Engineering and Design Tools - TSOC 302 and TSOC 303 - 5. Simulation
5.1 Introduction
A major change in design and manufacturing during the past 50 years has been the growth of (computer) simulation as a design tool. As it has become possible to simulate with increasing accuracy more areas of product performance, companies have realised that this is an increasingly effective tool to providing better products at lower cost.
Certain analogies have been known for many years (Prandtl, 1903, pointed out that the equation which must be solved to be solved to find the torsional rigidity and stress in a member of uniform cross section is of the same form as that representing the shape of a stretched membrane attached by its edges to a plane surface of the shape of the cross section and subjected to a uniform surface tension) and when electrical analogue computers were first built, many engineering problems were investigated. However it was the digital computer which really opened up the range of mathematical techniques available to engineers. Nowadays even quite mundane products may be the subject of sophisticated analysis - a manufacturer of shampoo carried out finite element analysis on the bottles to check how high they could be stacked before they would buckle!

Whereas in the early days of this work a mainframe computer costing hundreds of thousands of pounds was needed, together with programming expertise, now sub £1000 home desktop PCs are quite capable of carrying out the majority of the computation simulation that is of interest to engineers. User friendly software with graphics interfaces have also progressed rapidly. At one end are integrated 'multiphysics' applications that can solve problems involving stress, vibration, heat and fluid flow, magnetism, electric charge, including situations where more than one effect is occurring simultaneously - such as thermal stress. At the other end of the scale small specialist pieces of software are being developed to tackle specific problems.

As well as some knowledge of what is available, some understanding of the principles underlying typical packages is desirable if users are to be able to make appropriate use of them. In this section of the module the following topics will be considered:

  • 5.2 Types of simulation software useful to engineers and designers
  • 5.3 Some solution schemes for differential equations
  • 5.4 Difficulties arising in solving dynamic problems
  • 5.5 Validation of results

5.2.1 Spreadsheets
Before looking at specialised software it should be noted that top range spreadsheets provide a wide range of functions - together with the ability to incorporate computer code - and this enables them to be used to solve a huge range of engineering problems provided the user has a good understanding of the system and how it can be modeled.

One of the assignments for this module involves setting up a spread sheet to model a simple mechanical system, some guidance is provided here.

5.2 Types of Simulation Software Useful to Engineers.

5.2.1 Finite Element Analysis The most mature packages are those for finite element analysis (FEA). Some of these have been under continuous development for over 30 years and are now able to offer a high degree of sophistication and user friendly interfaces which require a minimum of specialist knowledge to start to use. Although the majority of these packages are primarily aimed at the mainstream engineering analysis: stress, vibration, thermal effects, increasingly the capabilities of these packages are being broadened.

Some of the advantages and disadvantages of FEA are summarized below:

  • Irregular boundaries can be accommodated easily.
  • Different materials in different zones can be accommodated.
  • A variety of non linear material behaviour can be provided for.
  • Non linear geometry effects may be allowed for.

However there are a number of potential problem areas that must be considered when appraising results:

  • It is important to accurately model the geometry in areas where the stress is critical - elsewhere simplification is usually acceptable.
  • In many problems it is surprisingly difficult to accurately model the constraints that are present in the real components.

Link to notes on introductory FEA theory

5.2.2 Finite Difference Methods These methods, which are based on the numerical approximations to the appropriate differential equations, have been in use for many years. They tend to be used in fluids computation work rather than for mechanics of solids computation (where FEA is preferred). There are a couple of disadvantages which may need to be considered:

  • Irregular boundaries can cause difficulties
  • Different properties for different zones can be more difficult to incorporate

However automatic meshing tools minimise these difficulties from the users view point.

5.2.3 Boundary Element Method This uses a more complex mathematical basis and reduces the order of the problem by 1, but gives fully populated matrices to solve, which are often non symmetric. One advantage of the method is that it easily handles boundaries at 'infinity', but it is only used to a limited degree.

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David J Grieve, 21st November 2002.