This book explores the numerical algorithms underpinning modern finite element based computational mechanics software. It covers all the major numerical methods that are used in computational mechanics. It reviews the basic concepts in linear algebra and advanced matrix theory, before covering solution of systems of equations, symmetric eigenvalue solution methods, and direct integration of discrete dynamic equations of motion, illustrated with numerical examples. This book suits a graduate course in mechanics based disciplines, and will help software developers in computational mechanics. Increased understanding of the underlying numerical methods will also help practicing engineers to use the computational mechanics software more effectively.
Table of Contents
Review of Matrix Analysis. Review of Methods of Analysis In Structural Mechanics. Solution of System of Linear Equations. Iterative Solution Methods for System of Linear Equations. Conjugate Gradient Methods. Solution Methods for System of Nonlinear Equations. Eigenvalue Solution Methods. Direct Integration of Dynamic Equation of Motion. The Generalized Difference Method.
Jamshid Ghaboussi is Professor Emeritus at University of Illinois at Urbana-Champaign. He has over 45 years of experience in teaching and research in Computational Mechanics, Computational Intelligence and Soft Computing in Engineering Applications. Dr. Xiping Wu is a Principal Engineer in Civil and Marine Engineering with Shell International Exploration & Production Inc.
"This book is a collection of the most relevant numerical methods used in computational mechanics. It is a clear and rigorous presentation of algorithms corresponding to numerical methods for solving systems of linear and nonlinear algebraic equations, for finding eigenvalues and eigenvectors of matrices, and for integration of dynamic equations of motion. This hands-on presentation will certainly be welcomed by users of computational mechanics software interested in gaining a better understanding of the implemented algorithms as well as developers of software. In addition, the book could be used as a textbook for a graduate level course in computational mechanics."
— Corina S. Drapaca, Pennsylvania State University, USA