Energy Principles and Variational Methods in Applied Mechanics
Energy Principles and Variational Methods in Applied Mechanics

Author: J. N. Reddy

Publisher: John Wiley & Sons

Published: 2002-08-09

Total Pages: 618

ISBN-13: 9780471179856

DOWNLOAD EBOOK

A systematic presentation of energy principles and variationalmethods The increasing use of numerical and computational methods inengineering and applied sciences has shed new light on theimportance of energy principles and variational methods. EnergyPrinciples and Variational Methods in Applied Mechanicsprovides a systematic and practical introduction to the use ofenergy principles, traditional variational methods, and the finiteelement method to the solution of engineering problems involvingbars, beams, torsion, plane elasticity, and plates. Beginning with a review of the basic equations of mechanics andthe concepts of work, energy, and topics from variational calculus,this book presents the virtual work and energy principles, energymethods of solid and structural mechanics, Hamilton'sprinciple for dynamical systems, and classical variational methodsof approximation. A unified approach, more general than that foundin most solid mechanics books, is used to introduce the finiteelement method. Also discussed are applications to beams andplates. Complete with more than 200 illustrations and tables, EnergyPrinciples and Variational Methods in Applied Mechanics, SecondEdition is a valuable book for students of aerospace, civil,mechanical, and applied mechanics; and engineers in design andanalysis groups in the aircraft, automobile, and civil engineeringstructures, as well as shipbuilding industries.

Energy and Variational Methods in Applied Mechanics
Energy and Variational Methods in Applied Mechanics

Author: J. N. Reddy

Publisher: Wiley-Interscience

Published: 1984-09-20

Total Pages: 560

ISBN-13: 9780471896739

DOWNLOAD EBOOK

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 Methods in Applied Mechanics
Energy Methods in Applied Mechanics

Author: Henry L. Langhaar

Publisher: Courier Dover Publications

Published: 2016-11-16

Total Pages: 370

ISBN-13: 0486811131

DOWNLOAD EBOOK

Integrated, modern treatment explores applications to dynamics of rigid bodies, analysis of elastic frames, general elastic theory, theory of plates and shells, theory of buckling, and theory of vibrations. Includes answers to problems. 1962 edition.

Variational and Quasi-Variational Inequalities in Mechanics
Variational and Quasi-Variational Inequalities in Mechanics

Author: Alexander S. Kravchuk

Publisher: Springer Science & Business Media

Published: 2007-09-04

Total Pages: 337

ISBN-13: 1402063776

DOWNLOAD EBOOK

The essential aim of this book is to consider a wide set of problems arising in the mathematical modeling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities and their transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems.

The Method of Weighted Residuals and Variational Principles
The Method of Weighted Residuals and Variational Principles

Author: Bruce A. Finlayson

Publisher: SIAM

Published: 2013-12-30

Total Pages: 429

ISBN-13: 1611973236

DOWNLOAD EBOOK

This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds. Problem sets make this book ideal for self-study or as a course text.

Solid Mechanics
Solid Mechanics

Author: Clive L. Dym

Publisher: Springer Science & Business Media

Published: 2013-04-05

Total Pages: 698

ISBN-13: 1461460344

DOWNLOAD EBOOK

Solid Mechanics: A Variational Approach, Augmented Edition presents a lucid and thoroughly developed approach to solid mechanics for students engaged in the study of elastic structures not seen in other texts currently on the market. This work offers a clear and carefully prepared exposition of variational techniques as they are applied to solid mechanics. Unlike other books in this field, Dym and Shames treat all the necessary theory needed for the study of solid mechanics and include extensive applications. Of particular note is the variational approach used in developing consistent structural theories and in obtaining exact and approximate solutions for many problems. Based on both semester and year-long courses taught to undergraduate seniors and graduate students, this text is geared for programs in aeronautical, civil, and mechanical engineering, and in engineering science. The authors’ objective is two-fold: first, to introduce the student to the theory of structures (one- and two-dimensional) as developed from the three-dimensional theory of elasticity; and second, to introduce the student to the strength and utility of variational principles and methods, including briefly making the connection to finite element methods. A complete set of homework problems is included.

Mechanics of Structures
Mechanics of Structures

Author: Walter Wunderlich

Publisher: CRC Press

Published: 2019-12

Total Pages: 912

ISBN-13: 9780367454609

DOWNLOAD EBOOK

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.

Energy Methods for Free Boundary Problems
Energy Methods for Free Boundary Problems

Author: S.N. Antontsev

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 338

ISBN-13: 1461200911

DOWNLOAD EBOOK

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.

Computational Solid Mechanics
Computational Solid Mechanics

Author: Marco L. Bittencourt

Publisher: CRC Press

Published: 2014-09-19

Total Pages: 670

ISBN-13: 1482246538

DOWNLOAD EBOOK

Presents a Systematic Approach for Modeling Mechanical Models Using Variational Formulation-Uses Real-World Examples and Applications of Mechanical ModelsUtilizing material developed in a classroom setting and tested over a 12-year period, Computational Solid Mechanics: Variational Formulation and High-Order Approximation details an approach that e