Computer Aided Engineering - MECH 335 - Now part of DSGN 313

1 Introduction
This module provides aims to make students competent to tackle a range of problems using CAE. An introduction to some numerical techniques is provided, the use of software is developed and critical appraisal of results is emphasised.
For stress, thermal and many other types of analysis, only the simplest of configurations can be solved by exact analytic methods. For the vast majority of engineering components some alternative method is needed and the usual approach involves a method of approximation requiring some numerical techniques to solve, which in turn requires the use of a digital computer.

2 Numerical Techniques
There are 3 main methods of numerical approximation:

Finite difference (FD) method
Finite element analysis (FEA)
Boundary element method (BEM) These methods all have some advantages and disadvantages. FEA is a variant of some classical approximation methods, whereas the FD method is an older procedure that has been used in one form or another almost since the inception of differential calculus. FEA was first adapted for stress analysis problem solving by Southwell. Ever since FEA were first used, there have been arguments about their relative merits versus the longer established FD method.

FEA
FEA involves mathematical approximations associated with the displacement function of a particular element and geometric approximations to the component shape. An advantage of FEA is that it can be used to analyse virtually any structural problem in a routine manner - hence non homogeneous material can be accommodated as the assembly of elements with different properties is straightforward.

FD Method
The FD method uses a finite difference approximation to the (partial) differential equations that describe the behaviour of the system. A significant difficulty in solving the equations is that with fine meshes, needed for adequate accuracy, there may be instability in determining the solution. Discontinuous interfaces, such as abrupt changes in material properties or geometry require special treatment. FD tend to be used more for Fluids problems than for Mechanics problems.

BEM
The BEM method reduces the dimensionality of the problem by 1, so the overall size of the computation the smaller than in FEA or FD, but the matrices produced are assymetric and densley packed and may require just as much computational effort to solve as when using FEA or FD. The method is particularly suited to problems with high stress gradients such as fracture mechanics. Boundaries that are nominally at 'infinity' may readily by handled whereas such boundaries increase the size of FEA and FD problems. The underlying mathematics is however more complex than the other two methods.

In this module the computational work will be done using FEA.
Students will also need to be familiar with:
Torsion theory as applied to non circular section: solid and hollow - closed and open. This will be covered in lectures for Plymouth based students and by self study and tutorial sessions for the distance learning students.
Two dimensional stress and strain transformations - Knowledge of this is assumed. If you are unsure about any of this check out the Engineering Science module MECH226.

Study Programme - See DSGN 313 pages.

Topics
Finite difference method
Basic introduction to FEA theory
FEA: assembly, boundary conditions, loads and solutions
Errors in FEA and interpretation of results
Torsion of hollow sections
Torsion of solid sections

The Assignment
Each group will be allocated two hollow rectangular or square lengths of aluminium box section. One of these will be 'closed' and one 'open' - having a longitudinal slit along one wall. Strain gauges are fixed to one wall of these sections. You are required to investigate the behaviour of this sample under torsion, using three techniques:

You will then compare the results from the three different techniques and explain the reasons for the differences (25% of marks).

The assignment due date: See DSGN 313 pages.
N.B: It is most important that you not only identify possible sources of error and possible reasons for the differences in the results from the three methods, but you MUST state, with reasons, which sources of error are likely to be significant and which are less so.

References:
'Finite Elements - A Gentle Introduction', by D Henwood and J Bonet, Macmillan, 1996.
'Basic Principles of the Finite Element Method', by K M Entwistle, IoM, 1999.
'Mechanics of Solids and Structures', D W A Rees, McGraw-Hill, 1990, ISBN: 0-07-707222-7.
'Advanced Mechanics of Materials', A P Boresi and O M Sidebottom, John Wiley and Sons, 4th Ed. 1985, ISBN: 0-471-84323-7.
'Mechanics and Materials for Design', N H Cook, 1985, ISBN: 0-07-Y66157-X
'Advanced Solid Mechanics', P R Lancaster and D Mitchell, Macmillan Press, 1980, ISBN: 0 333 24018 8, now out of print, but may be available second hand.
'Roarks Formulas for Stress and Strain', 6th Ed., Ed by W C Young, McGraw-Hill International Editions, 1989.
'Stress Concentration Factors', by R E Peterson, John Wiley and Sons, 1974.
'Shock and Vibration Handbook', Ed. C M Harris, McGraw-Hill, 1988.

Return to Index of Online Documentation.

David J Grieve, 6th January 2006.