Review of The Finite Element Method for Solid and Structural Mechanics, 6th Edition, by O. C. Zienkiewicz and R. L. Taylor: Elsevier Butterworth-Heinemann, Jordan Hill, Oxford OX2 8DP, U.K.; 2005; ISBN: 0-7506-6321-9; 631 pp. Price: $94.95.

The 6th edition of the classic text on The Finite Element Method by O. C. Zienkiewicz has come a long way since it was published first in 1967 by McGraw-Hill, Berkshire, England. The original 272 pages of text on The Finite Element Method in Structural and Continuum Mechanics written in collaboration with Y. K. Cheung, University of Hong Kong, has increased more than six-fold and turned into a comprehensive treatment comprised of three substantial volumes of more than 600 pages each:This review is limited to the first two volumes of the sixth edition with focus on the second volume because of the interest and background of the reviewer.

The first volume on The FEM: Its Basis and Fundamentals of FEM sets the stage for linear applications. Although introductory in nature, this volume is not a text book in the usual sense of classroom use with homework assignments and solution manuals. It is a powerful review of current findings, with numerous historical anecdotes and references to recent and past publications at the end of each of the 19 chapters. Among the classical topics on finite-element approximations in 1D, 2D, and 3D, the first volume addresses mixed element formulations, error estimates, PUM approximations and extended finite-element methods as well as time discretization methods.

The second volume on The FEM for Solid and Structural Mechanics contains 19 chapters and two appendices. Roughly speaking, Chapters 1, 2, and 3 set the stage for nonlinear analysis of solids in Chapters 4, 5, and 6 which deal with nonlinear material behavior, nonlinear geometric problems and the combination of these two sources of nonlinearity. Chapter 4 provides a concise review of inelastic material behavior with focus on continuum plasticity for mixed isotropic–kinematic hardening based on the tensorial format of nine stress and strain components before dimensional reduction to six components using Voigt notation. Chapter 5 contains the fundamentals of large deformation analysis within the total and updated Lagrangean descriptions in mixed and irreducible variational settings. Chapter 6 combines material and geometric nonlinearities within the format of finite elasticity, viscoelasticity and elastoplasticity, taking special note of the product decomposition of isochoric and deviatoric deformations. Chapters 7 and 8 address contact, constraints and connections between rigid and flexible bodies. Chapter 9 contributed by N. Bi’cani’c, University of Glasgow, presents on overview of “Discrete Element Methods” with focus on the underlying contact problems. The subsequent Chapters 10–15 address the dimensional reduction from solids to structures. Chapter 10 starts with rod analysis using classical Euler-Bernoulli theory for “thin” or rather “slender” members and alternative “thick” approximations based on Timoshenko theory. Chapters 11 and 12 deal with the generalization of rods to thin and thick plates within the format of displacement and mixed variational settings. Chapters 13 and 14 review classical applications of flat elements to thin shells and their extension to curvilinear elements for shells of revolution. Chapter 15 includes a separate treatment of so-called degenerate solid elements for modeling thick plates and shells. After a brief treatment of the “finite-strip” method and its powerful applications to prismatic box structures and axisymmetric shells in Chapter 16, the book includes a separate treatment of large displacement and instability problems in Chapter 17. In Chapter 18, by B. Schrefler, University of Padua, the timely topic of “Multiscale Modelling” is addressed and illustrated with challenging applications from the oil and nuclear industries. Chapter 19 of the book concludes with remarks on the companion computer program FEAPpv (personal version) written in Fortran $90∕95$ which is available at no cost from R. L. Taylor at University of California, Berkeley. In fact, this is the great strength of this book which brings together theory and practice by translating the complexity of nonlinear continuum finite-element theory into the computer implementation of transient analysis of structures and solids in 3D.

In summary, the self-contained text lends itself to advanced graduate studies in computational mechanics. It features a modern continuum mechanics-based treatment of solids and structures and provides an outstanding resource for graduate students and researchers in advanced topics of nonlinear finite-element analysis.