CAE

Computer Aided Engineering - MECH 227 - Home Page

1 Introduction
This module aims to give students an introduction to CAE to enable them to tackle a range of problems using appropriate software. 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
2.1 Stress, vibration and thermal analysis, etc.
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:
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.

2.2 Motion Analysis
The software for motion analysis is more specialised and in some ways more sophisticated than FEA software. It is also rather long winded to use as a solid models of the constituent components need to be produced in Solid Works, then these need to be assembled and only then can the motion analysis be carried out. The software then 'writes' the equations that it needs to solve, compiles the code and executes it to provide the solution.

3 Software
The work undertaken in this module will use Solid Works and Cosmos software.

4 Instructions for developing the models are given in the links below.

Study Programme

Week commencing: Topic:
8 - 1 - 2007 Module introduction. Finite difference method
FEA - Cosmos: Non Symmetric Loading of a 90 degree angle
15 - 1 - 2007 Introduction to FEA theory
22 - 1 - 2007 FEA theory continued
29 - 1 - 2007 Errors in FEA and interpretation of results
5 - 2 - 2007 FEA for vibration analysis
12 - 2 - 2007 FEA for Design Optimisation
19 - 2 - 2007 Analytical motion analysis:
The Scotch yoke
The Slider Crank, part 1; and part 2.
Torque generated by piston force on crank
26 - 2 - 2007 Computer Aided Motion Analysis
5 - 3 - 2007 Motion analysis continued
12 - 3 - 2007 onwards Tutorial support with assignments

4 The Assignments
Students should normally work in groups of 3 for these assignments.
4.1 Assignment 1 - Continuing with the Design DSGN 221 Assignment
The component that you analysed for the second DSGN 221 assignment should be modeled in Solid Works and analysed with Cosmos.

4.2 Guidance
It is much better to start by developing a very simple model and running it to get some results. This model can then be improved and run again to try and get more realistic results. By starting with an almost trivial model, it should be possible to improve the model in 3 or 4 stages.
To assess whether the results seem believable, always first look at the deformed shape and consider - is this deformed shape believable? Compare the computed results with those obtained by the hand calculations reported in the DSGN 221 report. If there are significant differences check you have not made a mistake with the loads or the restraints, the latter is very easy to do.

4.3 Requirements for the First Report
The report needs to include:

4.4 Assignment 2 - Motion Analysis
Select a system involving some mechanism to which you have access, to enable you to carry out measurements. You will need to be able to measure the dimensions of the mechanism, with a ruler or tape measure and also to weigh it. If the shape is simple you can calculate the appropriate moments of inertia, but for complex shapes you will have to carry out one or more experimental determinations - probably using compound pendulum theory.
If you have chosen a system where there is an analytical solution, or if you are able to produce a graphical solution for one particular configuration, then you should do evaluate this.

4.5 Requirements for the Second Report
The report needs to include:

5 Marking Scheme - for both reports:


Presentation: 10%
Derivation and description of the model: 30%
Quality of results, computed and calculated: 30%
Discussion of results: 30%

The first assignment is due in by 11.00 am Monday 5th March 2007.
The second assignment is due in by 11.00 am on New DateThursday 26th April 2007.

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 different methods, but you MUST state, with reasons, which sources of error are likely to be significant and which are less so.

NB: A problem sometimes occurs when 'adding in' COSMOSWorks - the computer 'hangs'
There are no known issues as such with starting up the analysis add-ins in SolidWorks. One possible cause of a hang up is lack of minimum required space on the users U: drive, which I believe is the default destination for temporary files created on start-up. Freeing up some space on the U: drive may resolve this problem. Also, working from a temporary folder on the local machine, perhaps created by the user on the D: drive, is strongly recommended, as large data files can be created. The destination for all results files etc. should also be set to this location, through the COSMOSWorks > options > results (tab) menu.

References:
'Finite Element Analysis for Design Engineers', P M Kurowski, SAE International, 2004, ISBN: 0-7680-1140-X.
'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.
'Mechanics and Materials for Design', N H Cook, 1985, ISBN: 0-07-Y66157-X
'Roarks Formulas for Stress and Strain', 6th Ed., Ed by W C Young, McGraw-Hill International Editions, 1989.
'Shock and Vibration Handbook', Ed. C M Harris, McGraw-Hill, 1988.

Return to Index of Online Documentation.

David J Grieve, 15th March 2007.