An Introduction To Modern Variational Techniques In Mechanics And Engineering
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Author |
: Bozidar D. Vujanovic |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 350 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9780817681623 |
ISBN-13 |
: 0817681620 |
Rating |
: 4/5 (23 Downloads) |
Synopsis An Introduction to Modern Variational Techniques in Mechanics and Engineering by : Bozidar D. Vujanovic
* Atanackovic has good track record with Birkhauser: his "Theory of Elasticity" book (4072-X) has been well reviewed. * Current text has received two excellent pre-pub reviews. * May be used as textbook in advanced undergrad/beginning grad advanced dynamics courses in engineering, physics, applied math departments. *Also useful as self-study reference for researchers and practitioners. * Many examples and novel applications throughout. Competitive literature---Meirovich, Goldstein---is outdated and does not include the synthesis of topics presented here.
Author |
: Bozidar D. Vujanović |
Publisher |
: Birkhauser |
Total Pages |
: 346 |
Release |
: 2004 |
ISBN-10 |
: 3764333995 |
ISBN-13 |
: 9783764333997 |
Rating |
: 4/5 (95 Downloads) |
Synopsis An Introduction to Modern Variational Techniques in Mechanics and Engineering by : Bozidar D. Vujanović
Author |
: J.T. Oden |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 313 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642963124 |
ISBN-13 |
: 3642963129 |
Rating |
: 4/5 (24 Downloads) |
Synopsis Variational Methods in Theoretical Mechanics by : J.T. Oden
This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. He also gratefully acknowledge that much of our own research work on variational theory was supported by the U.S. Air Force Office of Scientific Research. He are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and pains taking job of typing the manuscript. J. T. ODEN J. N. REDDY Table of Contents PREFACE 1. INTRODUCTION 1.1 The Role of Variational Theory in Mechanics. 1 1.2 Some Historical Comments ......... . 2 1.3 Plan of Study ............... . 5 7 2. MATHEMATICAL FOUNDATIONS OF CLASSICAL VARIATIONAL THEORY 7 2.1 Introduction . . . . . . . .
Author |
: Clive L. Dym |
Publisher |
: Springer |
Total Pages |
: 685 |
Release |
: 2013-04-05 |
ISBN-10 |
: 1461460352 |
ISBN-13 |
: 9781461460350 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Solid Mechanics by : Clive L. Dym
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.
Author |
: J. N. Reddy |
Publisher |
: John Wiley & Sons |
Total Pages |
: 1069 |
Release |
: 2017-07-21 |
ISBN-10 |
: 9781119087397 |
ISBN-13 |
: 1119087392 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Energy Principles and Variational Methods in Applied Mechanics by : J. N. Reddy
A comprehensive guide to using energy principles and variational methods for solving problems in solid mechanics This book provides a systematic, highly practical introduction to the use of energy principles, traditional variational methods, and the finite element method for the solution of engineering problems involving bars, beams, torsion, plane elasticity, trusses, and plates. It begins with a review of the basic equations of mechanics, the concepts of work and energy, and key topics from variational calculus. It presents virtual work and energy principles, energy methods of solid and structural mechanics, Hamilton’s principle for dynamical systems, and classical variational methods of approximation. And it takes a more unified approach than that found in most solid mechanics books, to introduce the finite element method. Featuring more than 200 illustrations and tables, this Third Edition has been extensively reorganized and contains much new material, including a new chapter devoted to the latest developments in functionally graded beams and plates. Offers clear and easy-to-follow descriptions of the concepts of work, energy, energy principles and variational methods Covers energy principles of solid and structural mechanics, traditional variational methods, the least-squares variational method, and the finite element, along with applications for each Provides an abundance of examples, in a problem-solving format, with descriptions of applications for equations derived in obtaining solutions to engineering structures Features end-of-the-chapter problems for course assignments, a Companion Website with a Solutions Manual, Instructor's Manual, figures, and more Energy Principles and Variational Methods in Applied Mechanics, Third Edition is both a superb text/reference for engineering students in aerospace, civil, mechanical, and applied mechanics, and a valuable working resource for engineers in design and analysis in the aircraft, automobile, civil engineering, and shipbuilding industries.
Author |
: Paolo Maria Mariano |
Publisher |
: Springer Nature |
Total Pages |
: 315 |
Release |
: 2022-02-08 |
ISBN-10 |
: 9783030900519 |
ISBN-13 |
: 3030900517 |
Rating |
: 4/5 (19 Downloads) |
Synopsis Variational Views in Mechanics by : Paolo Maria Mariano
This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on “Calculus of Variations in Mechanics and Related Fields”. The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include: Topology optimization Identification of material properties Optimal control Plastic flows Gradient polyconvexity Obstacle problems Quasi-monotonicity Variational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.
Author |
: Kevin W. Cassel |
Publisher |
: Cambridge University Press |
Total Pages |
: 433 |
Release |
: 2013-07-22 |
ISBN-10 |
: 9781107022584 |
ISBN-13 |
: 1107022584 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Variational Methods with Applications in Science and Engineering by : Kevin W. Cassel
This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.
Author |
: Francesco dell'Isola |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 363 |
Release |
: 2012-01-15 |
ISBN-10 |
: 9783709109830 |
ISBN-13 |
: 3709109833 |
Rating |
: 4/5 (30 Downloads) |
Synopsis Variational Models and Methods in Solid and Fluid Mechanics by : Francesco dell'Isola
F. dell'Isola, L. Placidi: Variational principles are a powerful tool also for formulating field theories. - F. dell'Isola, P. Seppecher, A. Madeo: Beyond Euler-Cauchy Continua. The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument. - B. Bourdin, G.A. Francfort: Fracture. - S. Gavrilyuk: Multiphase flow modeling via Hamilton's principle. - V. L. Berdichevsky: Introduction to stochastic variational problems. - A. Carcaterra: New concepts in damping generation and control: theoretical formulation and industrial applications. - F. dell'Isola, P. Seppecher, A. Madeo: Fluid shock wave generation at solid-material discontinuity surfaces in porous media. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.
Author |
: Lánczos Kornél |
Publisher |
: |
Total Pages |
: 307 |
Release |
: 1952 |
ISBN-10 |
: OCLC:909085169 |
ISBN-13 |
: |
Rating |
: 4/5 (69 Downloads) |
Synopsis The Variational Principles of Mechanics by : Lánczos Kornél
Author |
: Edgardo O. Taroco |
Publisher |
: John Wiley & Sons |
Total Pages |
: 606 |
Release |
: 2020-02-25 |
ISBN-10 |
: 9781119600909 |
ISBN-13 |
: 1119600901 |
Rating |
: 4/5 (09 Downloads) |
Synopsis Introduction to the Variational Formulation in Mechanics by : Edgardo O. Taroco
Introduces readers to the fundamentals and applications of variational formulations in mechanics Nearly 40 years in the making, this book provides students with the foundation material of mechanics using a variational tapestry. It is centered around the variational structure underlying the Method of Virtual Power (MVP). The variational approach to the modeling of physical systems is the preferred approach to address complex mathematical modeling of both continuum and discrete media. This book provides a unified theoretical framework for the construction of a wide range of multiscale models. Introduction to the Variational Formulation in Mechanics: Fundamentals and Applications enables readers to develop, on top of solid mathematical (variational) bases, and following clear and precise systematic steps, several models of physical systems, including problems involving multiple scales. It covers: Vector and Tensor Algebra; Vector and Tensor Analysis; Mechanics of Continua; Hyperelastic Materials; Materials Exhibiting Creep; Materials Exhibiting Plasticity; Bending of Beams; Torsion of Bars; Plates and Shells; Heat Transfer; Incompressible Fluid Flow; Multiscale Modeling; and more. A self-contained reader-friendly approach to the variational formulation in the mechanics Examines development of advanced variational formulations in different areas within the field of mechanics using rather simple arguments and explanations Illustrates application of the variational modeling to address hot topics such as the multiscale modeling of complex material behavior Presentation of the Method of Virtual Power as a systematic tool to construct mathematical models of physical systems gives readers a fundamental asset towards the architecture of even more complex (or open) problems Introduction to the Variational Formulation in Mechanics: Fundamentals and Applications is a ideal book for advanced courses in engineering and mathematics, and an excellent resource for researchers in engineering, computational modeling, and scientific computing.