In the preface to Volume 1, I expressed my trepidation at starting to write a book on non-linear finite elements and the associated mechanics. These doubts grew as I worked on Volume 2, which attempts to cover ‘advanced topics’. These topics include many areas which are still the subject of considerable controversy. None the less, I have finally completed this second volume, although in so doing, I have almost certainly made mistakes. In persevering, I have received much encouragement from a number of readers of Volume 1 who have urged me not to abandon the second volume and who have made me believe that there is some need for a book of this kind. As with the subject-matter of the first book, there are many specialist texts which cover the background mechanics. My aim has not been to replace such books and, indeed, I have attempted to reference these books with a view to encouraging wider reading. Instead, my aim has been to emphasise the numerical implementation. As with the earlier volume, an engineering approach is adopted in contrast to a strict mathematical development.

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