# The Finite Element Method: Its Basis and Fundamentals

Butterworth-Heinemann, Aug 31, 2013 - Technology & Engineering - 756 pages

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 a significant rearrangement of the book’s content to enable clearer development of the finite element method, with major new chapters and sections added to cover:

• Weak forms
• Variational forms
• Multi-dimensional field problems
• Automatic mesh generation
• Plate bending and shells
• Developments in meshless techniques

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.

• A proven keystone reference in the library of any engineer needing to understand and apply the finite element method in design and development
• Founded by an influential pioneer in the field and updated in this seventh edition by an author team incorporating academic authority and industrial simulation experience
• Features reworked and reordered contents for clearer development of the theory, plus new chapters and sections on mesh generation, plate bending, shells, weak forms and variational forms

### Contents

 1 The Standard Discrete System and Origins of the Finite Element Method 1 2 Problems in Linear Elasticity and Fields 21 1D Problems 47 1D Problems 93 A Multidimensional Finite Element Method 115 6 Shape Functions Derivatives and Integration 151 Two and ThreeDimensional Finite Elements 211 8 The Patch Test Reduced Integration and Nonconforming Elements 257
 16 Adaptive Finite Element Refinement 545 17 Automatic Mesh Generation 573 18 Computer Procedures for Finite Element Analysis 641 Matrix Algebra 647 Some Vector Algebra 655 TensorIndicial Notation in the Approximation of Elasticity Problems 661 Solution of Simultaneous Linear Algebraic Equations 671 Triangle and Tetrahedron Integrals 681

 Complete Field Methods 285 10 Incompressible Problems Mixed Methods and Other Procedures of Solution 315 11 Multidomain Mixed Approximations 361 SemiDiscretization of Field and Dynamic Problems 379 Thin and Thick Plates 407 14 Shells as a Special Case of ThreeDimensional Analysis 467 15 Errors Recovery Processes and Error Estimates 493
 Integration by Parts in Two or Three Dimensions Greens Theorem 683 Solutions Exact at Nodes 685 1 Matrix Diagonalization or Lumping 689 Author Index 697 Subject Index 705 Copyright

### About the author (2013)

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 Professor of the Graduate School at the Department of Civil and Environmental Engineering, University of California at 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.