Authors:
- Presents absolute essentials of the Finite Element Method
- Offers a basic introduction to some essential mathematical concepts and to the mechanics of a continuum
- Written by an author with long years of experience teaching finite element classes
- Illustrated through the classical model problem of linearized elasticity
- The second edition includes an extensive repository of Sample Tests and Sample Projects
- Includes supplementary material: sn.pub/extras
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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
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:
• Weighted residual methods and Galerkin approximations,
• A model problem for one-dimensional linear elastostatics,
• Weak formulations in one dimension,
• Minimum principles in one dimension,
• Error estimation in one dimension,• Construction of Finite Element basis functions in one dimension,
• Gaussian Quadrature,
• Iterative solvers and element by element data structures,
• A model problem for three-dimensional linear elastostatics,
• Weak formulations in three dimensions,
• Basic rules for element construction in three-dimensions,
• Assembly of the system and solution schemes,
• An introduction to time-dependent problems and
• An introduction to rapid computation based on domain decomposition
and basic parallel processing.
The approach is to introduce the basic concepts first in one-dimension, then move on to three-dimensions. A relatively informal style is adopted. This primer is intended to be a “starting point”, which can be later augmented by the large array of rigorous, detailed, books in the area of Finite Element analysis. In addition to overall improvements to the first edition, this second edition also adds several carefully selected in-class exam problems from exams given over the last 15 years at UC Berkeley, as well as a large number of take-home computer projects. These problems and projects are designed to be aligned to the theory provided in the main text of this primer.
Authors and Affiliations
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University of California, Berkeley, USA
Tarek I. Zohdi
About the author
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.
Bibliographic Information
Book Title: A Finite Element Primer for Beginners
Book Subtitle: The Basics
Authors: Tarek I. Zohdi
DOI: https://doi.org/10.1007/978-3-319-70428-9
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-70427-2Published: 04 January 2018
eBook ISBN: 978-3-319-70428-9Published: 30 December 2017
Edition Number: 2
Number of Pages: XIII, 135
Number of Illustrations: 41 b/w illustrations
Topics: Solid Mechanics, Computational Science and Engineering, Complexity, Numerical and Computational Physics, Simulation, Engineering Fluid Dynamics, Mathematical Modeling and Industrial Mathematics