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Introduction to the finite element method. (English) Zbl 0806.73001

New York etc.: Prentice Hall. xv, 410 p. (1992).
The objectives of this book are to present an introductory text for students in various fields of engineering. The reader needs only a general background in basic mechanics, matrix algebra, and differential and integral calculus. The intention of the authors is to provide the finite element approach for arbitrary differential equations. To this end, all differential equations used in the course are comprehensively derived, and particular attention is given to the evaluation of the physical importance of different terms involved in the equations. Then the emphasis is placed on the weak formulation of the corresponding boundary value problems and on the implementation of the Galerkin method. Thus the book presents a two-fold approach giving an introduction to the typical differential equations of the engineering mechanics on the one hand, and an introduction to the finite element treatment of these equations on the other hand.
The book is divided into 20 chapters. In the authors’ opinion, chapters 1-11 (about 230 pages) provide the minimum course. The main topics included in this introductory part are: matrix algebra, Green and Gauß theorems, strong and weak forms of differential equations, shape functions, weighted residual methods, finite element meshes, and global nodal point numbering. The techniques developed here are mainly applied to the one- and two-dimensional heat flow problems.
Chapters 12-18 (approximately 130 pages) can be considered as an extension to various intermediate courses. These chapters present a good discussion of linear elasticity problems (concepts of stress and strain, Saint-Venant’s torsion theory, beams and plates) together with some related mathematical aspects (convergence criteria, general approximation techniques, three- and four-node elements, completeness and compatibility requirements). Finally, the full course is completed by chapters 19 and 20 containing more advanced topics such as isoparametric finite elements, integral transformations, and numerical integration techniques.
The presentation of fundamental ideas is supported by many examples and by detailed subject index; the text is written very clearly. Therefore this book can be of interest for all newcomers in the finite element methods.
Reviewer: O.Titow (Berlin)

MSC:

74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74S05 Finite element methods applied to problems in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
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