A Finite Element Primer
NAFEMS
First Published - January 1992 - Reissued 2003
Hardback, 277 Pages
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 Many of today's finite element systems are intended to be robust
and friendly; and may be used by engineers and scientists who are
unfamiliar with the finite element method, its virtues and its
vices. Indeed, some finite element systems may be embedded in a
CAD/CAE package and the user may be a production engineer,
designer, or systems analyst who not only does not understand the
characteristics of finite element systems, but may very well not
even wish to know.
The problems of the novice have been identified and addressed in
this primer. The aim is not to write just another finite element
text book. There are scores of these, and many are daunting for the
new reader since, not unaturally, many go into algebraic detail of
specific elements or they highlight areas of current research. The
aim is also not to write a detailed instruction manual, since this
cannot be done without referring to a specific system. Indeed, all
commerical systems have their own introductory and users' manuals,
together with more advanced programmers' manuals in some cases, and
these are usually comprehensive. They do not, however, discuss the
various vices or failings of the system, for obvious reasons.
This Primer will try to explain the basis of the Finite Element
Method, stressing the essentially simple fundamental concepts
without digressing into lengthy algebra or oversmart mathematics.
There will be no functional analysis in Hilbert spaces, and
Lagrange multipliers will just be mentioned, even though they are
used sparingly. Some algebra is inevitable, otherwise the text
becomes a descriptive routine rather like explaining the fitting
together of pieces of a jigsaw, and this can lead to all sorts of
confusion. However, the algebra can be kept concise using matrix
notation which is obligatory in discussing these methods. The
Primer will strip some of the mysteries from the method and in
particular will explain precisely what the method does exactly, and
what it does approximately, and as a consequence which errors are
important and which are not. Some errors are very useful sources of
guidance.
Following fundamental chapters into the nature of the method for
static problems and various types of structures, the nature of
proprietary finite element systems will be discussed, together with
those features which the user has the right to expect. The latter
parts of the Primer will extend the method to dynamic problems,
non-linear and elasto-plastic and buckling problems, heat transfer,
and in Chapter 12 examples will be given to illustrate some of the
modelling difficulties encountered in making a finite element
idealisation in the first place.
It will be assumed that the reader has a basic understanding of
applied mechanics and that differentiation or integration are not
completely foreign concepts. The validity of a material's
constitutive laws will not be questioned. The opening section even
runs through a quick introduction to matrices and their
manipulation- we realise that nowadays most engineers are familiar
with matrix algebra but it does also give us an opportunity to
gently introduce the notation used in this text.
In most chapters, the fundamentals behind the finite element method
are very briefly discussed. It is possible of course to omit this,
and simply state the equations which are necessary to formulate the
numerical models. However, it has been shown that a grasp of the
fundamentals is useful in judging errors, choosing idealisations,
and even understanding user-manuals! Such introductions can be
omitted if familiar.
If the reader therefore finds eoms parts of the Primer to
elementary, we apologise. If any find parts a little demanding,
then perhaps the balance is about right.
Contents
1. Introduction
2. Structural Analysis
3. General Continuum
4. Beams
5. Two-dimensional Membranes
6. Bricks, Plates and Shells
7. Mesh Specification
8. Assembly and Solution
9. Results Processing
10. Dynamics
11. Nonlinear Analysis
12. Modelling
13. Other Field Problems
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