Variational Incremental And Energy Methods In Solid Mechanics And Shell Theory

Author : J. Mason
Publisher : Elsevier
Page : 383 pages
File Size : 51,8 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9781483289649

Get Book

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 : Jayme Mason
Publisher : Unknown
Page : 0 pages
File Size : 47,7 Mb
Release : 1980
Category : Engineering mathematics
ISBN : 0444417583

Get Book

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

Author : Gerald Wempner,Demosthenes Talaslidis
Publisher : CRC Press
Page : 552 pages
File Size : 46,8 Mb
Release : 2002-10-29
Category : Science
ISBN : 9781420036428

Get Book

Mechanics of Solids and Shells by Gerald Wempner,Demosthenes Talaslidis Pdf

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.

Author : Ivan Giorgio,Luca Placidi,Emilio Barchiesi,Bilen Emek Abali,Holm Altenbach
Publisher : Springer Nature
Page : 739 pages
File Size : 42,9 Mb
Release : 2022-05-03
Category : Science
ISBN : 9783031045486

Get Book

Theoretical Analyses, Computations, and Experiments of Multiscale Materials by Ivan Giorgio,Luca Placidi,Emilio Barchiesi,Bilen Emek Abali,Holm Altenbach Pdf

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.

Author : George Z. Voyiadjis,D. Karamanlidis
Publisher : Elsevier
Page : 324 pages
File Size : 41,6 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483290966

Get Book

Advances in the Theory of Plates and Shells by George Z. Voyiadjis,D. Karamanlidis Pdf

Plates and shells play an important role in structural, mechanical, aerospace and manufacturing applications. The theory of plates and shells have advanced in the past two decades to handle more complicated problems that were previously beyond reach. In this book, the most recent advances in this area of research are documented. These include topics such as thick plate and shell analyses, finite rotations of shell structures, anisotropic thick plates, dynamic analysis, and laminated composite panels. The book is divided into two parts. In Part I, emphasis is placed on the theoretical aspects of the analysis of plates and shells, while Part II deals with modern applications. Numerous eminent researchers in the various areas of plate and shell analyses have contributed to this work which pays special attention to aspects of research such as theory, dynamic analysis, and composite plates and shells.

Author : J. Mason
Publisher : Elsevier
Page : 413 pages
File Size : 50,7 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9781483289915

Get Book

Methods of Functional Analysis for Application in Solid Mechanics by J. Mason Pdf

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.

Author : Issam Doghri
Publisher : Springer Science & Business Media
Page : 587 pages
File Size : 48,5 Mb
Release : 2013-03-09
Category : Science
ISBN : 9783662041680

Get Book

Mechanics of Deformable Solids by Issam Doghri Pdf

Three subjects of major interest in one textbook: linear elasticity, mechanics of structures in linear isotropic elasticity, and nonlinear mechanics including computational algorithms. After the simplest possible, intuitive approach there follows the mathematical formulation and analysis, with computational methods occupying a good portion of the book. There are several worked-out problems in each chapter and additional exercises at the end of the book, plus mathematical expressions are bery often given in more than one notation. The book is intended primarily for students and practising engineers in mechanical and civil engineering, although students and experts from applied mathematics, materials science and other related fields will also find it useful.

Author : S. Nemat-Nasser
Publisher : Elsevier
Page : 429 pages
File Size : 54,9 Mb
Release : 2017-01-31
Category : Technology & Engineering
ISBN : 9781483145839

Get Book

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 : Yavuz Basar,Dieter Weichert
Publisher : Springer Science & Business Media
Page : 201 pages
File Size : 43,9 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783662042991

Get Book

Nonlinear Continuum Mechanics of Solids by Yavuz Basar,Dieter Weichert Pdf

The aim of the book is the presentation of the fundamental mathematical and physical concepts of continuum mechanics of solids in a unified description so as to bring young researchers rapidly close to their research area. Accordingly, emphasis is given to concepts of permanent interest, and details of minor importance are omitted. The formulation is achieved systematically in absolute tensor notation, which is almost exclusively used in modern literature. This mathematical tool is presented such that study of the book is possible without permanent reference to other works.

Author : D. Givoli
Publisher : Elsevier
Page : 316 pages
File Size : 52,9 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9781483291086

Get Book

Numerical Methods for Problems in Infinite Domains by D. Givoli Pdf

This volume reviews and discusses the main numerical methods used today for solving problems in infinite domains. It also presents in detail one very effective method in this class, namely the Dirichlet-to-Neumann (DtN) finite element method. The book is intended to provide the researcher or engineer with the state-of-the-art in numerical solution methods for infinite domain problems, such as the problems encountered in acoustics and structural acoustics, fluid dynamics, meteorology, and many other fields of application. The emphasis is on the fundamentals of the various methods, and on reporting recent progress and forecasting future directions. An appendix at the end of the book provides an introduction to the essentials of the finite element method, and suggests a short list of texts on the subject which are categorized by their level of mathematics.

Author : Xudong Wang,S.K. Ghosh
Publisher : Elsevier
Page : 256 pages
File Size : 53,6 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483290393

Get Book

Advanced Theories of Hypoid Gears by Xudong Wang,S.K. Ghosh Pdf

In order to develop more efficient types of gears, further investigation into the theories of engagement is necessary. Up until now most of the research work on the theories of engagement has been carried out separately on different groups, and based on individual types of profiles. This book aims at developing some universal theories, which can not only be used for all types of gears, but can also be utilized in other fields such as sculptured surfaces. The book has four characteristics: the investigations are concentrated on mismatched tooth surfaces; all the problems are dealt with from a differential geometry point of view; most theories and algorithms are universal in application; and the algorithms are easy to follow and can be used in real situations. In the process of developing the algorithms, the authors have introduced some mathematical methods which are believed to be innovative with regard to the theories of engagement known so far. A theoretical treatment is presented throughout the book, supported by numerical examples and experiments. With the computer programs listed at the end of the volume, any of the proposed methods can be easily utilized in practice. The book is intended for postgraduate students, lecturers, professors, or research staff in mechanical/manufacturing engineering, mathematics and R & D departments of research institutes and universities. It will also be useful for engineers working in the gear manufacturing sector of industry.

Author : George Z. Voyiadjis,L.C. Bank,L.J. Jacobs
Publisher : Elsevier
Page : 447 pages
File Size : 49,7 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483291543

Get Book

Mechanics of Materials and Structures by George Z. Voyiadjis,L.C. Bank,L.J. Jacobs Pdf

A wide range of topics in the area of mechanics of materials and structures are covered in this volume, ranging from analysis to design. There is no special emphasis on a specific area of research. The first section of the book deals with topics on the mechanics and damage of concrete. It also includes two papers on granular packing structure changes and cumulative damage in polymers. In the second part more theoretical topics in mechanics are discussed, such as shell theory and nonlinear elasticity. The following section dicusses areas dealing primarily with plasticity, viscoelasticity, and viscoplasticity. These include such topics as dynamic and cyclic plasticity. In the final section the subject is structural dynamics, including seismic analysis, composite frames and nonlinear analysis of bridges. The volume is compiled in honor of Professor Maciej P. Bieniek who has served as a teacher and researcher at several universities, and who has made many significant contributions in the evaluation, rehabilitation, and design of infrastructures.

Author : J. Balaš,J. Sládek,V. Sládek
Publisher : Elsevier
Page : 699 pages
File Size : 53,7 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483291741

Get Book

Stress Analysis by Boundary Element Methods by J. Balaš,J. Sládek,V. Sládek Pdf

The boundary element method is an extremely versatile and powerful tool of computational mechanics which has already become a popular alternative to the well established finite element method. This book presents a comprehensive and up-to-date treatise on the boundary element method (BEM) in its applications to various fields of continuum mechanics such as: elastostatics, elastodynamics, thermoelasticity, micropolar elasticity, elastoplasticity, viscoelasticity, theory of plates and stress analysis by hybrid methods. The fundamental solution of governing differential equations, integral representations of the displacement and temperature fields, regularized integral representations of the stress field and heat flux, boundary integral equations and boundary integro-differential equations are derived. Besides the mathematical foundations of the boundary integral method, the book deals with practical applications of this method. Most of the applications concentrate mainly on the computational problems of fracture mechanics. The method has been found to be very efficient in stress-intensity factor computations. Also included are developments made by the authors in the boundary integral formulation of thermoelasticity, micropolar elasticity, viscoelasticity, plate theory, hybrid method in elasticity and solution of crack problems. The solution of boundary-value problems of thermoelasticity and micropolar thermoelasticity is formulated for the first time as the solution of pure boundary problems. A new unified formulation of general crack problems is presented by integro-differential equations.

Author : Jacob Aboudi
Publisher : Elsevier
Page : 341 pages
File Size : 46,7 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483290997

Get Book

Mechanics of Composite Materials by Jacob Aboudi Pdf

In the last decade the author has been engaged in developing a micromechanical composite model based on the study of interacting periodic cells. In this two-phase model, the inclusion is assumed to occupy a single cell whereas the matrix material occupies several surrounding cells. A prominent feature of the micromechanical method of cells is the transition from a medium, with a periodic microstructure to an equivalent homogeneous continuum which effectively represents the composite material. Of great importance is the significant advantage of the cells model in its capability to analyze elastic as well as nonelastic constituents (e.g. viscoelastic, elastoplastic and nonlinear elastic), thus forming a unified approach in the prediction of the overall behaviour of composite material. This book deals almost exclusively with this unified theory and its various applications.

Author : B. Druyanov,R. Nepershin
Publisher : Elsevier
Page : 426 pages
File Size : 46,6 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483290379

Get Book

Problems of Technological Plasticity by B. Druyanov,R. Nepershin Pdf

In this book the classical rigid-plastic model of deformed workpiece and the characteristic (slipline) method of analysis is assumed. The rigid-plastic solid assumption is deemed reasonable for the problems of technological plasticity with large scale plastic flow, where small elastic stains are negligible. Along with classical results of the theory of plasticity the book includes many original analytical and numerical solutions of the problems of technological plasticity obtained by the authors in Russia and unknown for most western readers. The results of the analyses are given by analytical formulae and many graphs and tables, so the book will be useful for the practical and research engineers. It may also be used as a textbook by graduate students and engineers.