Computational Continuum Mechanics

( 1 )

Overview

This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large-deformation finite element formulation and then a formulation that can ...

See more details below
Hardcover
$117.47
BN.com price
(Save 6%)$125.00 List Price
Other sellers (Hardcover)
  • All (6) from $100.33   
  • New (4) from $100.33   
  • Used (2) from $117.46   

Overview

This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large-deformation finite element formulation and then a formulation that can efficiently solve small deformation problems that characterize very and moderately stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practicing engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dynamics, and other fields of science and engineering using the general continuum mechanics theory.

About the Author:
Ahmed A. Shabana is the Richard and Loan Hill Professor of Engineering at the University of Illinois, Chicago

Read More Show Less

Product Details

  • ISBN-13: 9781107016026
  • Publisher: Cambridge University Press
  • Publication date: 1/31/2012
  • Edition number: 2
  • Pages: 340
  • Sales rank: 1,066,330
  • Product dimensions: 7.10 (w) x 10.10 (h) x 1.00 (d)

Meet the Author

Ahmed Shabana is University Distinguished Professor and the Richard and Loan Hill Professor of Engineering at the University of Illinois at Chicago. Professor Shabana is the author of the books, Dynamics of Multibody Systems 3rd edition, Computational Dynamics 3rd edition, Railroad Vehicle Dynamics, Theory of Vibration: An Introduction 2nd edition, and Vibration of Discrete and Continuous Systems 2nd edition. He has served on the editorial board of several journals, and he is the Founding Chair of the ASME Technical Committee on Multi-Body Systems and Nonlinear Dynamics. He is a Fellow of the American Society of Mechanical Engineers (ASME).

Read More Show Less

Table of Contents

Preface     ix
Introduction     1
Matrices     2
Vectors     6
Summation Convention     12
Cartesian Tensors     13
Polar Decomposition Theorem     25
D'Alembert's Principle     27
Virtual Work Principle     34
Approximation Methods     37
Discrete Equations     40
Momentum, Work, and Energy     43
Parameter Change and Coordinate Transformation     45
Problems     48
Kinematics     51
Motion Description     52
Strain Components     60
Other Deformation Measures     67
Decomposition of Displacement     69
Velocity and Acceleration     71
Coordinate Transformation     75
Objectivity     82
Change of Volume and Area     85
Continuity Equation     89
Reynolds' Transport Theorem     90
Examples of Deformation     92
Problems     100
Forces and Stresses     103
Equilibrium of Forces     103
Transformation of Stresses     106
Equations of Equilibrium     107
Symmetry of the Cauchy Stress Tensor     109
Virtual Work of the Forces     111
Deviatoric Stresses     120
Stress Objectivity     123
Energy Balance     127
Problems     129
Constitutive Equations     131
Generalized Hooke's Law     132
Anisotropic Linearly Elastic Materials     134
Material Symmetry     135
Homogeneous Isotropic Material     137
Principal Strain Invariants     144
Special Material Models for Large Deformations     146
Linear Viscoelasticity     150
Nonlinear Viscoelasticity     164
A Simple Viscoelastic Model for Isotropic Materials     171
Fluid Constitutive Equations     173
Navier-Stokes Equations     174
Problems     175
Plasticity Formulations     177
One-Dimensional Problem     179
Loading and Unloading Conditions     180
Solution of the Plasticity Equations     181
Generalization of the Plasticity Theory: Small Strains     190
J[subscript 2] Flow Theory with Isotropic/Kinematic Hardening     197
Nonlinear Formulation for Hyperelastic-Plastic Materials      214
Hyperelastic-Plastic J[subscript 2] Flow Theory     225
Problems     230
Finite Element Formulation: Large-Deformation, Large-Rotation Problem     231
Displacement Field     233
Element Connectivity     240
Inertia and Elastic Forces     243
Equations of Motion     246
Numerical Evaluation of the Elastic Forces     250
Finite Elements and Geometry     256
Two-Dimensional Euler-Bernoulli Beam Element     263
Two-Dimensional Shear Deformable Beam Element     267
Three-Dimensional Cable Element     269
Three-Dimensional Beam Element     270
Thin-Plate Element     272
Higher-Order Plate Element     274
Element Performance     275
Other Finite Element Formulations     280
Updated Lagrangian and Eulerian Formulations     282
Problems     284
Finite Element Formulation: Small-Deformation, Large-Rotation Problem     286
Background     287
Rotation and Angular Velocity     291
Floating Frame of Reference     296
Intermediate Element Coordinate System     297
Connectivity and Reference Conditions      300
Kinematic Equations     306
Formulation of the Inertia Forces     307
Elastic Forces     311
Equations of Motion     313
Coordinate Reduction     314
Integration of Finite Element and Multibody System Algorithms     317
Problems     319
References     321
Index     327

Read More Show Less

Customer Reviews

Average Rating 5
( 1 )
Rating Distribution

5 Star

(1)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)