This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of incompressible fluids), and solid mechanics (elasticity, beams and plates). Both geometric as well as material nonlinearities are considered, and static and transient (i.e. time-dependent) responses are studied. Although there exist a number of books on nonlinear finite elements that serve as good references for engineers who are familiar with the subject and wish to learn advanced topics or the latest developments, there is currently no book which is suitable as a textbook for a first course on nonlinear finite element analysis. This book fills the void in the market, providing a clear understanding of the concepts of nonlinear finite element analyses through detailed theoretical formulations and computer implementation steps, examples and exercises. In addition, the book serves as a prelude to more advanced books on the subject.
Table of Contents
1. Introduction ; 2. The Finite Element Method: A Review ; 3. Heat Transfer and other Field Problems in One Dimension ; 4. Nonlinear Bending of Straight Beams ; 5. Heat Transfer and other Field Problems in Two Dimensions ; 6. Nonlinear Bending of Elastic Plates ; 7. Flows of Viscous Incompressible Fluids ; 8. Nonlinear Analysis of Time-Dependent Problems ; 9. Finite Element Formulations of Solids and Structures ; 10. Material Nonlinearities and Coupled Problems ; A1 Solution Procedures for Nonlinear Equations ; A2 Banded Symmetric and Unsymmetric Solvers
Junuthula Narasimha Reddy is Distinguished Professor and the inaugural holder of the Oscar S. Wyatt Endowed Chair in the Department of Mechanical Engineering at Texas A&M University, College Station, Texas. He has authored numerous papers on the theory and finite element analysis of laminated composite plates and shells, computational fluid mechanics, numerical heat transfer, and applied mathematics. He has been the recipient of many awards: Walter L. Huber Civil Engineering Research Prize of the American Society of Civil Engineers (ASCE), the Worcester Reed Warner Medal and the Charles Russ Richards Memorial Award of the American Society of Mechanical Engineers (ASME), the 1997 Archie Higdon Distinguished Educator Award from the American Society of Engineering Education (ASEE), the 1998 Nathan M. Newmark Medal from ASCE, and Excellence in Composites award from the American Society of Composites. He is Editor-in-Chief for three journals and serves on many other editorial boards.