric formulations.
(Refer Slide Time: 1:05)
As I told you
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 27
In the last class, we were discussing about the temperature distribution. I hope all of
you understood till
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 6
There are some questions on what we did in the last class. Let us clarify some of the
doubts because I know t
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 22
We had started our discussions on an alternate formulation for stiffness matrix in a
triangular element. Rem
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 9
In the last class we were talking about, if you remember we are talking about, Mises
criteria. We called this
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 25
Let us now look at some heat transfer applications of finite element analysis.
(Refer Slide Time: 1:05)
As I
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 21
Is there any question on what we did in the portions which we covered in the last
class? No. I hope now all
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 29
In the last class, we were talking about contact and we were really getting into the
modeling aspects of the
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 30
Yeah, in the last class we defined or discussed the contact element and we said that
the key concept in the
Introduction to Finite Element Method
Dr. R. Krishnakumar
Department of Mechanical Engineering
Indian Institute of Technology, Madras
Lecture - 31
We were looking at non-linear problems in the last class and we said that we will
continue with the non-line
Content
Module:3
Element Properties (09)
Lecture 1: Natural Coordinates (Page:1-8)
3.1.2 Two Dimensional Triangular Elements
3.1.3 Shape Function using Area Coordinates
Lecture 2: Triangular Elements (Page:9-17)
3.2.1 Shape function using Cartesian coordi