The Finite Element Method

O. C. Zienkiewicz was one of the early pioneers of the finite element method and is internationally recognized as a leading figure in its development and wide-ranging application. He was awarded numerous honorary degrees, medals and awards over his career, including the Royal Medal of the Royal Society and Commander of the British Empire (CBE). He was a founding author of The Finite Element Method books and developed them through six editions over 40 years up to his death in 2009. Previous positions held by O.C. Zienkiewicz include UNESCO Professor of Numerical Methods in Engineering at the International Centre for Numerical Methods in Engineering, Barcelona, Director of the Institute for Numerical Methods in Engineering at the University of Wales, Swansea, U.K. R.L Taylor is a Professor of the Graduate School at the Department of Civil and Environmental Engineering, University of California, Berkeley, USA. Awarded the Daniel C. Drucker Medal by the American Society of Mechanical Engineering in 2005, the Gauss-Newton Award and Congress Medal by the International Association for Computational Mechanics in 2002, and the Von Neumann Medal by the US Association for Computational Mechanics in 1999. Sanjay Govindjee is a Professor of Civil Engineering and the Horace, Dorothy, and Katherine Johnson Endowed Professor at the University of California, Berkeley. His main research interests are in theoretical and computational mechanics with an emphasis on micro-mechanics, shape memory alloys, and elastomers. He also serves as a consultant to several governmental agencies and private corporations. He is an active member in major societies such as the American Society of Mechanical Engineers and the US Association for Computational Mechanics. He is also a registered Professional Mechanical Engineer in the state of California. Noteworthy honors 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 (Humboldt Research Award).

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 & 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