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Variational, Incremental and Energy Methods in Solid Mechanics and Shell Theory

Author: J. Mason

Publisher: Elsevier

Published: 2013-10-22

Total Pages: 383

ISBN-13: 1483289648

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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.

Book Synopsis Variational, Incremental and Energy Methods in Solid Mechanics and Shell Theory by : J. Mason

Download or read book Variational, Incremental and Energy Methods in Solid Mechanics and Shell Theory written by J. Mason and published by Elsevier. This book was released on 2013-10-22 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Incremental, and Energy Methods in Solid Mechanics and Shell Theory

Author: Jayme Mason

Publisher:

Published: 1980

Total Pages: 0

ISBN-13: 9780444417589

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Book Synopsis Variational, Incremental, and Energy Methods in Solid Mechanics and Shell Theory by : Jayme Mason

Download or read book Variational, Incremental, and Energy Methods in Solid Mechanics and Shell Theory written by Jayme Mason and published by . This book was released on 1980 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Variational Methods in the Mechanics of Solids

Author: S. Nemat-Nasser

Publisher: Elsevier

Published: 2017-01-31

Total Pages: 429

ISBN-13: 1483145832

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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.

Book Synopsis Variational Methods in the Mechanics of Solids by : S. Nemat-Nasser

Download or read book Variational Methods in the Mechanics of Solids written by S. Nemat-Nasser and published by Elsevier. This book was released on 2017-01-31 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mechanics of Solids and Shells

Author: Gerald Wempner

Publisher: CRC Press

Published: 2002-10-29

Total Pages: 534

ISBN-13: 1420036424

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As the theories and methods have evolved over the years, the mechanics of solid bodies has become unduly fragmented. Most books focus on specific aspects, such as the theories of elasticity or plasticity, the theories of shells, or the mechanics of materials. While a narrow focus serves immediate purposes, much is achieved by establishing the common foundations and providing a unified perspective of the discipline as a whole. Mechanics of Solids and Shells accomplishes these objectives. By emphasizing the underlying assumptions and the approximations that lead to the mathematical formulations, it offers a practical, unified presentation of the foundations of the mechanics of solids, the behavior of deformable bodies and thin shells, and the properties of finite elements. The initial chapters present the fundamental kinematics, dynamics, energetics, and behavior of materials that build the foundation for all of the subsequent developments. These are presented in full generality without the usual restrictions on the deformation. The general principles of work and energy form the basis for the consistent theories of shells and the approximations by finite elements. The final chapter views the latter as a means of approximation and builds a bridge between the mechanics of the continuum and the discrete assembly. Expressly written for engineers, Mechanics of Solids and Shells forms a reliable source for the tools of analysis and approximation. Its constructive presentation clearly reveals the origins, assumptions, and limitations of the methods described and provides a firm, practical basis for the use of those methods.

Book Synopsis Mechanics of Solids and Shells by : Gerald Wempner

Download or read book Mechanics of Solids and Shells written by Gerald Wempner and published by CRC Press. This book was released on 2002-10-29 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the theories and methods have evolved over the years, the mechanics of solid bodies has become unduly fragmented. Most books focus on specific aspects, such as the theories of elasticity or plasticity, the theories of shells, or the mechanics of materials. While a narrow focus serves immediate purposes, much is achieved by establishing the common foundations and providing a unified perspective of the discipline as a whole. Mechanics of Solids and Shells accomplishes these objectives. By emphasizing the underlying assumptions and the approximations that lead to the mathematical formulations, it offers a practical, unified presentation of the foundations of the mechanics of solids, the behavior of deformable bodies and thin shells, and the properties of finite elements. The initial chapters present the fundamental kinematics, dynamics, energetics, and behavior of materials that build the foundation for all of the subsequent developments. These are presented in full generality without the usual restrictions on the deformation. The general principles of work and energy form the basis for the consistent theories of shells and the approximations by finite elements. The final chapter views the latter as a means of approximation and builds a bridge between the mechanics of the continuum and the discrete assembly. Expressly written for engineers, Mechanics of Solids and Shells forms a reliable source for the tools of analysis and approximation. Its constructive presentation clearly reveals the origins, assumptions, and limitations of the methods described and provides a firm, practical basis for the use of those methods.

Mechanics of Structured Media

Author: A.P.S. Selvadurai

Publisher: Elsevier

Published: 2016-06-06

Total Pages: 512

ISBN-13: 1483164136

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Mechanics of Structured Media

Book Synopsis Mechanics of Structured Media by : A.P.S. Selvadurai

Download or read book Mechanics of Structured Media written by A.P.S. Selvadurai and published by Elsevier. This book was released on 2016-06-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics of Structured Media

Probabilistic Approach to Mechanisms

Author: B.Z. Sandler

Publisher: Elsevier

Published: 2013-10-22

Total Pages: 314

ISBN-13: 1483289869

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This book discusses the application of probabilistics to the investigation of mechanical systems. The book shows, for example, how random function theory can be applied directly to the investigation of random processes in the deflection of cam profiles, pitch or gear teeth, pressure in pipes, etc. The author also deals with some other technical applications of probabilistic theory, including, amongst others, those relating to pneumatic and hydraulic mechanisms and roller bearings. Many of the aspects are illustrated by examples of applications of the techniques under discussion.

Book Synopsis Probabilistic Approach to Mechanisms by : B.Z. Sandler

Download or read book Probabilistic Approach to Mechanisms written by B.Z. Sandler and published by Elsevier. This book was released on 2013-10-22 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the application of probabilistics to the investigation of mechanical systems. The book shows, for example, how random function theory can be applied directly to the investigation of random processes in the deflection of cam profiles, pitch or gear teeth, pressure in pipes, etc. The author also deals with some other technical applications of probabilistic theory, including, amongst others, those relating to pneumatic and hydraulic mechanisms and roller bearings. Many of the aspects are illustrated by examples of applications of the techniques under discussion.

Nonlinear Problems In Engineering - Proceedings Of The Enea Workshops On Nonlinear Dynamics - Vol 4

Author: Costantino Carmignani

Publisher: World Scientific

Published: 1991-10-31

Total Pages: 290

ISBN-13: 9814555479

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The papers collected in this volume, presented at the workshop on 'Nonlinear Problems in Engineering', held in ENEA Rome (Italy) from 6 - 7 May 1991, and sponsored by ENEA, report nonlinear problems of prevailing engineering interest. Both nonlinear static and dynamic topics are dealt with; in particular, plastic behavior of materials, elastic-plastic models, fracture mechanics, geophysical prospecting, theory of nonlinear control, mixing models for chemical reactors, nonlinear responses of structures, rotor dynamics, and impact loads on structures.

Book Synopsis Nonlinear Problems In Engineering - Proceedings Of The Enea Workshops On Nonlinear Dynamics - Vol 4 by : Costantino Carmignani

Download or read book Nonlinear Problems In Engineering - Proceedings Of The Enea Workshops On Nonlinear Dynamics - Vol 4 written by Costantino Carmignani and published by World Scientific. This book was released on 1991-10-31 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers collected in this volume, presented at the workshop on 'Nonlinear Problems in Engineering', held in ENEA Rome (Italy) from 6 - 7 May 1991, and sponsored by ENEA, report nonlinear problems of prevailing engineering interest. Both nonlinear static and dynamic topics are dealt with; in particular, plastic behavior of materials, elastic-plastic models, fracture mechanics, geophysical prospecting, theory of nonlinear control, mixing models for chemical reactors, nonlinear responses of structures, rotor dynamics, and impact loads on structures.

Three-Dimensional Elasticity

Author:

Publisher: Elsevier

Published: 1988-04-01

Total Pages: 448

ISBN-13: 9780080875415

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This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.

Book Synopsis Three-Dimensional Elasticity by :

Download or read book Three-Dimensional Elasticity written by and published by Elsevier. This book was released on 1988-04-01 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.

Theoretical Analyses, Computations, and Experiments of Multiscale Materials

Author: Ivan Giorgio

Publisher: Springer Nature

Published: 2022-05-03

Total Pages: 739

ISBN-13: 3031045483

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This book is devoted to the 60th birthday of the Prof. Francesco dell’Isola, who is known for his long-term contribution in the field of multiscale materials. It contains several contributions from researchers in the field, covering theoretical analyses, computational aspects and experiments.

Book Synopsis Theoretical Analyses, Computations, and Experiments of Multiscale Materials by : Ivan Giorgio

Download or read book Theoretical Analyses, Computations, and Experiments of Multiscale Materials written by Ivan Giorgio and published by Springer Nature. This book was released on 2022-05-03 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the 60th birthday of the Prof. Francesco dell’Isola, who is known for his long-term contribution in the field of multiscale materials. It contains several contributions from researchers in the field, covering theoretical analyses, computational aspects and experiments.

Mathematical Elasticity

Author: Philippe G. Ciarlet

Publisher: SIAM

Published: 2022-01-22

Total Pages: 521

ISBN-13: 1611976782

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The first book of a three-volume set, Three-Dimensional Elasticity covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It includes the known existence theorems, either via the implicit function theorem or via the minimization of the energy (John Ball’s theory). An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

Book Synopsis Mathematical Elasticity by : Philippe G. Ciarlet

Download or read book Mathematical Elasticity written by Philippe G. Ciarlet and published by SIAM. This book was released on 2022-01-22 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of a three-volume set, Three-Dimensional Elasticity covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It includes the known existence theorems, either via the implicit function theorem or via the minimization of the energy (John Ball’s theory). An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.