Finite Element Methods for Engineering Sciences

Theoretical Approach and Problem Solving Techniques

By: Joel Chaskalovic

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Hardcover | 1 October 2008

At a Glance

Hardcover
268 Pages

Dimensions(cm)
24.13 x 16.51 x 1.27

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This self-tutorial offers a concise yet thorough grounding in the mathematics necessary for successfully applying FEMs to practical problems in science and engineering. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite-element methods instead of passively absorbing the material, as in most standard textbooks. The enlarged English-language edition, based on the original French, also contains a chapter on the approximation steps derived from the description of nature with differential equations and then applied to the specific model to be used. Furthermore, an introduction to tensor calculus using distribution theory offers further insight for readers with different mathematical backgrounds.

Industry Reviews

From the reviews:

"This is a textbook devoted to finite element methods (FEMs). ... As a whole, this book is an introductory tutorial from mathematical standpoint, convenient for students with moderate mathematical knowledge and training." (Fumio Kikuchi, Zentralblatt MATH, Vol. 1160, 2009)

"This book addresses a very popular topic, finite element methods (FEM)--a powerful engineering tool. The availability of commercial FEM software allows engineers and researchers to get approximate results for many engineering problems that are hardly solved by a pure theoretical approach. ... This book will be a very useful theoretical reference for people who are trying to develop a new type of finite element. ... Summing Up: Recommended. ... upper-division undergraduates through professionals with a strong mathematical background." (X. Le, Choice, Vol. 46 (11), 2009)

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You Can Find This Book In

Non-Fiction Engineering & Technology Technology in General Engineering in General Mathematics Calculus & Mathematical Analysis Numerical Analysis Mechanical Engineering & Materials Mechanical Engineering Applied Mathematics Computing & I.T.Computer Science

Artificial Intelligence

Summary of Courses on Finite Elements	p. 1
Some Essential Mathematical Tools	p. 1
Adapted Functional Spaces and Their Properties	p. 1
The Essential Initial Results Never to be Ever Forgotten!	p. 3
A Set of Fundamental Inequalities	p. 4
Elementary Concepts on Distributions	p. 6
Nature of the Finite Elements Method	p. 18
For Mathematical Modelling	p. 18
Structure and Functional Framework of Equations Having Partial Derivatives	p. 20
Construction of a Variational Formulation	p. 21
Existence, Uniqueness and Regularity of a Weak Solution	p. 24
Equivalence Between Strong and Weak Formulations	p. 31
Methodology and Approximation Cascades	p. 35
Some Fundamental Classes of Finite Elements	p. 39
Variational Formulation and Approximations	p. 39
Convergence of the Finite Elements Method	p. 43
Description of Ordinary Finite Elements	p. 47
Finite Elements with a Space Variable	p. 48
Finite Elements with Two Space Variables	p. 51
Finite Elements with Three Space Variables	p. 60
Variational Formulations	p. 63
Dirichlet's Problem	p. 64
Statement	p. 64
Solution	p. 67
The Neumann Problem	p. 76
Statement	p. 76
Solution	p. 79
The Fourier-Dirichlet Problem	p. 89
Statement	p. 89
Solution	p. 92
Periodic Problem	p. 102
Statement	p. 102
Solution	p. 105
Finite Elements in Deformable Solid Body Mechanics	p. 113
Mixed Stress-Displacement Problems	p. 113
Statement	p. 113
Solution	p. 120
Clamped Plate	p. 134
Statement	p. 134
Solution	p. 139
Finite Elements Applied to Strength of Materials	p. 147
Beam Subjected to Simple Traction	p. 148
Case of a Restraint	p. 148
Case of an Elastic Support	p. 151
Beam Subject to Simple Bending	p. 168
Beam Fitted With a Restraint and Having a Freely Movable Bearing	p. 168
Clamped-clamped beam - Euler-Bernoulli theory	p. 190
Solution	p. 196
Finite Elements Applied to Non Linear Problems	p. 211
Viscous Burgers Equation	p. 211
Solution	p. 215
Non-Linear Integro-Differential Equation	p. 228
Statement	p. 228
Solution	p. 231
Riccati Differential Equation	p. 240
Statement	p. 240
Solution	p. 243
References	p. 251
Index	p. 253
Table of Contents provided by Ingram. All Rights Reserved.

Finite Element Methods for Engineering Sciences

Theoretical Approach and Problem Solving Techniques

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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