Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)

Book Description

Elastic plates form a class of very important mechanical structures that appear in a wide range of practical applications, from building bodies to microchip production. As the sophistication of industrial designs has increased, so has the demand for greater accuracy in analysis. This in turn has led modelers away from Kirchoff's classical theory for thin plates and toward increasingly refined models that yield not only the deflection of the middle section, but also account for transverse shear deformation. The improved performance of these models is achieved, however, at the expense of a much more complicated system of governing equations and boundary conditions. In this Monograph, the authors conduct a rigorous mathematical study of a number of boundary value problems for the system of partial differential equations that describe the equilibrium bending of an elastic plate with transverse shear deformation. Specifically, the authors explore the existence, uniqueness, and continuous dependence of the solution on the data. In each case, they give the variational formulation of the problems and discuss their solvability in Sobolev spaces. They then seek the solution in the form of plate potentials and reduce the problems to integral equations on the contour of the domain. This treatment covers an extensive range of problems and presents the variational method and the boundary integral equation method applied side-by-side. Readers will find that this feature of the book, along with its clear exposition, will lead to a firm and useful understanding of both the model and the methods.

Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods (Studies in Applied and Numerical Mathematics)

Average customer rating:

Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods (Studies in Applied and Numerical Mathematics)
N. Kikuchi , and J. T. Oden
Manufacturer: Society for Industrial Mathematics
ProductGroup: Book
Binding: Paperback

General | Mathematics | Science | Subjects | Books

jp-unknown2 | Specialty Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 0898714680

Book Description

The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes.

Gauge Theory and Variational Principles (Global Analysis, Pure and Applied)

Average customer rating:

A useful reference text for gauge theory.
Spivak on Steroids
A mathematically tight and well-motivated work
Clean and modern exposition
This book is all that is bad about abstract mathematical physics writing

Gauge Theory and Variational Principles (Global Analysis, Pure and Applied)
David Bleecker
Manufacturer: Addison Wesley Publishing Company
ProductGroup: Book
Binding: Hardcover

General | Physics | Science | Subjects | Books

Waves & Wave Mechanics | Physics | Science | Subjects | Books

ASIN: 0201100967

Customer Reviews:

A useful reference text for gauge theory........2007-07-28

A useful reference text for gauge theory. While Bleecker includes an introductory chapter to cover prerequisites (tensor analysis, differential forms, Lie groups etc) the text assumes some familiarity with these techniques and gauge theory. The text is in the "definition, theorem, proof" format. Bleecker gives fairly detailed proofs which help the reader to follow most steps. The text is short and the price reasonable, so the absence of second quantization gauge potentials, for example, is perhaps understandable. While there are chapters on gauge invariance and Action density I found the material didn't go into the detail I was looking for on invariance problems (discussion of theorems of Noether, Caratheodory's methods, Lie algebras and groups). I rated this text lower because of the complete absence of exercises and the limited references and bibliography (about three pages in total).

Spivak on Steroids.......2007-02-24

As the title suggests this "text" serves as an introduction to the QFT and guage theories recast in the "modern" mathematical setting of differential geometry.
This book is only 167 ( 1/2 regular size paper ) pages long. Although self-contained I highly recommend the reader have a working knowledge of QFT and at least an introductory course in GR. The mathematical tools of the reader should include a course in analysis on manifolds at the Spivak level or higher, acquintance with fibre bundles and basic lie groups. For example in the first chapter ( 22 pages ) the author covers differential forms, manifolds, Stokes theorem, lie derivative, deRham cohomology, lie groups and algebras. The next 20 page chapter covers principal bundles and connections ( 3 definitions all shown to be equivalent and these turn out to be the physical equivalent of gauge potentials ) followed by lie algebra valued forms, exterior covariant derivative curvature and the structure equation.
Chapter 3 defines particle fields as mappings from the principal bundle to a vector space which are equivariant or to the space of sections of the associated vector bundle. We now see that guage transformations are nothing more but the automorphisms of the bundle with certain requirements. Langrangians are developed as mappings of the space of 1 jets to the reals. G invariance of langrangians is defined and is shown to be an insufficient criteria for invariance under gauge transformations. However, we see that introduction of a connection and hence covariant exterior derivative on the bundle our Langrangian becomes gauge invariant.
The next chapter introduces action densities and shows that a particular particle field obeys the principle of least action iff it is stationary which is true iff Langrange's equation holds. There is alot of mathematical notation and machinery developed here. At this stage spin zero electrodynamics are treated.
Current are defined on PFB and a conservation of charge for g-invariant Langrangians with stationary particle fields is shown to be true. This chapter introduces the "self interaction" term for the gauge field and shows that a particle field and connection ( gauge potential ) obey the principle of least action iff they satisfy BOTH langrange equation and the inhomgeneous field equation.
The next chapter introduces spinor bundles ( to add spin particles to our repretoire ) requiring modifications of the previous mathematical tools leading to the appropriate Langrangian. Lagrange's equation is shown to reduce to the dirac free field equation.
The next chapter shows how to deal with interactions between the particle fields with spin and guage fields. This requires "spliced bundles" ( one where the particles with spin live and the other where guage fields live ) which requires another straight forward modification of our mathematical tools...redefining particle fields, Langrangians, currents, and action densities in the process. We see that in this general setting the particle fields and gauge potentials ( connection ) are stationary ( satisfy principle of least action ) iff they satisfy two generalized versions of lagranges equation and an inhomegeneous field equation. The author shows how these reduce the the special cases of the dirac electron field and yang mills field to the dirac and yang-mills equations and the inhomegeneous maxwell and yang-mills equations, respectively.
Chapter 8 goes over the mathematics of general relativity in about 10 pages.
Chapter 9 attempts to unify gauge theories and gravitation showing that the Einstein field equations and the Yang-Mills equations follow from a single variational principle dependent upon the scalar curvature of the metric defined on a suitable PFB. Problems of this unification are explained.
The final chapter explores symmetry breaking monopoles and instantons.

As you can see there is alot to absorb with the prerequisites noted above.
The book has no examples or exercise but each theorem is proved. There is also a page with corrections which is refreshing and a page summarizing the notation and page they are first introduced.

A mathematically tight and well-motivated work.......2006-07-06

Professor Bleecker has succeeded in writing a book for mathematicians and physicists. And, it's all there. I would rate this work 5-star, except I fear some physicists might find the mathematical format a bit tough (definition, theorem, lemma, etc.) As a mathematician studying physics I hope I am wrong. I find this book user-friendly due to its formality and "compactness". I caution those w/o a fair degree of mathematical acumen that this big, little book is a good deal more formal than, say, Gilmore's "Lie Groups, Lie Algebras, and Some of their Applications." But, then we all must bite the bullet. With effort, I think you will find this a chewable bullet.

Clean and modern exposition.......2006-06-19

Despite what another reviewer said, this book uses standard differential geometry notation. The notation is of the invariant (no index) style of Kobayashi and Nomizu.
I find it a delightful little book. It should be good for anyone with a background in manifold theory and Lie groups.

This book is all that is bad about abstract mathematical physics writing.......2006-05-16

Am I new to gauge theory: no.
Why does he make me feel I am?

Are these new generalized symbols really necessary to his treatment.
Apparently the author believes that rather than use words to explain
theorems...
He can rely almost entirely on this new set of symbols
that he has used to translate gauge theory to fiber bundles.
Why is it that so many times
the reader is the one who is made to do the work
of teaching himself and learning new "languages"
when the author claims he will be teaching you?

I feel that I have to warn the reader, that although he claims to be "mainstream"
differential geometry, he lies.
he uses very non-standard ( at least for the papers I've read)
notation and instead of starting at the simple gives the most abstract examples
of the notation even in chapter "0".

I grade this book as a "F"... way below even the worst
group theory book I have by an English set of professors!
I'm really as sorry as I can be, but he got me for the money,
by false advertising...
It is a very badly written book,
more a "show off"... see what I can do book,
than a I will teach you to understand book.
I had to go back to other books to compare the notation
so many times that I stack them with this book.
I spent half a year plotting solitons in Mathematica,
and I don't recognize anything in his treatment of them.
Monopoles and Instantons are even worse in this book, if possible.
It is not that I I don't believe he is using correct mathematics,
it is just that it is so hard to tell if he is!
Roger L. Bagula

Contact problems in elasticity: A study of variational inequalities and finite methods for a class of contact problems in elasticity (TICOM report)

Average customer rating:

Contact problems in elasticity: A study of variational inequalities and finite methods for a class of contact problems in elasticity (TICOM report)
Noboru Kikuchi
Manufacturer: Texas Institute for Computational Mechanics, the University of Texas at Austin
ProductGroup: Book
Binding: Unknown Binding

General | Physics | Science | Subjects | Books
ASIN: B0006XONC2

Direct Variational Methods and Eigenvalue Problems in Engineering (Mechanics of Elastic Stability)

Average customer rating:

Direct Variational Methods and Eigenvalue Problems in Engineering (Mechanics of Elastic Stability)
U. Leipholz
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Engineering | Professional & Technical | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Mechanics | Physics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 9028601066

Energy and Variational Methods in Applied Mechanics

Average customer rating:

Energy and Variational Methods in Applied Mechanics
J. N. Reddy
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

General | Engineering | Professional & Technical | Subjects | Books

Mechanics | Physics | Science | Subjects | Books

General | Arts & Photography | Subjects | Books

General | Engineering | New & Used Textbooks | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Arts & Photography | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 047189673X

Book Description

A practical introduction to the use of the finite-element method and variational methods to solve engineering problems about beams, bars, torsion, and plane elasticity. Includes a concise section on composite-material laminated plates and shells. Contains numerous examples, exercises, problems, and references.

Energy Principles and Variational Methods in Applied Mechanics

Average customer rating:

Energy Principles and Variational Methods in Applied Mechanics
J. N. Reddy
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

General | Engineering | Professional & Technical | Subjects | Books

General | Science | Subjects | Books

Mechanics | Physics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 047117985X

Book Description

A systematic presentation of energy principles and variational methods

The increasing use of numerical and computational methods in engineering and applied sciences has shed new light on the importance of energy principles and variational methods. Energy Principles and Variational Methods in Applied Mechanics provides a systematic and practical introduction to the use of energy principles, traditional variational methods, and the finite element method to the solution of engineering problems involving bars, beams, torsion, plane elasticity, and plates.

Beginning with a review of the basic equations of mechanics and the concepts

of work, energy, and topics from variational calculus, this book presents

the virtual work and energy principles, energy methods of solid and structural mechanics, Hamilton's principle for dynamical systems, and classical variational methods of approximation. A unified approach, more general than that found in most solid mechanics books, is used to introduce the finite element method. Also discussed are applications to beams and plates.

Product Description

The book systematically presents variational principles and methods of analysis for applied elasticity and structural mechanics. The variational approach is used consistently for both, constructing numerical procedures and deriving basic governing equations of applied mechanics of solids; it is the derivation of equations where this approach is most powerful and best grounded by mathematics. The book is oriented towards experts in civil engineering, researchers, developers of software for mechanical strength, stability, and oscillation analysis; it can be used by practical engineers who employ software tools to do their job and who want to know more about the theoretical background of the strength analysis. The book will be useful to senior and postgraduate students of engineering, to professors of structural analysis at civil or mechanical engineering departments of technical universities.

Mechanics of Structures Variational and Computational Methods, 2nd Edition

Average customer rating:

Mechanics of Structures Variational and Computational Methods, 2nd Edition
Walter Wunderlich , and Walter D. Pilkey
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

General | Engineering | Professional & Technical | Subjects | Books

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mechanics | Physics | Science | Subjects | Books

General | Arts & Photography | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 0849307007

Book Description

Resoundingly popular in its first edition, the second edition of Mechanics of Structures: Variational and Computational Methods promises to be even more so, with broader coverage, expanded discussions, and a streamlined presentation. The authors begin by describing the behavior of deformable solids through the differential equations for the strength of materials and the theory of elasticity. They next introduce variational principles, including mixed or generalized principles, and derive integral forms of the governing equations. Discussions then move to computational methods, including the finite element method, and these are developed to solve the differential and integral equations. New in the second edition: · A one-dimensional introduction to the finite element method, complete with illustrations of numerical mesh refinement · Expansion of the use of Galerkin's method. · Discussion of recent developments in the theory of bending and torsion of thin-walled beams. · An appendix summarizing the fundamental equations in differential and variational form · Completely new treatment of stability, including detailed examples · Discussion of the principal values of geometric properties and stresses · Additional exercises As a textbook or as a reference, Mechanics of Structures builds a unified, variational foundation for structure mechanics, which in turn forms the basis for the computational solid mechanics so essential to modern engineering.

Models and Analysis of Quasistatic Contact: Variational Methods (Lecture Notes in Physics)

Average customer rating:

Models and Analysis of Quasistatic Contact: Variational Methods (Lecture Notes in Physics)
Meir Shillor , Mircea Sofonea , and Józef J. Telega
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Physics | Science | Subjects | Books

Mathematical Physics | Physics | Science | Subjects | Books

Mechanics | Physics | Science | Subjects | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Engineering | Amazon Upgrade | Stores | Books

Professional & Technical | Amazon Upgrade | Stores | Books

Science | Amazon Upgrade | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 3540229159

Book Description

The mathematical theory of contact mechanics is a growing field in engineering and scientific computing. This book is intended as a unified and readily accessible source for mathematicians, applied mathematicians, mechanicians, engineers and scientists, as well as advanced students. The first part describes models of the processes involved like friction, heat generation and thermal effects, wear, adhesion and damage. The second part presents many mathematical models of practical interest and demonstrates the close interaction and cross-fertilization between contact mechanics and the theory of variational inequalities. The last part reviews further results, gives many references to current research and discusses open problems and future developments. The book can be read by mechanical engineers interested in applications. In addition, some theorems and their proofs are given as examples for the mathematical tools used in the models.

Customer Reviews:

WATCH OUT - OLD MATERIAL, NEW COVER!.......2005-05-17

As a huge fan of Takahashi's Mermaid stories, I was excited to see that a new volume had come out. The original graphic novels are Mermaid Forrest, Mermaid's Scar, and Mermaid's Gaze. This volume is numbered 4, to give the impression that there are new tales here, but don't be fooled! This volume is simply Mermaid's Gaze republished with a new title and cover (it is also printed back to front). If you don't have this already, I highly recommend it, but I do think publisher Viz pulled a fast one on Takihashi's fans here.

Books:

Books Index

Books Home

Recommended Books