Welcome to the Home page for reliable FE analyses.
The site has been set up to assist readers of a A Practical Guide to Reliable Finite Element Modelling, in particular, by giving access to some of the demonstation examples that illustrate the methodology. However, the book represents only one approach to the problem of creating finite element models where the impact of error and uncertainty is controlled. Because of this limitation in the scope there is real interest in extending the ideas presented by drawing together information from other analysts working in this area. If you have ideas on how to undertake this type of analysis and would like to have them presented to the wider finite element community this site is prepared to publish them - provided they make a contribution to the development of the subject.
Support for the Book
The methods and techniques used to control the impact of errors and uncertainties developed in the book are illustrated by MathCad examples. It seems reasonable to assume that a reader, particularly someone new to the field, might wish to gain familiarity with these techniques by running the examples and then modifying them to create alternative problems. MathCad was selected for this task because it explicitly uses the mathematical expressions employed in the creation of finite element models and its use in the book allows the reader to clearly see the relationship between the control techniques and the underlying mathematical formulation. In addition, the input data can easily be changed so that alternative problems can be set up and used to gain a fuller understanding of the methodology described in the book.
Of course, if you want to work with the MathCad examples found in the mathCad examples and sensitivities 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 office via the web site - http://www.ptc.com/company/contacts/index.html
MathCad Examples
This page gives access to a MathCad programs that can be used to create general 2-dimensional pin-jointed frameworks modelled by simple 2-noded bar elements or to generate a 1-dimensional beam using a simple beam element. In the case of the framework the problem types included both static and dynamic cases. Although a single framework layout is presented the program can be used for the solution of other 2-dimensional pin-jointed framework problems. The beam program can be used for the analysis of a 1-dimensional beam subjected to distributed or point loads with any type of boundary condition.
- 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.
- 1-D beam example: The third example employs a beam that is encastre at one end, simply supported at the other and subjected to a uniform load that is distributed along part of its length. This problem can be found in Roark's Formulas for Stress & Strain 6th Edition on page 103 as example 2c. For this application the finite element problem is solved using the penalty method.
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. Some of the examples presented in the book are shown on this page and the reader is invited to gain familiarity with the methods by modifying the demonstration examples.