1R3. Introductory Finite Element Method. Mechanical Engineering Series. - CS Desai (Dept of Civil Eng and Eng Mech, Univ of Arizona, Tucson AZ) and T Kundu (Univ of Arizona, Tucson AZ). CRC Press LLC, Boca Raton FL. 2001. 496 pp. ISBN 0-8493-0243-9. $89.95.
Reviewed by Xiaoyan Lei (Dept of Civil Eng, E China Jiaotong Univ, Nanchang, 330013, China).
This is an excellent addition to the available textbooks on finite element method. The book is intended mainly for undergraduate and beginning graduate students. It distinguishes itself in comparison to other textbooks in its description and organization. Its approach is sufficiently elementary so that it can be introduced with the background of essentially undergraduate subjects. In addition, the treatment is broad enough so that the reader or the teacher interested in various topics such as stress-deformation analysis, fluid and heat flow, potential flow, time-dependent problems, diffusion, torsion, and wave propagation can use and teach from it. The mathematical formulations and fundamental concepts illustrated with simple examples and summaries or comments and plenty of exercises presented at the end of each chapter are other merits of the book.
In what follows, a brief description of the contents of the book is given (14 chapters and three Appendices).
Chapter 1 presents a philosophical discussion of the finite element method. Chapter 2 gives a description of the eight basic steps and fundamental principles of variational calculus. Chapters 3 to 5 cover one-dimensional problems in stress deformation analysis and steady and time dependent flow of heat and fluids.
Chapter 6 deals with the finite element codes that can solve different types of problems. The codes presented are thoroughly documented and detailed so that they can be used and understood without difficulty. Chapter 7 introduces the idea of higher order approximation for the problem of beam bending and beam column. One-dimensional problems in mass transport and wave propagation are covered in Chapters 8 and 9, respectively.
Chapter 10 presents the basic finite element formulation for two- and three-dimensional problems. Different types of two-dimensional problems are discussed in Chapters 11 to 14. The chapters on torsion (Ch 11) and other field problems (Ch 12) havebeen chosen because they involve only one degree of freedom at a point. Chapters 13 and 14 cover two-dimensional stress deformation problems involving two and higher degrees of freedom at a point.
Appendix 1 gives descriptions, solutions, and comparisons for a problem by using a number of methods: closed form, Galerkin, collocation, sub domain least squares, Ritz, finite difference, and finite element. Appendix 2 introduces the commonly-used direct and iterative procedures for the solution of algebraic simultaneous equations. Appendix 3 presents details of a number of computer codes relevant to various topics in the text.
Introductory Finite Element Method is a very useful book for undergraduate students and teachers that deal with the finite element method. It is well produced, the printing is generally clear, and the diagrams are well done. The book is highly recommended for undergraduate students and teachers in universities.