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Finite Element Method: Volume 1, The Basics of The Finite Element Method provides a complete introduction to the method, and is essential reading for undergraduates, postgraduates and professional engineers 
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Finite Element Method: Volume 2, Solid Mechanics concentrates on non-linear solid and structural mechanics and is ideal for postgraduate students and professional engineers working in this discipline 
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Finite Element Method: Volume 3, Fluid Dynamics covers the whole range of fluid dynamics and is ideal reading for postgraduate level students and professional engineers working in this discipline 
O. C. Zienkiewicz & R. L. Taylor, «Finite Element Method: Volume 1, 2,3»
Butterworth-Heinemann | ISBN:0750650494 | 5 edition (August 28, 2000) | 712 pages | 


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Vol. 1. The Finite Element Method - The Basis
Volume 1 is an essential text for people trying to acquaint themselves with the subject and requiring an up to date presentation of theory and possibilities. It deals strictly with linear problems and the matter presented allows engineers and scientists with different backgrounds to become acquainted with the subject. The mathematics is kept at a fairly simple level to cover a wide readership. The book should also be useful to students of mathematics albeit they might be used to a different notation than that used in this text.

The arrangement of Vol.1 differs some what from that of Vol.1 in the fourth edition. A rearrangement of text was made to include the general chapter dealing the concepts of mathematical formulations early in the book (Ch.3). This allows the reader to become acquainted rapidly with the mathematical background and where the finite element method fits into the general scheme of numerical approximation.

In addition several chapters dealing with dynamics and transient phenomena have been moved from Vol.2 to this volume. These have been updated and include various approximation procedures recently used (e.g. Discontinuous Galerkin).

Though many of the chapters have not been substantially altered, they have been updated to include most recent references and thinking. However many new ideas and subjects are presented in this volume. In particular the following developments should be noted.

(1) The recently developed procedures of recovery for increasing the accuracy of the results are presented. These lead naturally to the most efficient procedures of error estimation and adaptivity. The two chapters 14 and 15 present this subject in a thoroughly up to date manner and here all the recent procedures have been made available.

(2) The subject of mixed methods (Ch.11) has been elaborated further from the fourth edition and much attention has been given to recent developments of hybrid methods including even such methods as Discontinuous Galerkin method (Ch.13). Attention has been given to the so-called "enhanced strain" methods that today are widely used in various applications of solid mechanics.

(3) The subject of incompressible behaviour is given special attention and a whole chapter (Ch.12) is devoted to it. Here recent work on various procedures of stabilisation is presented in comparative manner and readers can acquaint themselves with the present day developments in this area. Thus chapters 11,12 and 13 have been very substantially rewritten.

(4) In the last decade, much progress has been achieved in the development of the so called meshless (element free methods) methods. Here so called partition of unity procedures have allowed a considerable expansion of FEM possibilities. Chapter 16 presents the present state of the art and here the reader will find many of the concepts that are today at the "sharp end" of research. These are given in an assessable manner that may guide the developments in the early part of the next millennium.

One important development that is included in the fifth edition is the omission of detailed program listings that have been characteristics of all previous editions. The reason for this is fairly rapid development of the computer software and the need for providing updates that can eliminate errors and show the most recent development. We present for each volume a full program list and computer procedures on this webpage.
Vol. 2. The Finite Element Method - Solid Mechanics
Volume 2 is partially rewritten and some new chapters particularly in the area of large deformation and strain are incorporated. In particular we start this volume with the description of non-linear methodologies of solution for the problem of non-linear material behaviour and introduce right in the beginning the concepts necessary for description of various constitutive laws ranging from viscoelasticity through plasticity to creep.

The chapters dealing with shell and plate formulation which were initially the subject of the finite element attack are brought up to date by recent developments in which so called linked interpolations are used. We mentioned those in the fourth edition but since its publication the development has been rapid and the elements presented here are probably among those which are the best. For this reason we eliminated some of the descriptive matter for the very simple elements previously used in the plate theory and concentrate attention on recent development of both thick and thin approximations for plates, shells etc.

A largely rewritten series of chapters deal with non-linear geometry, stability and buckling of structures as well as large deformation theory necessary for impact studies. Here a simple introduction to large deformation behaviour is given and the reader can thus avoid the complex introduction usually belonging to advanced texts of mechanics. Most of the presentation of this chapter and indeed others of this book uses indicial notation and the generalised notion of strain and stress. Several of the chapters in the new Vol.2 essentially repeat the topics previously dealt with in Vol.2 of the fourth edition that remain still valid today. These include such things as finite strip methods etc.
Vol. 3. The Finite Element Method - Fluid Dynamics
This volume as the title indicates is directed entirely at those whose main interest is in the fluid mechanics area. Here however a very wide application field is covered ranging from incompressible slow viscous flow to high-speed supersonic flows. Such specialised applications as shallow water flow, ocean waves and metal or plastic forming are also included in this text as specific examples.

What is entirely novel in this text is the manner of presentation and the introduction of a unified algorithm, which is applicable to all the fields of study in the fluid mechanics area. This algorithm which has been developed only a few years ago has now superseded in view of the authors many older ones and provides a unique and simple approach to most problems. The new algorithm is based on the so-called Characteristic Galerkin method of dealing with convection dominated problems. Thus with suitable splitting the full fluid mechanics equations can be divided into two parts. The first of these dealing with a set of scalar transport is convection dominated and uses the Characteristic Galerkin process. The second presents a self-adjoint problem in terms of pressure for which Galerkin procedures can be directly applied. Although some of the concepts have been given in the fourth edition, most of the presentation is new and here very little remains from the previous edition. We believe Vol.3 is the one from which many can learn the basic concepts of computational fluid dynamics.

We introduce here methodologies capable of dealing with supersonic and hypersonic behaviours at the same time showing that the same formulation applies well to the study of shallow water tidal phenomena being able to predict such things as the `bore' that occurs in many highly tidal areas.

The new algorithm stabilises both the convective part of the equations and the incompressible phenomena.

Many new topics are included and in particular application to the study of wave resistance of ships and other free surface phenomena can now be modelled using the new algorithm fairly simply. Also in the same chapter, we deal with buoyancy phenomena by which various convection problems can be solved. These are of importance in heat transfer engineering as well as in environmental studies.

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