Boundary Integral Equations In Elasticity Theory

Author : A.M. Linkov
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 47,8 Mb
Release : 2013-11-11
Category : Science
ISBN : 9789401599146

Get Book

Boundary Integral Equations in Elasticity Theory by A.M. Linkov Pdf

by the author to the English edition The book aims to present a powerful new tool of computational mechanics, complex variable boundary integral equations (CV-BIE). The book is conceived as a continuation of the classical monograph by N. I. Muskhelishvili into the computer era. Two years have passed since the Russian edition of the present book. We have seen growing interest in numerical simulation of media with internal structure, and have evidence of the potential of the new methods. The evidence was especially clear in problems relating to multiple grains, blocks, cracks, inclusions and voids. This prompted me, when preparing the English edition, to place more emphasis on such topics. The other change was inspired by Professor Graham Gladwell. It was he who urged me to abridge the chain of formulae and to increase the number of examples. Now the reader will find more examples showing the potential and advantages of the analysis. The first chapter of the book contains a simple exposition of the theory of real variable potentials, including the hypersingular potential and the hypersingular equations. This makes up for the absence of such exposition in current textbooks, and reveals important links between the real variable BIE and the complex variable counterparts. The chapter may also help readers who are learning or lecturing on the boundary element method.

Author : N. F. Morozov,M. V. Paukshto
Publisher : Springer-Verlag
Page : 375 pages
File Size : 40,6 Mb
Release : 2013-11-21
Category : Technology & Engineering
ISBN : 9783663116264

Get Book

The Integral Equations of the Theory of Elasticity by N. F. Morozov,M. V. Paukshto Pdf

Author : Gavin R. Thomson,Christian Constanda
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 41,9 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9780817682415

Get Book

Stationary Oscillations of Elastic Plates by Gavin R. Thomson,Christian Constanda Pdf

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations. Stationary Oscillations of Elastic Plates studies the latter in the context of stationary vibrations of thin elastic plates. The techniques presented here reduce the complexity of classical elasticity to a system of two independent variables, modeling problems of flexural-vibrational elastic body deformation with the aid of eigenfrequencies and simplifying them to manageable, uniquely solvable integral equations. The book is intended for an audience with a knowledge of advanced calculus and some familiarity with functional analysis. It is a valuable resource for professionals in pure and applied mathematics, and for theoretical physicists and mechanical engineers whose work involves elastic plates. Graduate students in these fields can also benefit from the monograph as a supplementary text for courses relating to theories of elasticity or flexural vibrations.

Author : N. I. Muskhelishvili
Publisher : Courier Corporation
Page : 466 pages
File Size : 42,7 Mb
Release : 2013-02-19
Category : Mathematics
ISBN : 9780486145068

Get Book

Singular Integral Equations by N. I. Muskhelishvili Pdf

DIVHigh-level treatment of one-dimensional singular integral equations covers Holder Condition, Hilbert and Riemann-Hilbert problems, Dirichlet problem, more. 1953 edition. /div

Author : William Charles Hector McLean
Publisher : Cambridge University Press
Page : 376 pages
File Size : 51,7 Mb
Release : 2000-01-28
Category : Mathematics
ISBN : 052166375X

Get Book

Strongly Elliptic Systems and Boundary Integral Equations by William Charles Hector McLean Pdf

This 2000 book provided the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains.

Author : Christian Constanda,Dale Doty,William Hamill
Publisher : Springer
Page : 0 pages
File Size : 48,6 Mb
Release : 2016-04-01
Category : Mathematics
ISBN : 3319263072

Get Book

Boundary Integral Equation Methods and Numerical Solutions by Christian Constanda,Dale Doty,William Hamill Pdf

This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and researchers in the fields of boundary integral equation methods, computational mechanics and, more generally, scientists working in the areas of applied mathematics and engineering. Given its detailed presentation of the material, the book can also be used as a text in a specialized graduate course on the applications of the boundary element method to the numerical computation of solutions in a wide variety of problems.

Author : N.I. Muskhelishvili
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400999947

Get Book

Singular Integral Equations by N.I. Muskhelishvili Pdf

In preparing this translation for publication certain minor modifications and additions have been introduced into the original Russian text, in order to increase its readibility and usefulness. Thus, instead of the first person, the third person has been used throughout; wherever possible footnotes have been included with the main text. The chapters and their subsections of the Russian edition have been renamed parts and chapters respectively and the last have been numbered consecutively. An authors and subject index has been added. In particular, the former has been combined with the list of references of the original text, in order to enable the reader to find quickly all information on anyone reference in which he may be especially interested. This has been considered most important with a view to the difficulties experienced outside Russia in obtaining references, published in that country. Russian names have been printed in Russian letters in the authors index, in order to overcome any possible confusion arising from transliteration.

Author : E.G. Ladopoulos
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 53,9 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9783662042915

Get Book

Singular Integral Equations by E.G. Ladopoulos Pdf

The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Author : George C. Hsiao,Wolfgang L. Wendland
Publisher : Springer Science & Business Media
Page : 635 pages
File Size : 55,5 Mb
Release : 2008-05-07
Category : Mathematics
ISBN : 9783540685456

Get Book

Boundary Integral Equations by George C. Hsiao,Wolfgang L. Wendland Pdf

This book is devoted to the mathematical foundation of boundary integral equations. The combination of ?nite element analysis on the boundary with these equations has led to very e?cient computational tools, the boundary element methods (see e.g., the authors [139] and Schanz and Steinbach (eds.) [267]). Although we do not deal with the boundary element discretizations in this book, the material presented here gives the mathematical foundation of these methods. In order to avoid over generalization we have con?ned ourselves to the treatment of elliptic boundary value problems. The central idea of eliminating the ?eld equations in the domain and - ducing boundary value problems to equivalent equations only on the bou- ary requires the knowledge of corresponding fundamental solutions, and this idea has a long history dating back to the work of Green [107] and Gauss [95, 96]. Today the resulting boundary integral equations still serve as a major tool for the analysis and construction of solutions to boundary value problems.

Author : Heinz Antes,P. D. Panagiotopoulos
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 48,8 Mb
Release : 1992
Category : Mathematics
ISBN : 3764325925

Get Book

The Boundary Integral Approach to Static and Dynamic Contact Problems by Heinz Antes,P. D. Panagiotopoulos Pdf

1 Introductory Material.- 2 The Direct and Indirect B.I.E.M. for Bilateral Problems.- 3 Boundary Integral Formulations for Some Special Elastostatic B.V.Ps.- 4 On the Numerical Implementation of Boundary Element Equations.- 5 Extension to Dynamic Problems.- 6 Dynamic Interaction Problems.- 7 B.I. Formulations for the Signorini-Fichera Inequality Problem.- 8 Mathematical Study of the B.I. Formulations of the Signorini-Fichera B.V.P..- 9 Boundary Integral Formulation of the Frictional Unilateral Contact B.V.P..- 10 Boundary Integral Formulations for the Monotone Multivalued Boundary Conditions.- 11 Elastodynamic Unilateral Problems. A B.I.E. Approach.- 12 Nonconvex Unilateral Contact Problems.- 13 Miscellanea.- References.

Author : H Antes,P D Panagiotopoulos
Publisher : Unknown
Page : 328 pages
File Size : 43,5 Mb
Release : 1992-07-31
Category : Electronic
ISBN : 3034886519

Get Book

The Boundary Integral Approach to Static and Dynamic Contact Problems by H Antes,P D Panagiotopoulos Pdf

Author : H. Antes,P.D. Panagiotopoulos
Publisher : Birkhäuser
Page : 313 pages
File Size : 44,6 Mb
Release : 2013-03-07
Category : Science
ISBN : 9783034886505

Get Book

The Boundary Integral Approach to Static and Dynamic Contact Problems by H. Antes,P.D. Panagiotopoulos Pdf

The fields of boundary integral equations and of inequality problems, or more gen erally, of nonsmooth mechanics, have seen, in a remarkably short time, a considerable development in mathematics and in theoretical and applied mechanics. The engineering sciences have also benefited from these developments in that open problems have been attacked succesfully and entirely new methodologies have been developed. The contact problems of elasticity is a class of problems which has offered many open questions to deal with, both to the research workers working on the theory of boundary integral equations and to those working on the theory of inequality problems. Indeed, the area of static and dynamic contact problems could be considered as the testing workbench of the new developments in both the inequality problems and in the boundary integral equations. This book is a first attempt to formulate and study the boundary integral equations arising in inequality contact problems. The present book is a result of more than two decades of research and teaching activity of the first author on boundary integral equations and, of the second author, on inequality problems, as well as the outgrowth of seminars and courses for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessa loniki, the Universities of Bochum, of Hamburg and Braunschweig, the Pontificia Univ. Catolica in Rio de Janeiro etc.

Author : V.G. Maz'ya
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581755

Get Book

Analysis IV by V.G. Maz'ya Pdf

A linear integral equation is an equation of the form XEX. (1) 2a(x)cp(x) - Ix k(x, y)cp(y)dv(y) = f(x), Here (X, v) is a measure space with a-finite measure v, 2 is a complex parameter, and a, k, f are given (complex-valued) functions, which are referred to as the coefficient, the kernel, and the free term (or the right-hand side) of equation (1), respectively. The problem consists in determining the parameter 2 and the unknown function cp such that equation (1) is satisfied for almost all x E X (or even for all x E X if, for instance, the integral is understood in the sense of Riemann). In the case f = 0, the equation (1) is called homogeneous, otherwise it is called inhomogeneous. If a and k are matrix functions and, accordingly, cp and f are vector-valued functions, then (1) is referred to as a system of integral equations. Integral equations of the form (1) arise in connection with many boundary value and eigenvalue problems of mathematical physics. Three types of linear integral equations are distinguished: If 2 = 0, then (1) is called an equation of the first kind; if 2a(x) i= 0 for all x E X, then (1) is termed an equation of the second kind; and finally, if a vanishes on some subset of X but 2 i= 0, then (1) is said to be of the third kind.

Author : T. C. T. Ting,Thomas Chi-tsai Ting
Publisher : Oxford University Press on Demand
Page : 591 pages
File Size : 41,6 Mb
Release : 1996
Category : Science
ISBN : 9780195074475

Get Book

Anisotropic Elasticity by T. C. T. Ting,Thomas Chi-tsai Ting Pdf

Elasticity is a property of materials which returns them to their original shape after forces applied to change the shape have been removed. This advanced text explores the problems of composite or anisotropic materials and their elasticity.

Author : Hung-darh Alexander Cheng
Publisher : Unknown
Page : 344 pages
File Size : 52,6 Mb
Release : 1981
Category : Boundary value problems
ISBN : CORNELL:31924004574962

Get Book

Boundary Integral Equation Formulation for Porous-elasticity with Applications in Soil Mechanics and Geophysics by Hung-darh Alexander Cheng Pdf