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finite element analysis
Welcome to the web site devoted to developing methods for reliable FE analyses.
This web site has been set up to support those reading the recently published book by Alan Morris entitleda practical guide to reliable finite element modelling ISBN 978-0-470-01832-3 published by Wiley in 2008. The site is also devoted to developing ideas on how to improve the reliability of finite element analysis solutions through the elimination of errors and reduction of the impact uncertainties. So we are interested in finding out what others analyst do in order to create finite element models that stand a reasonable chance of accurately simulating the real world behaviour of a structure when it has entered operational use.
Support for the Book
The book illustrates many of the methods and techniques used to control the impact of errors and uncertainties by means of MathCad examples. It seemed to us that an analyst, particularly a new analyst, might want to gain familiarity with these techniques by running the examples and then modifying them to create alternative problems. MathCad was selected because it directly uses mathematical expressions and the user can clearly see the relationship between the techniques and the underlying mathematical formulation. In addition, a user can easily change the input data so that these alternative problems can be easily set up and worked with, once the original formulation has been established.
Of course, if you want to work with the MathCad examples found in the framework and sensitivity pages it is necessary to have a working version of MathCad 11 or better on your computer. MathCad is being developed and sold by Parametric Technology (better known as PTC) from whom a 30-day trial copy of MathCad can be obtained. Although it is possible to download such a trail copy from one of their hidden links the best way is to get in touch with your local PTC listed here: http://www.ptc.com/company/contacts/index.html
Site Map
Let's now have a brief look at what the rest of this site contains so that you know where to jump to in order to get the information you're looking for
Home Page
You are actually on the Home Page which clearly contains the basic information to assist you in understanding what you might gain by using this site.
About Us
This page simply tells you something about the individual (i.e.me) responsible for creating the book and for this web site.
About the Book
This provides a brief description of the book and its target audience. It also lists the chapter headings
Framework
This page gives access to a MathCad program that can be used to create general 2-dimensional pin-jointed frameworks modelled by simple 2-noded bar elements. The problem types included both static and dynamic cases as described below. Although a single framework layout is presented the program can be used for any 2-dimensional pin-jointed framework problem. It is presented because most of the simple demonstration examples used in the book employ this type of simple structural form.
2-D pin-jointed static example: This presents a 2-D framework with static loads applied at framework nodes. Two solution processes are deployed. One where the global stiffness matrix has appropriate rows and columns deleted in order to accommodate zero-valued displacements at the boundary. The second uses a penalty method approach to accommodate the boundary conditions; in this case the solution process can accommodate both zero valued or non-zero valued displacements at the boundary points
2-D pin-jointed dynamic example: The second example employs the general 2-dimensional pin-jointed framework to demonstrate the application of this simple layout in the solution of problems where the structure's natural frequencies and mode shapes are required.
Sensitivities
The main purpose of the book is to provide a methodology, called FEMEC, which can be used by an analyst or an analysis team in order to control the differences between the values for structural behavioural parameters predicted by a finite element analysis and those which occur when the structure enters operational service. In order to facilitate this process the book introduces a number of sensitivity methods that can be employed to generate bounds on the impact that error and uncertainty have on the results from a finite element analysis. The methods use direct, indirect and artificial sensitivities and these are applied to both static and dynamic problems. The examples presented in the book which relate to the calculation of direct sensitivities are shown in this page and the reader is invited to gain familiarity with the methods by modifying the demonstration examples.
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