Boundary Value Problems Of Finite Elasticity
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Boundary Value Problems Of Finite Elasticity
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Author : Tullio Valent
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Boundary Value Problems Of Finite Elasticity written by Tullio Valent and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Science categories.
In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be sides being quite spontaneous, allows us to consider a great many inter esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b], in order to obtain local existence and uniqueness for the traction problem in hyperelasticity under dead loads, inspired many of the ideas which led to this monograph. Chapter I aims to give a very brief introduction to some general concepts in the mathematical theory of elasticity, in order to show how the boundary value problems studied in the sequel arise. Chapter II is very technical; it supplies the framework for all sub sequent developments.
The Finite Element Method For Boundary Value Problems
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Author : Karan S. Surana
language : en
Publisher: CRC Press
Release Date : 2016-11-17
The Finite Element Method For Boundary Value Problems written by Karan S. Surana and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-17 with Science categories.
Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.
Numerical Approximation Methods For Elliptic Boundary Value Problems
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Author : Olaf Steinbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-22
Numerical Approximation Methods For Elliptic Boundary Value Problems written by Olaf Steinbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-22 with Mathematics categories.
This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.
Contact Problems In Elasticity
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Author : N. Kikuchi
language : en
Publisher: SIAM
Release Date : 1988-01-01
Contact Problems In Elasticity written by N. Kikuchi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Science categories.
The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.
Mathematical Elasticity
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Author : Philippe G. Ciarlet
language : en
Publisher: SIAM
Release Date : 2022-01-22
Mathematical Elasticity written by Philippe G. Ciarlet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-22 with Mathematics categories.
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.
Linear Theories Of Elasticity And Thermoelasticity
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Author : Clifford Truesdell
language : en
Publisher: Springer
Release Date : 2013-12-17
Linear Theories Of Elasticity And Thermoelasticity written by Clifford Truesdell and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-17 with Technology & Engineering categories.
Fundamentals Of Structural Mechanics
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Author : Keith D. Hjelmstad
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-11-12
Fundamentals Of Structural Mechanics written by Keith D. Hjelmstad and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-12 with Technology & Engineering categories.
A solid introduction to basic continuum mechanics, emphasizing variational formulations and numeric computation. The book offers a complete discussion of numerical method techniques used in the study of structural mechanics.
Three Dimensional Elasticity
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Author :
language : en
Publisher: Elsevier
Release Date : 1994-01-19
Three Dimensional Elasticity written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-19 with Technology & Engineering categories.
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.
Advanced Mechanics Of Materials And Applied Elasticity
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Author : Anthony E. Armenàkas
language : en
Publisher: CRC Press
Release Date : 2005-08-19
Advanced Mechanics Of Materials And Applied Elasticity written by Anthony E. Armenàkas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-19 with Science categories.
This book presents both differential equation and integral formulations of boundary value problems for computing the stress and displacement fields of solid bodies at two levels of approximation - isotropic linear theory of elasticity as well as theories of mechanics of materials. Moreover, the book applies these formulations to practical solutions in detailed, easy-to-follow examples. Advanced Mechanics of Materials and Applied Elasticity presents modern and classical methods of analysis in current notation and in the context of current practices. The author's well-balanced choice of topics, clear and direct presentation, and emphasis on the integration of sophisticated mathematics with practical examples offer students in civil, mechanical, and aerospace engineering an unparalleled guide and reference for courses in advanced mechanics of materials, stress analysis, elasticity, and energy methods in structural analysis.
Mathematical Theory Of Elastic And Elasto Plastic Bodies
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Author : J. Necas
language : en
Publisher: Elsevier
Release Date : 2017-02-01
Mathematical Theory Of Elastic And Elasto Plastic Bodies written by J. Necas and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-01 with Science categories.
The book acquaints the reader with the basic concepts and relations of elasticity and plasticity, and also with the contemporary state of the theory, covering such aspects as the nonlinear models of elasto-plastic bodies and of large deflections of plates, unilateral boundary value problems, variational principles, the finite element method, and so on.