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Non-linear finite element analysis of solids and structures: Volume 1: Essentials
This book was originally intended as a sequal to my book Finite Elements and Solution
Proc.t.dures,fhr Structural Anufysis, Vol 1 -Linear Analysis, Pineridge Press, Swansea,
1986. However, as the writing progressed, it became clear that the range of contents
was becoming much wider and that it would be more appropriate to start a totally
new book. Indeed, in the later stages of writing, it became clear that this book should
itself be divided into two volumes; the present one on ‘essentials’ and a future one on
‘advanced topics’. The latter is now largely drafted so there should be no further
changes in plan!
Some years back, I discussed the idea of writing a book on non-linear finite elements
with a colleague who was much better qualified than I to write such a book. He
argued that it was too formidable a task and asked relevant but esoteric questions
such as ‘What framework would one use for non-conservative systems?’ Perhaps
foolishly, I ignored his warnings, but 1 am, nonetheless, very aware of the daunting
task of writing a ‘definitive work’ on non-linear analysis and have not even attempted
such a project.
Instead, the books are attempts to bring together some concepts behind the various
strands of work on non-linear finite elements with which I have been involved. This
involvement has been on both the engineering and research sides with an emphasis
on the production of practical solutions. Consequently, the book has an engineering
rather than a mathematical bias and the developments are closely wedded to computer
applications. Indeed, many of the ideas are illustrated with a simple non-linear finite
element computer program for which Fortran listings, data and solutions are included
(floppy disks with the Fortran source and data files are obtainable from the publisher
by use of the enclosed card). Because some readers will not wish to get actively
involved in computer programming, these computer programs and subroutines are
also represented by flowcharts so that the logic can be followed without the finer detail.
Before describing the contents of the books, one should ask ‘Why further books
on non-linear finite elements and for whom are they aimed?’ An answer to the first
question is that, although there are many good books on linear finite elements, there
are relatively few which concentrate on non-linear analysis (other books are discussed
in Section 1.1). A further reason is provided by the rapidly increasing computer power
and increasingly user-friendly computer packages that have brought the potential
advantages of non-linear analysis to many engineers. One such advantage is the
ability to make important savings in comparison with linear elastic analysis by
allowing, for example, for plastic redistribution. Another is the ability to directly
simulate the collapse behaviour of a structure, thereby reducing (but not eliminating)
the heavy cost of physical experiments.
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