Nonlinear Finite Elements for Continua and Structures

Book Description

Nonlinear Finite Elements for Continua and Structures Ted Belytschko, Wing Kam Liu, Brian Moran Northwestern University, Evanston, Illinois This book provides a comprehensive description of the major methodologies of nonlinear finite element analysis for solid mechanics, as applied to continua and structures. Treatment of the subject is integrated in such a way that the reader can gain an understanding of the fundamental methods, a feeling for the comparative usefulness of different approaches and an appreciation of the difficulties inherent in nonlinear analysis. In-depth coverage of the following is given:
* Lagrangian and arbitrary Lagrangian Eulerian treatments of continua
* many of the material laws used in today's software and research
* solution methods, including explicit and implicit time integration methods and methods for equilibrium problems
* basic concepts such as stability and smoothness, and techniques such as linearization and regularization
* methods for shells and structures
* contact-impact problems
* element technology, including multi-field elements
Ideal for self-study, no other book provides such a comprehensive description of nonlinear finite element analysis for solid mechanics. This is an invaluable reference not only for final year undergraduates, postgraduates, academics and engineers working on sophisticated finite element software and in the field of solid mechanics, but also for all users of nonlinear finite element programs.

Customer Reviews:

Simply the best there is.......2006-06-16

This book is simply the best nonlinear FEA book out there. While most other books stop at the Total and Updated Legrangian formulations, this book goes way beyond that and teaches you some really advanced FEA techniques. The treatment of material is thourough and meticulous. Unlike what some other reviewers have said, this book is NOT a bunch of research papers thrown together, but is very well organized with consistent notation and timely explanations. This book is ideal for self study as well as reference for scientists and engineers. However, watch out for some typos that may throw you off-track. This is the only complaint I have about the book.

A good reference, but need further revision.......2004-10-15

The approach taken by this book is neither too mathematical, which makes the subject untractable, nor too engineering-lized, which missed out important insights. I am an engineer with a master degree in mechanical engineering. I found this book very readable, given enough coffine and a good mood. The subjects covered are self-contained.

However this book needs further improvement to be called classic. First, contact-impact chapter is palely presented. LS-DYNA theory manual provides a more complete description on this subject. Secondly, typos need to be reduced. Thirdly, the language is somewhat boring. Fourthly, I would like to see a Latex-ized version of this book.

The new gold standard.......2004-06-02

This has got to be the best book out there now on how to construct nonlinear FE. For me, the book was worth it even if just for the lucent review of nonlinear continuum mechanics.

Distinguished.......2003-04-15

By systematic way of intuition, the authors successfully grasp the philosophy of nonlinear phenomena. The methods of explanation in TL, UL, and ALE are obviously pronounced. If the books of Prof. Zienkiewicz and Prof.Taylor, Prof.Bathe are treasures of FEM, this book is worth in that place.

Outstanding!.......2002-11-26

Though I had been somehow prepared by the positive comments of the other reviewers before buying this book, I must admit that I was impressed from the very beginning of study. Non linear FE is a "hard" subject, however the authors proceed in the most systematic and comprehensive way, addressing the most important aspects of non linear fem analysis in a single volume. The book contains everything you need from the field of Continuum Mechanics and is ideal for self - study. Valuable references, handy summary boxes and exercises at the end of each chapter are included.

Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability (Mechanical Engineering Series)

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Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability (Mechanical Engineering Series)
James F. Doyle
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387952160

Book Description

This book deals with the computational analysis of thin-walled structures such as aircraft, ships, and containment vessels. Building on the author's earlier book Static and Dynamic Analysis of Structures, it shows how to use computational methods to tackle some of the fundamental problems of structural mechanics, with particular emphasis on nonlinear phenomena. Where the earlier book dealt with linear systems, the central theme running through this volume is the notion that unstable equilibria are associated with motions and large displacements and therefore require a full nonlinear analysis. The discussion begins with an overview of the basic mechanics of deformable bodies, including variational formulations, and then considers the large deflection behavior of shell and frame structures using a finite-element analysis. The second part of the book begins with a summary of linear vibrations of structures, including an introduction to modal analysis; it continues with computational formulations of nonlinear dynamic analyses of structures and refines the concept of dynamic equilibrium in the context of large deflections. The book concludes with a discussion of stability, including the difficult problem of stability of motions in the large. By describing the methods on which commercial software pakckages are based, this book allows an engineer to evaluate the results these computations produce. It therefore should be useful to practicing engineers and graduate students.

Transformations Through Space and Time: An Analysis of Nonlinear Structures, Bifurcation Points and Autoregressive Dependencies (Nato Science Series D:)

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Transformations Through Space and Time: An Analysis of Nonlinear Structures, Bifurcation Points and Autoregressive Dependencies (Nato Science Series D:)

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 9024733626

Gradient Flows: In Metric Spaces and in the Space of Probability Measures (Lectures in Mathematics. ETH Zürich)

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Gradient Flows: In Metric Spaces and in the Space of Probability Measures (Lectures in Mathematics. ETH Zürich)
Luigi Ambrosio , Nicola Gigli , and Giuseppe Savaré
Manufacturer: Birkhäuser Basel
ProductGroup: Book
Binding: Paperback

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ASIN: 3764324287

Book Description

This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance.
The two parts have some connections, due to the fact that the space of probability measures provides an important model to which the "metric" theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested in non-smooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability.

Analysis of Geometrically Nonlinear Structures

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Analysis of Geometrically Nonlinear Structures
Robert Levy , and William R. Spillers
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 1402016549

Book Description

This book provides a simple extension of the methods of linear structural analysis to the case of geometrically nonlinear effects. Its importance derives from the theorem stating that "in the presence of pre stress, geometrically nonlinear effects are of the same order as linear elastic effects". It is the precursor of efforts to include nonlinear effects in elementary discussions of structural analysis.

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Useless

Nonlinear Analysis of Structures
M. Sathyamoorthy
Manufacturer: CRC
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Binding: Hardcover

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ASIN: 0849396522

Book Description

This book provides comprehensive treatment of the nonlinear behavior of various types of structural elements such as beams, frames, trusses, mechanisms, plates, shells, and sandwich and composite structural elements. Information is included on the various types of nonlinearities, stress-strain relations and the development of nonlinear governing equations derived from nonlinear elastic theory. The author has designed the book to strike a good balance between the mathematical and applied side of the topic. Many applications, examples, and problems are presented in the text.

Customer Reviews:

Useless.......2006-02-21

I bought this book because I wanted to learn how to solve nonlinear problems numerically (after all, I am a practicing engineer, and I need numerical results). Instead, the book offers a myriad of MACSYMA generated closed form solutions -some half a page long, to specific problems. Where is the general methodology? How about identifying the symbols used in the equations, out of courtesy to the reader? Why are the references 20 pages long at the end of each chapter? Couldn't they have been deferred to the end of the book, and been more concise?
Bottom line: very disappointing and useless; I wasted my money.

Complexity: Hierarchical Structures and Scaling in Physics (Cambridge Nonlinear Science Series)

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Complexity: Hierarchical Structures and Scaling in Physics (Cambridge Nonlinear Science Series)
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Dirac Structures and Integrability of Nonlinear Evolution Equations (Nonlinear Science)

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Dirac Structures and Integrability of Nonlinear Evolution Equations (Nonlinear Science)
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Invariant Sets for Windows: Resonance Structures, Attractors, Fractals, and Patterns (World Scientific Series on Nonlinear Science. Series a, Monographs and Treatises, V. 37.)

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Invariant Sets for Windows: Resonance Structures, Attractors, Fractals, and Patterns (World Scientific Series on Nonlinear Science. Series a, Monographs and Treatises, V. 37.)
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Mathematical Models for Elastic Structures

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A review of papers on modern theories of structures
Do not buy this book

Mathematical Models for Elastic Structures
Piero Villaggio
Manufacturer: Cambridge University Press
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Binding: Hardcover

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During the seventeenth century, several useful theories of elastic structures emerged, with applications to civil and mechanical engineering problems. Recent and improved mathematical tools have extended applications into new areas such as mathematical physics, geomechanics, and biomechanics. This book offers a critically filtered collection of the most significant theories dealing with elastic slender bodies. It includes mathematical models involving elastic structures that are used to solve practical problems with particular emphasis on nonlinear problems.

Customer Reviews:

A review of papers on modern theories of structures.......2004-04-10

This is a compendium of the recent research literature on mathematical methods in structural mechanics. Judging by the bibiograpghy, the author himself has contributed nothing or next to nothing to this subject, leaving the informed reader wondering why he chose to write this particular book. The expert reader familiar with the literature will notice the author's overly strong reliance on the literal texts of research papers, to the extent that the style and even notation vary from one section to another. Thus the book reads like a superficial transcription of the work of others. The author has made little or no effort to synthesize the literature into a coherent exposition. This is a particular disappointment given the author's strong reputation as a researcher. Thus, what emerges is a rather disjoint and haphazard review of the works of those papers which the author finds appealing, without any sign of a common theme nor any hint of discernment. The book stands in stark contrast to a number of excellent and thoughtful monographs written by those who have actually contributed to the subject. Those who know the author's excellent research papers in other fields of Mechanics will feel sorely disppointed.

Do not buy this book.......2004-03-16

This book is very expensive and contains classical theories mixed with a lot of useless mathematics; absolutely not recomended to everybody.

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