Variational Methods In Theoretical Mechanics PDF Download
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Author | : J.T. Oden |
Publisher | : Springer Science & Business Media |
Total Pages | : 313 |
Release | : 2012-12-06 |
Genre | : Technology & Engineering |
ISBN | : 3642963129 |
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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 | : J. T. Oden |
Publisher | : |
Total Pages | : 328 |
Release | : 1982-11-01 |
Genre | : |
ISBN | : 9783642688126 |
Download Variational Methods in Theoretical Mechanics Book in PDF, ePub and Kindle
Author | : J. Tinsley Oden |
Publisher | : |
Total Pages | : 309 |
Release | : 1998 |
Genre | : |
ISBN | : 9787515803029 |
Download Variational methods in theoretical mechanics Book in PDF, ePub and Kindle
Author | : Cornelius Lanczos |
Publisher | : |
Total Pages | : 0 |
Release | : 1970 |
Genre | : Dynamics |
ISBN | : |
Download The Variational Principles of Mechanics Book in PDF, ePub and Kindle
Author | : J T Oden |
Publisher | : |
Total Pages | : 318 |
Release | : 1976-03-01 |
Genre | : |
ISBN | : 9783642963131 |
Download Variational Methods in Theoretical Mechanics Book in PDF, ePub and Kindle
Author | : Philippe Blanchard |
Publisher | : Springer Science & Business Media |
Total Pages | : 469 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461200490 |
Download Mathematical Methods in Physics Book in PDF, ePub and Kindle
Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.
Author | : Martin Fuchs |
Publisher | : Springer |
Total Pages | : 276 |
Release | : 2007-05-06 |
Genre | : Mathematics |
ISBN | : 3540444424 |
Download Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids Book in PDF, ePub and Kindle
Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.
Author | : Francesco dell'Isola |
Publisher | : Springer Science & Business Media |
Total Pages | : 363 |
Release | : 2012-01-15 |
Genre | : Technology & Engineering |
ISBN | : 3709109833 |
Download Variational Models and Methods in Solid and Fluid Mechanics Book in PDF, ePub and Kindle
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 | : V.I. Arnol'd |
Publisher | : Springer Science & Business Media |
Total Pages | : 530 |
Release | : 2013-04-09 |
Genre | : Mathematics |
ISBN | : 1475720637 |
Download Mathematical Methods of Classical Mechanics Book in PDF, ePub and Kindle
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Author | : J. N. Reddy |
Publisher | : Wiley-Interscience |
Total Pages | : 560 |
Release | : 1984-09-20 |
Genre | : Science |
ISBN | : 9780471896739 |
Download Energy and Variational Methods in Applied Mechanics Book in PDF, ePub and Kindle
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.