Variational Methods in the Mechanics of Solids

Author: S. Nemat-Nasser
Publisher: Elsevier
ISBN: 1483145832
Format: PDF
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Variational Methods in the Mechanics of Solids contains the proceedings of the International Union of Theoretical and Applied Mechanics Symposium on Variational Methods in the Mechanics of Solids, held at Northwestern University in Evanston, Illinois, on September 11-13, 1978. The papers focus on advances in the application of variational methods to a variety of mathematically and technically significant problems in solid mechanics. The discussions are organized around three themes: thermomechanical behavior of composites, elastic and inelastic boundary value problems, and elastic and inelastic dynamic problems. This book is comprised of 58 chapters and opens by addressing some questions of asymptotic expansions connected with composite and with perforated materials. The following chapters explore mathematical and computational methods in plasticity; variational irreversible thermodynamics of open physical-chemical continua; macroscopic behavior of elastic material with periodically spaced rigid inclusions; and application of the Lanczos method to structural vibration. Finite deformation of elastic beams and complementary theorems of solid mechanics are also considered, along with numerical contact elastostatics; periodic solutions in plasticity and viscoplasticity; and the convergence of the mixed finite element method in linear elasticity. This monograph will appeal to practitioners of mathematicians as well as theoretical and applied mechanics.

Energy Principles and Variational Methods in Applied Mechanics

Author: J. N. Reddy
Publisher: John Wiley & Sons
ISBN: 1119087384
Format: PDF
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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.

Energy and Finite Element Methods in Structural Mechanics

Author: Irving Herman Shames
Publisher: New Age International
ISBN: 9788122407495
Format: PDF, Mobi
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This Book Is The Outcome Of Material Used In Senior And Graduate Courses For Students In Civil, Mechanical And Aeronautical Engineering. To Meet The Needs Of This Varied Audience, The Author Have Laboured To Make This Text As Flexible As Possible To Use.Consequently, The Book Is Divided Into Three Distinct Parts Of Approximately Equal Size. Part I Is Entitled Foundations Of Solid Mechanics And Variational Methods, Part Ii Is Entitled Structural Mechanics; And Part Iii Is Entitled Finite Elements.Depending On The Background Of The Students And The Aims Of The Course Selected Portions Can Be Used From Some Or All Of The Three Parts Of The Text To Form The Basis Of An Individual Course.The Purpose Of This Useful Book Is To Afford The Student A Sound Foundation In Variational Calculus And Energy Methods Before Delving Into Finite Elements. He Goal Is To Make Finite Elements More Understandable In Terms Of Fundamentals And Also To Provide The Student With The Background Needed To Extrapolate The Finite Element Method To Areas Of Study Other Than Solid Mechanics. In Addition, A Number Of Approximation Techniques Are Made Available Using The Quadratic Functional For A Boundary-Value Problem.Finally, The Authors; Aim Is To Give Students Who Go Through The Entire Text A Balanced And Connected Exposure To Certain Key Aspects Of Modern Structural And Solid Mechanics.

Variational Incremental and Energy Methods in Solid Mechanics and Shell Theory

Author: J. Mason
Publisher: Elsevier
ISBN: 1483289648
Format: PDF, ePub, Docs
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Studies in Applied Mechanics, 4: Variational, Incremental, and Energy Methods in Solid Mechanics and Shell Theory covers the subject of variational, incremental, and energy methods in Solid Mechanics and Shell Theory from a general standpoint, employing general coordinates and tensor notations. The publication first ponders on mathematical preliminaries, kinematics and stress in three-dimensional solid continua, and the first and second laws of thermodynamics. Discussions focus on the principles of virtual displacements and virtual forces, kinematics of rigid body motions, incremental stresses, kinematics of incremental deformation, description of motion, coordinates, reference and deformed states, tensor formulas for surfaces, and differentials and derivatives of operators. The text then elaborates on constitutive material laws, deformation and stress in shells, first law of thermodynamics applied to shells, and constitutive relations and material laws for shells. Concerns cover hyperelastic incremental material relations, material laws for thin elastic shells, incremental theory and stability, reduced and local forms of the first law of thermodynamics, and description of deformation and motion in shells. The book examines elastic stability, finite element models, variational and incremental principles, variational principles of elasticity and shell theory, and constitutive relations and material laws for shells. The publication is a valuable reference for researchers interested in the variational, incremental, and energy methods in solid mechanics and shell theory.

Variational Models and Methods in Solid and Fluid Mechanics

Author: Francesco dell'Isola
Publisher: Springer Science & Business Media
ISBN: 3709109833
Format: PDF, ePub, Mobi
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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.

Solid Mechanics

Author: Clive L. Dym
Publisher: Springer Science & Business Media
ISBN: 1461460344
Format: PDF, ePub, Mobi
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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.

Methods of Functional Analysis for Application in Solid Mechanics

Author: J. Mason
Publisher: Elsevier
ISBN: 1483289915
Format: PDF, Kindle
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Publications oriented to the interests of engineering scientists and graduate students on topics of functional analysis and its applications are rare - this book has been written to fill the gap in the literature. It provides a readable account of basic mathematic topics, with illustrative examples and chapters devoted to finite elements, variational principles of elasticity and plasticity, variational inequalities and elastic stability. The text is entirely self-contained and covers a wide range of topics and ideas, from elementary concepts to modern theories and applications, and includes numerous references. It is written for engineers, graduate students and researchers who need a general knowledge of modern mathematical methods in solid mechanics.

Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids

Author: Martin Fuchs
Publisher: Springer
ISBN: 3540444424
Format: PDF, Docs
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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.