A First Course in Finite Elements

by Fish, Jacob; Belytschko, Ted

• ISBN13: 9780470035801
• ISBN10: 0470035803
• Edition: 1st
• Format: Paperback
• Copyright: 2007-05-21
• Publisher: WILEY

Summary

Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations. Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements: Adopts a generic approach to the subject, and is not application specific In conjunction with a web-based chapter, it integrates code development, theory, and application in one book Provides an accompanying Web site that includes ABAQUS Student Edition, Matlab data and programs, and instructor resources Contains a comprehensive set of homework problems at the end of each chapter Produces a practical, meaningful course for both lecturers, planning a finite element module, and for students using the text in private study. A First Course in Finite Elements is the ideal practical introductory course for junior and senior undergraduate students from a variety of science and engineering disciplines. The accompanying advanced topics at the end of each chapter also make it suitable for courses at graduate level, as well as for practitioners who need to attain or refresh their knowledge of finite elements through private study.

Author Biography

Jacob Fish The Rosalind and John J. Redfern, Jr. ’33 Chaired Professor in Engineering Rensselaer Polytechnic Institute, Troy, NY 12180

Dr. Fish has 20 years of experience (both industry and academia) in the field of multi-scale computational engineering, which bridges the gap between modeling, simulation and design of products based on multi-scale principles. Dr. Fish has published over one hundred journal articles and book chapters. Two of his papers, one on development of multilevel solution techniques for large scale systems presented at the 1995 ASME International Computers in Engineering Conference and the second one, on fatigue crack growth in aging aircraft presented at the 1993 Structures, Structural Dynamics, and Materials Conference have won the Best Paper Awards. Dr. Fish is a recipient of 2005 USACM Computational Structural Mechanics Award given “in recognition of outstanding and sustained contributions to the broad field of Computational Structural Mechanics”. He is editor of the International Journal for Multiscale Computational Engineering.

Ted Belytschko, Department of Mechanical Engineering2145 North Sheridan Road, Northwestern University, Evanston, IL 60208-311

Ted Belytschko's main interests lie in the development of computational methods for engineering problems.  He has developed explicit finite element methods that are widely used in crashworthiness analysis and virtual prototyping.  He is also interested in engineering education, and he chaired the committee that developed the "Engineering First Program" at Northwestern.  He obtained his B.S. and Ph.D. at Illinois Institute of Technology in 1965 and 1968, respectively.  He has been at Northwestern since 1977 where he is currently Walter P. Murphy Professor and McCormick Distinguished Professor of Computational Mechanics.  He is co-author of the book NONLINEAR FINITE ELEMENTS FOR CONTINUA AND STRUCTURES with W.K.Liu and B. Moran (published by Wiley and in the third printing) and he has edited more than 10 other books.  In January 2004, he was listed as the 4th most cited researcher in engineering. He is past Chairman of the Engineering Mechanics Division of the ASCE, the Applied Mechanics Division of ASME, past President of USACM, and a member of the National Academy of Engineering (elected in 1992) and the American Academy of Arts and Sciences (elected in 2002). He is the editor of Numerical Methods in Engineering.

Table of Contents

Preface

Introduction

Direct approach for Discrete Systems

Strong and Weak Forms for One-dimensional Problems

Approximation of Trial Solutions, Weight Functions and Gauss Quadrature for One-Dimensional Problems

Finite Element Formulation for One-Dimensional Problems

Strong and Weak Forms for Multi-Dimensional Scalar Field Problems

Approximation of Trial Solutions, Weight Functions and Gauss Quadrature for Multi-Dimensional Problems

Finite Element Formulation for Multi Dimensional Scalar Field Problems

Finite Element Formulation for Vector Field Problems - Linear Elasticity

Finite Element Formulation for Beams

Commercial Finite Element Program ABAQUS Tutorials

Appendix

Index

Table of Contents provided by Publisher. All Rights Reserved.