7/17/2019 FEA Exercise

http://slidepdf.com/reader/full/fea-exercise 1/2

School of Mechanical, Materials & Manufacturing Engineering

INDIVIDUAL COURSEWOR !RON" S#EE"

Mo$uleA$%ance$ Nuerical Metho$s in Engineering

'MM(NME)

Assignent "itle !inite Eleent Metho$

Nae of Stu$ent

Student ID Number I have read and understandthe University Regulations

referring to Plagiarism andconfirm that the content of this

document is my own work andhas not been plagiarised.

Student!s signature

"odule #onvenor

Personal tutor$

supervisor

Design$%ab &roupNumber 'if applicable(

Date of e)periment

'for laboratories only (

Submission deadline (* '++ Ma -.+-)

/lease Note* ALL COURSEWOR MUS" 0E SU0MI""ED 01 (/M ON "#E DA"E

2IVEN3 +ork handed in late will be penalised by a deduction of ,- absoluteper working day 'e)cluding weekends and ank /olidays0 but including

vacations(.

Date re*ort recei%e$ Deduction for late

submission

 

4

Re*ort Mar5 out of  

Deduction for late

submission Mar5er6

!INAL MAR

7/17/2019 FEA Exercise

http://slidepdf.com/reader/full/fea-exercise 2/2

!ee$7ac5 fro ar5er

Transient Heat Transfer

Use a Galerkin weak formulation with ve linear elements of length to

solve the following initial boundary value problem:

with initial temperature eld

2/10;2   ≤≤=   x xT 

and boundary conditions

0),5.0(

0),0(

=∂

∂

=

 x

t T 

t T 

  for 0≥t 

As time stepping algorithm use a full implicit approach with a time increment

of .

• Write the element equations for each of the ve elements using linear

weighting and interpolation functions in term of their local coordinatessystem.

• Write the corresponding local matri systems

• Write the matri assembly for the global solution 

• !olve the resulting ve by ve matri system to nd your solution at

the rst two time steps" i.e. and .

• #ompare your $inite %lement solution with the $inite &i'erence solutiongiven in class using the same time stepping algorithm" i.e. full implicit

approach.

2