The Finite Element Method: Its Basis and Fundamentals

Front Cover
Elsevier, May 26, 2005 - Technology & Engineering - 752 pages
The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms.• The classic FEM text, written by the subject's leading authors • Enhancements include more worked examples and exercises• With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problemsActive research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations. Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics. - The classic introduction to the finite element method, by two of the subject's leading authors - Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text
 

Contents

Chapter 1 The standard discrete system and origins of the finite element method
1
plane stress
19
Chapter 3 Generalization of the finite element concepts Galerkinweighted residual and variational approaches
54
some general families of C0 continuity
103
Chapter 5 Mapped elements and numerical integration infinite and singularity elements
138
Chapter 6 Problems in linear elasticity
187
Chapter 7 Field problems heat conduction electric and magnetic potential and fluid flow
229
Chapter 8 Automatic mesh generation
264
Chapter 17 The time dimension discrete approximation in time
589
Chapter 18 Coupled systems
631
Chapter 19 Computer procedures for finite element analysis
664
Matrix algebra
668
Tensorindicial notation in the approximation of elasticity problems
674
Solution of simultaneous linear algebraic equations
683
Some integration formulae for a triangle
692
Some integration formulae for a tetrahedron
693

Chapter 9 The patch test reduced integration and nonconforming elements
329
Chapter 10 Mixed formulation and constraints complete field methods
356
Chapter 11 Incompressible problems mixed methods and other procedures of solution
383
Chapter 12 Multidomain mixed approximations domain decomposition and frame methods
429
Chapter 13 Errors recovery processes and error estimates
456
Chapter 14 Adaptive finite element refinement
500
Chapter 15 Pointbased and partition of unity approximations Extended finite element methods
525
Chapter 16 The time dimension semidiscretization of field and dynamic problems and analytical solution procedures
563
Some vector algebra
694
Integration by parts in two or three dimensions Greens theorem
699
Solutions exact at nodes
701
Matrix diagonalization or lumping
704
Author index
711
Subject index
719
Color Plate Section
735
Copyright

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Page 19 - OC ZIENK.IEWICZ and YK CHEUNG, 'The finite element method for analysis of elastic isotropic and orthotropic slabs', Proc.‎
Page 20 - The displacement functions now define uniquely the state of strain within an element in terms of the nodal displacements. These strains, together with any initial strains and the...‎

About the author (2005)

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.J. Z. Zhu is a Senior Scientist at ProCAST, ESI Group, USA.

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