The Finite Element Method

Name: The Finite Element Method
Price: 286.99 USD
Availability: InStock
ISBN: 9780443160448

Its Basis and Fundamentals

by O. C. Zienkiewicz, R. L. Taylor, S. Govindjee

8th Edition

Publisher: Elsevier Butterworth Heinemann

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Book Details

Print ISBN	9780443160448
eText ISBN	9780443160455
Publisher	Elsevier Butterworth Heinemann
Publishing Year	2024
Edition	8th Edition
Language	English
Pages	650

The textbook The Finite Element Method, 8th Edition presents fundamental theory and worked examples for applying numerical mesh methods to engineering problems. The initial sections establish core mathematical foundations, beginning with discrete systems, one-dimensional field problems, and weak form approximations. Readers are guided through variational principles, numerical integration techniques, and isoparametric shape function formulations across multi-dimensional domains.

The narrative expands into physical continuum applications, concentrating on linear elasticity in two and three dimensions. Subsequent chapters analyze transient behavior in solid mechanics, incompressible media constraints, and mixed formulations. Dedicated modules address structural approximations, contrasting thin and thick plate bending models while evaluating shells as specialized three-dimensional continuum cases.

To consolidate theoretical concepts, the text features structured chapter summaries following major analytical developments. This eighth edition provides direct computational practice for senior undergraduate students, graduate students, researchers, and practicing engineers examining modern continuum mechanics.

Chapter 1: The standard discrete system and origins of the finite element method
Chapter 2: Problems in linear fields
Chapter 3: Weak forms and approximate solutions: 1-D field problems
Chapter 4: Finite element approximate solutions: 1-D field problems
Chapter 5: Finite element forms exact at nodes
Chapter 6: Variational forms and finite element approximation: 1-D problems
Chapter 7: Field problems: a multi-dimensional finite element method
Chapter 8: Shape functions, derivatives and integration
Chapter 9: Problems in linear elasticity
Chapter 10: Elasticity: two and three dimensional finite elements
Chapter 11: The patch test, reduced integration, and non-conforming elements
Chapter 12: Mixed formulation and constraints – complete field methods
Chapter 13: Incompressible problems, mixed methods and other procedures of solution
Chapter 14: Transient analysis of solids
Chapter 15: Finite element solutions: multi-physics problems
Chapter 16: Multi-physics battery simulation
Chapter 17: Multidomain mixed approximations
Chapter 18: The time dimension – semi-discretization of field and dynamic problems
Chapter 19: Plate bending approximation: thin and thick plates
Chapter 20: Shells as a special case of three-dimensional analysis
Chapter 21: Computer procedures for finite element analysis
Chapter A: Matrix algebra
Chapter B: Some vector algebra
Chapter C: Mathematical properties, error estimates and convergence
Chapter D: Tensor-indicial notation in elasticity problems
Chapter E: Solution of simultaneous linear algebraic equations
Chapter F: Integration by parts – Green's theorem
Chapter G: Triangle and tetrahedron integrals
Chapter H: Matrix diagonalization or lumping
Chapter I: Recovery process