Download or read book Boundary Value Problems of Finite Elasticity written by Tullio Valent and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality.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.
Download or read book Topics in Finite Elasticity written by Morton E. Gurtin and published by SIAM. This book was released on 1981-01-01 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite elasticity is a theory of elastic materials that are capable of undergoing large deformations. This theory is inherently nonlinear and is mathematically quite complex. This monograph presents a derivation of the basic equations of the theory, a discussion of the general boundary-value problems, and a treatment of several interesting and important special topics such as simple shear, uniqueness, the tensile deformations of a cube, and antiplane shear. The monograph is intended for engineers, physicists, and mathematicians.
Download or read book Finite element approximations of a class of highly nonlinear boundary value problems in finite elasticity written by John Tinsley Oden and published by . This book was released on 1978 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite element approximations of a class of nonlinear two point boundary value problems in finite elasticity written by John Tinsley Oden and published by . This book was released on 1974 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation written by Zohar Yosibash and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations. The book is divided into fourteen chapters, each containing several sections. Most of it (the first nine Chapters) addresses two-dimensional domains, where only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle material on a daily basis. Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, is still a topic of active research and interest, and is addressed herein. Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions. This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.
Download or read book Solving the Second Boundary Value Problem of Elasticity written by Ronald O. Hultgren and published by . This book was released on 1965 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A theory of finite element approximations for a class of nonlinear two point boundary value problems in finite elasticity written by John Tinsley Oden and published by . This book was released on 1977 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Exact Solutions of the Equations of Finite Elasticity written by Jeremiah Gerard Murphy and published by . This book was released on 1990 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Approximation Methods for Elliptic Boundary Value Problems written by Olaf Steinbach and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Finite Element Method for Boundary Value Problems written by Karan S. Surana and published by CRC Press. This book was released on 2016-11-17 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applications of Lie Point Symmetry Methods to Dynamic Boundary Value Problems in Finite Elasticity written by Nicolette Roussos and published by . This book was released on 2001 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Elasticity and Viscoelasticity written by Aleksey D. Drozdov and published by World Scientific. This book was released on 1996-01-01 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory. The objective is to expose the most intriguing aspects of elasticity and viscoelasticity with finite strains in such a way as to ensure mathematical correctness, on the one hand, and to demonstrate a wide spectrum of physical phenomena typical only of nonlinear mechanics, on the other.A novel aspect of the book is that it contains a number of examples illustrating surprising behaviour in materials with finite strains, as well as comparisons between theoretical predictions and experimental data for rubber-like polymers and elastomers.The book aims to fill a gap between mathematicians specializing in nonlinear continuum mechanics, and physicists and engineers who apply the methods of solid mechanics to a wide range of problems in civil and mechanical engineering, materials science, and polymer physics. The book has been developed from a graduate course in applied mathematics which the author has given for a number of years.
Download or read book Introductory Functional Analysis written by B.D. Reddy and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and finite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. It is intended for use by senior undergraduates and graduates in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a course in functional analysis, such as real analysis. Mature researchers wishing to learn the basic ideas of functional analysis will equally find this useful. Offers a good grounding in those aspects of functional analysis which are most relevant to a proper understanding and appreciation of the mathematical aspects of boundary-value problems and the finite element method.
Download or read book Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory written by Julian Braun and published by Logos Verlag Berlin GmbH. This book was released on 2016-11-15 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlinear elastic behavior of solid materials is often described in the context of continuum mechanics. Alternatively, one can try to determine the behavior of every single atom in the material. Classically, the connection between these two types of models is made with the Cauchy-Born rule. The aim of this book is to provide good criteria for the Cauchy-Born rule to be true and to make the connection between continuum and atomistic models precise. In particular, this includes rigorous proofs for the existence of solutions to the atomistic boundary value problem and their convergence to the corresponding continuum solutions in the limit of small interatomic distances.
Download or read book Uniqueness Theorems in Linear Elasticity written by Robin J. Knops and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniqueness in elasticity theory in the hope that such an exposition will provide a convenient access to the literature while at the same time indicating what progress has been made and what problems still await solution. Naturally, the continuing announcement of new results thwarts any attempt to provide a complete assessment. Apart from linear elasticity theory itself, there are several other areas where elastic uniqueness is significant.
Download or read book Dynamic Boundary Value Problems for Transversely Isotropic Cyclinders and Spheres in Finite Elasticity written by Gaza Hand-sup Maluleke and published by . This book was released on 2006 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of an Incremental Method to the Solution of General Plane Strain Boundary Value Problems in Finite Elasticity written by P. Sindelar and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
