Solid Mechanics A Variational Approach

Author : Clive L. Dym,Irving H. Shames
Publisher : Springer Science & Business Media
Page : 698 pages
File Size : 45,5 Mb
Release : 2013-04-05
Category : Science
ISBN : 9781461460343

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Solid Mechanics by Clive L. Dym,Irving H. Shames Pdf

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 : Clive L. Dym,Irving Herman Shames
Publisher : McGraw-Hill Companies
Page : 594 pages
File Size : 44,9 Mb
Release : 1973
Category : Mathematics
ISBN : UCSD:31822031546849

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Solid Mechanics: a Variational Approach by Clive L. Dym,Irving Herman Shames Pdf

Author : Clive L. Dym
Publisher : Unknown
Page : 128 pages
File Size : 45,7 Mb
Release : 1972
Category : Calculus of variations
ISBN : 0070185573

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Solutions Manual to Accompany Solid Mechanics by Clive L. Dym Pdf

Author : Marco L. Bittencourt
Publisher : CRC Press
Page : 670 pages
File Size : 53,5 Mb
Release : 2014-09-19
Category : Science
ISBN : 9781482246537

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Computational Solid Mechanics by Marco L. Bittencourt Pdf

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

Author : S. Nemat-Nasser
Publisher : Elsevier
Page : 429 pages
File Size : 46,7 Mb
Release : 2017-01-31
Category : Technology & Engineering
ISBN : 9781483145839

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Variational Methods in the Mechanics of Solids by S. Nemat-Nasser Pdf

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.

Author : Francesco dell'Isola,Sergey Gavrilyuk
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 42,7 Mb
Release : 2012-01-15
Category : Technology & Engineering
ISBN : 9783709109830

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Variational Models and Methods in Solid and Fluid Mechanics by Francesco dell'Isola,Sergey Gavrilyuk Pdf

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 : Alexander S. Kravchuk,Pekka J. Neittaanmäki
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 55,8 Mb
Release : 2007-09-04
Category : Technology & Engineering
ISBN : 9781402063770

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Variational and Quasi-Variational Inequalities in Mechanics by Alexander S. Kravchuk,Pekka J. Neittaanmäki Pdf

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.

Author : J. N. Reddy
Publisher : John Wiley & Sons
Page : 756 pages
File Size : 42,9 Mb
Release : 2017-08-07
Category : Technology & Engineering
ISBN : 9781119087373

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Energy Principles and Variational Methods in Applied Mechanics by J. N. Reddy Pdf

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 : Edgardo O. Taroco,Pablo J. Blanco,Raúl A. Feijóo
Publisher : John Wiley & Sons
Page : 606 pages
File Size : 41,7 Mb
Release : 2020-02-25
Category : Mathematics
ISBN : 9781119600909

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Introduction to the Variational Formulation in Mechanics by Edgardo O. Taroco,Pablo J. Blanco,Raúl A. Feijóo Pdf

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.

Author : Georgy Viktorovich Kostin,Vasily V. Saurin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 305 pages
File Size : 50,8 Mb
Release : 2017-11-20
Category : Science
ISBN : 9783110516258

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Dynamics of Solid Structures by Georgy Viktorovich Kostin,Vasily V. Saurin Pdf

This monograph covers new variational and projection methods to study the dynamics within solid structures. To cope with the underlying initial-boundary value problems, the method of integrodifferential relations is employed. Applications and examples in physics, mechanics and control engineering range from natural vibrations or forced motions of elastic and viscoelastic bodies to heat and mass transfer processes. Contents Generalized formulations of parabolic and hyperbolic problems Variational principles in linear elasticity Variational statements in structural mechanics Ritz method for initial-boundary value problems Variational and projection techniques with semi-discretization Integrodifferential approach to eigenvalue problems Spatial vibrations of elastic beams with convex cross-sections Double minimization in optimal control problems Semi-discrete approximations in inverse dynamic problems Modeling and control in mechatronics

Author : Gerhard A. Holzapfel
Publisher : Unknown
Page : 482 pages
File Size : 51,6 Mb
Release : 2000-04-06
Category : Mathematics
ISBN : STANFORD:36105028490071

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Nonlinear Solid Mechanics by Gerhard A. Holzapfel Pdf

Providing a modern and comprehensive coverage of continuum mechanics, this volume includes information on "variational principles"--Significant, as this is the only method by which such material is actually utilized in engineering practice.

Author : Victor Berdichevsky
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 51,9 Mb
Release : 2009-09-18
Category : Science
ISBN : 9783540884675

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Variational Principles of Continuum Mechanics by Victor Berdichevsky Pdf

Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.

Author : Yasuyuki Suzuki,Kalman Varga
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 53,6 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540495413

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Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems by Yasuyuki Suzuki,Kalman Varga Pdf

The quantum-mechanical few-body problem is of fundamental importance for all branches of microphysics and it has substantially broadened with the advent of modern computers. This book gives a simple, unified recipe to obtain precise solutions to virtually any few-body bound-state problem and presents its application to various problems in atomic, molecular, nuclear, subnuclear and solid state physics. The main ingredients of the methodology are a wave-function expansion in terms of correlated Gaussians and an optimization of the variational trial function by stochastic sampling. The book is written for physicists and, especially, for graduate students interested in quantum few-body physics.

Author : J. Mason
Publisher : Elsevier
Page : 383 pages
File Size : 43,8 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9781483289649

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Variational, Incremental and Energy Methods in Solid Mechanics and Shell Theory by J. Mason Pdf

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.

Author : Victor Berdichevsky
Publisher : Springer
Page : 0 pages
File Size : 48,8 Mb
Release : 2009-10-09
Category : Technology & Engineering
ISBN : 3540885064

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Variational Principles of Continuum Mechanics by Victor Berdichevsky Pdf

The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particular problems. Berdichevsky’s work differs from other books on the subject in focusing mostly on the physical origin of variational principles as well as establishing their interrelations. For example, the Gibbs principles appear as a consequence of the Einstein formula for thermodynamic fluctuations rather than as the first principles of the theory of thermodynamic equilibrium. Mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for the direct study of variational problems. In addition, a thorough account of variational principles discovered in various branches of continuum mechanics is given. This book, the second volume, describes how the variational approach can be applied to constructing models of continuum media, such as the theory of elastic plates; shells and beams; shallow water theory; heterogeneous mixtures; granular materials; and turbulence. It goes on to apply the variational approach to asymptotical analysis of problems with small parameters, such as the derivation of the theory of elastic plates, shells and beams from three-dimensional elasticity theory; and the basics of homogenization theory. A theory of stochastic variational problems is considered in detail too, along with applications to the homogenization of continua with random microstructures.