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.

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

J. N. Reddy , Distinguished Professor, Department of Mechanical, Engineering, Texas A&M University, Texas, USA