A Finite Element Primer for Beginners: The Basics

by Tarek I. Zohdi

Overview

The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:

(1) Weighted residual methods and Galerkin approximations,

(2) A model problem for one-dimensional linear elastostatics,

(3) Weak formulations in one dimension,

(4) Minimum principles in one dimension,

(5) Error estimation in one dimension,

(5) Construction of Finite Element basis functions in one dimension,

(6) Gaussian Quadrature,

(7) Iterative solvers and element by element data structures,

(8) A model problem for three-dimensional linear elastostatics,

(9) Weak formulations in three dimensions,

(10) Basic rules for element construction in three-dimensions,

(11) Assembly of the system and solution schemes,

(12) Assembly of the system and solution schemes,

(13) An introduction to time-dependent problems and

(14) A brief introduction to rapid computation based on domain decomposition and basic parallel processing.

Product Details

ISBN-13:	9783319090368
Publisher:	Springer-Verlag New York, LLC
Publication date:	08/12/2014
Series:	SpringerBriefs in Applied Sciences and Technology
Sold by:	Barnes & Noble
Format:	eBook
Pages:	108
File size:	2 MB

About the Author

The author, Tarek I. Zohdi is a world-leading scientist with a remarkable number of high class publications including over 135 archival refereed journal papers, seven books as well as various handbook and encyclopedia chapters. He serves on the editorial advisory boards of ten international journals. Also, he is an editor of the leading journal Computational Mechanics and co-founder and editor-in-chief of a new journal, Computational Particle Mechanics. He is also an editor of a book series on Computational Mechanics, published by John-Wiley.

He is currently a Chancellor’s Professor of Mechanical Engineering, Chair of the Computational and Data Science and Engineering Program at UC Berkeley and holder of the W. C. Hall Family Endowed Chair in Engineering. He also holds a Staff Scientist position at Lawrence Berkeley National Labs and an Adjunct Scientist position at the Children's Hospital Oakland Research Institute. His main research interests are in micromechanical material design, particulate flow and the mechanics of high-strength fabric, with emphasis on computational approaches for advanced manufacturing and nonconvex multiscale-multiphysics inverse problems.

Table of Contents

From the content: Weighted Residuals and Galerkin’s Method for a Generic
1-D Problem.- A Model Problem: 1-D Elastostatics.- A Finite Element Implementation in One Dimension.

Editorial Reviews

“The book by Zohdi … discusses the FEM 1D and 3D problems in linear elasticity. … The book looks attractive ad is easy to read. … this is a nice little elementary book on FEM, which has an attractive and non-intimidating form for the students beginning her/his FEM studies, or for individuals whose areas of interest is different but desire to get a taste of what FEM is all about.” (Dan Givoli, IACM Expressions, Issue 39, July, 2016)

From the Publisher