The Finite Element Method: Its Basis and Fundamentals

The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees the significant addition of content that address coupled field problems; this includes formulations and details of algorithms for thermoelastic, chemoelastic, poroelastic, and piezoelectric problems. The material is also illustrated in application to the nonlinear behaviour of energy storage in batteries. Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers, and professional engineers involved in finite element-based engineering analysis.

Table of Contents:
1. Introduction: Origins of the Finite Element Method and Solution of Discrete Systems 2. Field Problems: Finite Element Solution of 1-D Problems 3. Linear Elasticity: Finite Element Solution of 1-D Problems 4. Field Problems: Finite Element Solution in Multi-dimensions 5. Shape Functions 6. Elasticity Problems: Finite Element Solution in Multi-dimensions 7. Coupled Problems 8. Patch Test and Non-conforming Elements 9. Mixed Formulations 10. Multi-domain Approximations 11. Time Domain: Semi-Discretization of Transient Problems 12. Error and Error Estimates 13. Plate Bending: Thin and Thick Plates 14. Shells 15. Computer Procedures

About the Author :
Professor O.C. Zienkiewicz, CBE, FRS, FREng died on 2 January 2009. Prior to his death he was Professor Emeritus at the Civil and Computational Engineering Centre, University of Wales Swansea and previously was Director of the Institute for Numerical Methods in Engineering at the University of Wales Swansea, UK. He also held the UNESCO Chair of Numerical Methods in Engineering at the Technical University of Catalunya, Barcelona, Spain. He was the head of the Civil Engineering Department at the University of Wales Swansea between 1961 and 1989. During this period he established that department as one of the primary centres of finite element research. In 1968 he became the Founder Editor of the International Journal for Numerical Methods in Engineering which still remains today the major journal in this field. The recipient of 27 honorary degrees and many medals, Professor Zienkiewicz was a member of five academies – an honour he received for his many contributions to the fundamental developments of the finite element method. In 1978, he became a Fellow of the Royal Society and the Royal Academy of Engineering. This was followed by his election as a foreign member to the US National Academy of Engineering (1981), the Polish Academy of Science (1985), the Chinese Academy of Sciences (1998), and the National Academy of Science, Italy (Academia dei Lincei) (1999). He published the first edition of this book in 1967 and it remained the only book on the subject until 1971. Professor R.L. Taylor has more than 60 years of experience in the modelling and simulation of structures and solid continua including eighteen years in industry. He is Professor of the Graduate School and the Emeritus T.Y. and Margaret Lin Professor of Engineering at the University of California, Berkeley and also Corporate Fellow at Dassault Systèmes Americas Corp. in Johnston, Rhode Island. In 1991 he was elected to membership in the US National Academy of Engineering in recognition of his educational and research contributions to the field of computational mechanics. Professor Taylor is a Fellow of the US Association for Computational Mechanics – USACM (1996) and a Fellow of the International Association of Computational Mechanics – IACM (1998). He has received numerous awards including the Berkeley Citation, the highest honour awarded by the University of California, Berkeley, the USACM John von Neumann Medal, the IACM Gauss–Newton Congress Medal and a Dr.-Ingenieur ehrenhalber awarded by the Technical University of Hannover, Germany. Professor Taylor has written several computer programs for finite element analysis of structural and non-structural systems, one of which, FEAP, is used world-wide in education and research environments. A personal version, FEAPpv, available on GitHub, is incorporated into this book. S. Govindjee is the Horace, Dorothy, and Katherine Johnson Endowed Professor in Engineering and a Distinguish Professor of Civil and Environmental Engineering at the University of California, Berkeley (1993–2006, 2008–present). His main interests are in theoretical and computational mechanics with an emphasis on micro-mechanics, shape memory alloys, and elastomers. Prior to joining Berkeley he worked as an engineer at the Lawrence Livermore National Laboratory (1991–1993) in Livermore, California. He was also Professor of Mechanics at ETH Zürich (2006–2008) in Zürich, Switzerland. Dr. Govindjee serves as a consultant to several governmental agencies and private corporations. He is an active member of the American Society of Mechanical Engineers (ASME), the US Association for Computational Mechanics (USACM), and the International Association for Computational Mechanics (IACM) and has served or serves on the editorial boards of several major journals. He is also a registered Professional Mechanical Engineer in the state of California. He is the author of four texts books on engineering mechanics. Noteworthy honours include a National Science Foundation Career Award, the inaugural 1998 Zienkiewicz Prize and Medal, an Alexander von Humboldt Foundation Fellowship 1999, a Berkeley Chancellor’s Professorship 2006–2011, and a guest Professorship at ETH Zürich 2008–2013. In 2015 he was named a Fellow of the US Association for Computational Mechanics. In 2018 he received a Humboldt-Forschungspreis (Alexander von Humboldt Research Award).