The Finite Element Method: its Basis and Fundamentals

✍ Scribed by O. C. Zienkiewicz, R. L. Taylor and J.Z. Zhu (Auth.)

• Publisher: Butterworth-Heinemann
• Year: 2013
• Tongue: English
• Leaves: 753
• Edition: 7
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Content:
The Finite Element Method: Its Basis and Fundamentals, Page i
Author Biography, Page ii
The Finite Element Method: Its Basis and Fundamentals, Page iii
Copyright, Page iv
Dedication, Page v
List of Figures, Pages xix-xxxiii
List of Tables, Pages xxxv-xxxvi
Preface, Pages xxxvii-xxxviii
Chapter 1 - The Standard Discrete System and Origins of the Finite Element Method, Pages 1-20
Chapter 2 - Problems in Linear Elasticity and Fields, Pages 21-45
Chapter 3 - Weak Forms and Finite Element Approximation: 1-D Problems, Pages 47-92
Chapter 4 - Variational Forms and Finite Element Approximation: 1-D Problems, Pages 93-113
Chapter 5 - Field Problems: A Multidimensional Finite Element Method, Pages 115-149
Chapter 6 - Shape Functions, Derivatives, and Integration, Pages 151-209
Chapter 7 - Elasticity: Two- and Three-Dimensional Finite Elements, Pages 211-255
Chapter 8 - The Patch Test, Reduced Integration, and Nonconforming Elements, Pages 257-284
Chapter 9 - Mixed Formulation and Constraints: Complete Field Methods, Pages 285-314
Chapter 10 - Incompressible Problems, Mixed Methods, and Other Procedures of Solution, Pages 315-359
Chapter 11 - Multidomain Mixed Approximations, Pages 361-378
Chapter 12 - The Time Dimension: Semi-Discretization of Field and Dynamic Problems, Pages 379-405
Chapter 13 - Plate Bending Approximation: Thin and Thick Plates, Pages 407-466
Chapter 14 - Shells as a Special Case of Three-Dimensional Analysis, Pages 467-491
Chapter 15 - Errors, Recovery Processes, and Error Estimates, Pages 493-543
Chapter 16 - Adaptive Finite Element Refinement, Pages 545-572
Chapter 17 - Automatic Mesh Generation, Pages 573-640
Chapter 18 - Computer Procedures for Finite Element Analysis, Pages 641-645
Appendix A: Matrix Algebra, Pages 647-653
Appendix B: Some Vector Algebra, Pages 655-659
Appendix C: Tensor-Indicial Notation in the Approximation of Elasticity Problems, Pages 661-670
Appendix D: Solution of Simultaneous Linear Algebraic Equations, Pages 671-679
Appendix E: Triangle and Tetrahedron Integrals, Pages 681-682
Appendix F: Integration by Parts in Two or Three Dimensions (Green’s Theorem), Pages 683-684
Appendix G: Solutions Exact at Nodes, Pages 685-687
Appendix H: Matrix Diagonalization or Lumping, Pages 689-695
Author Index, Pages 697-704
Subject Index, Pages 705-714

✦ Subjects

Математика;Вычислительная математика;Метод конечных элементов;