JK Lakshmipat UniversityInstitute of Engineering and technology

Finite Element Method

Submitted to:Prof R.K. Agrawal

Submitted by:Bharat Sharma

2012BTechME008

Contents• Analytical methods v/s Numerical method• FEM• FVM• A Case study

Analytical Methods V/S Numerical Methods

Find the root of  f(x)=x−5

Analytical solution: f(x)=x−5=0add +5 to both sides to get the answer x=5

Numerical solution:Let's guess x=1:  f(1)=1−5=−4. A negative number. Let's guess x=6:  f(6)=6−5= 1. A positive number.And you get a range in which solution exists.

Why use Numerical method• Can Solve Complex Problems with ease• Example:- Higher Order Differential equations

Why use Analytical Method

• To validate results from Numerical Methods• Analytical solutions can be obtained exactly with pencil and paper

What is FEM ?• Finite Element Method• A type of Numerical Method• Used for solving a differential or integral equation. • It has been applied to a number of physical problems, where the

governing differential equations are available.

A Simple Approach

Area ?

Area of geometry = A1 + A2 + A3 – A4

1

2

3

4

Finite Element methodIt is not of course used to calculate areas, but things like displacements, temperatures,velocities, stresses and so on

Meshing

Is FVM related to FEM• Finite volumetric method• 3D version of FEM• Most of the commercial analysis software work on the principle of

FVM

A Case Study

Stress Analysis of LP RotorProblem:-

• To determine stresses in the existing rotor• To modify the defective Rotor geometry and limit the stress to the existing

value

Client : N.T.P.C. New Delhi Done by : IIT Madras

You can see that there is a small hole there. The problem is that this small hole or defect which has been created due to improper manufacturing, it so happens that it is at a place where the stresses are also high

Can’t you just manufacture another ?• Rotor is very expensive, it is about 10 crores

• Lead time to manufacture this rotor is nearly 6 months

• A particular thermal power project worth about 3000 crores is going to stand still.

And Rotor is very big

NTPC wanted to

• Check whether this manufactured rotor is tolerable • If not then can we modify this

What IIT Did• Compared stresses in good LP rotor and modified rotor

After some modifications and 4 iterations they were able to make the stresses equal in a matter of about 5 days

and they used FEM.