Basic Principles of the Finite Element Method

"I think this is a marvellous book which will go a long way towards removing the mystery of the method, and in allowing the more intelligent use of programs such as the ABAQUS in the context of materials science." - Professor H K D H Bhadeshia FRS, University of Cambridge

This book provides an introductory text which lays out the basic theory of the finite element method in a form that will be comprehensible to engineering and materials science students. Although this book was written with materials scientists in mind, it will prove useful to all those interested in learning the fundamentals of the finite element method.

The method is now widely used in research in materials science and technology. For example, it is the basis for the determination of the stress distribution in loaded specimens used in deformation and fracture studies. It is used to predict the mechanical behaviour of composite and of cellular solids and it is used to analyse materials processing of metals and polymers. Materials science researchers use one of the many available commercial finite element packages to model problems in these areas. Scientists and technologists are not always well informed about the principles of the analytical methods that these packages use. One reason for this is that they find the existing texts difficult to read. There is an extensive list of finite element books written mostly for engineers or mathematicians. In them, the authors make assumptions that the reader has a facility with matrix algebra, has a grounding in applied mechanics and has an awareness of energy principles that do not feature prominently in undergraduate materials science courses and, in consequence, are rarely the stock in trade of materials science researchers or technologists.

The objective of this book is to provide an introductory text which lays out the basic theory of the finite element method in a form that will be comprehensible to materials scientists. It presents the basic ideas in a sequential and measured fashion, avoiding the use of specialist vocabulary that is not clearly defined. The basic principles are illustrated by a diversity of examples which serve to reinforce the particular aspects of the theory, and there are three finite element analyses which are presented in extenso with the detailed mathematics exposed. By this means, some of the mystery that can envelop commercial finite element packages is penetrated.