Complex Variable Methods In Elasticity
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Complex Variable Methods In Elasticity
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Author : A. H. England
language : en
Publisher: Courier Corporation
Release Date : 2003-01-01
Complex Variable Methods In Elasticity written by A. H. England and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
The plane strain and generalized plane stress boundary value problems of linear elasticity are the focus of this graduate-level text, which formulates and solves these problems by employing complex variable theory. The text presents detailed descriptions of the three basic methods that rely on series representation, Cauchy integral representation, and the solution via continuation. Its five-part treatment covers functions of a complex variable, the basic equations of two-dimensional elasticity, plane and half-plane problems, regions with circular boundaries, and regions with curvilinear boundaries. Worked examples and sets of problems appear throughout the text. 1971 edition. 26 figures.
Complex Variable Methods In Elasticity
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Author : A. H. England
language : en
Publisher: Courier Corporation
Release Date : 2012-05-10
Complex Variable Methods In Elasticity written by A. H. England and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-10 with Mathematics categories.
Plane strain and generalized plane stress boundary value problems of linear elasticity are discussed as well as functions of a complex variable, basic equations of 2-dimensional elasticity, plane and half-plane problems, more. 1971 edition. Includes 26 figures.
Complex Variable Methods In Plane Elasticity
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Author : Jian-Ke Lu
language : en
Publisher: World Scientific
Release Date : 1995
Complex Variable Methods In Plane Elasticity written by Jian-Ke Lu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This book deals systematically with the mathematical theory of plane elasto-statics by using complex variable methods, together with many results originated by the author. The problems considered are reduced to integral equations, Fredholem or singular, which are rigorously proved to be uniquely solvable. Particular attention is paid to the subjects of crack problems in the quite general case, especially those of composite media, which are solved by a unified method. The methods used in this book are constructive so that they may be used in practice.
Complex Variable Methods In Plane Elasticity
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Author : Jian-ke Lu
language : en
Publisher: World Scientific
Release Date : 1995-09-30
Complex Variable Methods In Plane Elasticity written by Jian-ke Lu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-30 with Mathematics categories.
This book deals systematically with the mathematical theory of plane elasto-statics by using complex variable methods, together with many results originated by the author. The problems considered are reduced to integral equations, Fredholem or singular, which are rigorously proved to be uniquely solvable. Particular attention is paid to the subjects of crack problems in the quite general case, especially those of composite media, which are solved by a unified method. The methods used in this book are constructive so that they may be used in practice.
Applications Of Vector Analysis And Complex Variables In Engineering
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Author : Otto D. L. Strack
language : en
Publisher: Springer Nature
Release Date : 2020-04-18
Applications Of Vector Analysis And Complex Variables In Engineering written by Otto D. L. Strack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-18 with Technology & Engineering categories.
This textbook presents the application of mathematical methods and theorems tosolve engineering problems, rather than focusing on mathematical proofs. Applications of Vector Analysis and Complex Variables in Engineering explains the mathematical principles in a manner suitable for engineering students, who generally think quite differently than students of mathematics. The objective is to emphasize mathematical methods and applications, rather than emphasizing general theorems and principles, for which the reader is referred to the literature. Vector analysis plays an important role in engineering, and is presented in terms of indicial notation, making use of the Einstein summation convention. This text differs from most texts in that symbolic vector notation is completely avoided, as suggested in the textbooks on tensor algebra and analysis written in German by Duschek and Hochreiner, in the 1960s. The defining properties of vector fields, the divergence and curl, are introduced in terms of fluid mechanics. The integral theorems of Gauss (the divergence theorem), Stokes, and Green are introduced also in the context of fluid mechanics. The final application of vector analysis consists of the introduction of non-Cartesian coordinate systems with straight axes, the formal definition of vectors and tensors. The stress and strain tensors are defined as an application. Partial differential equations of the first and second order are discussed. Two-dimensional linear partial differential equations of the second order are covered, emphasizing the three types of equation: hyperbolic, parabolic, and elliptic. The hyperbolic partial differential equations have two real characteristic directions, and writing the equations along these directions simplifies the solution process. The parabolic partial differential equations have two coinciding characteristics; this gives useful information regarding the character of the equation, but does not help in solving problems. The elliptic partial differential equations do not have real characteristics. In contrast to most texts, rather than abandoning the idea of using characteristics, here the complex characteristics are determined, and the differential equations are written along these characteristics. This leads to a generalized complex variable system, introduced by Wirtinger. The vector field is written in terms of a complex velocity, and the divergence and the curl of the vector field is written in complex form, reducing both equations to a single one. Complex variable methods are applied to elliptical problems in fluid mechanics, and linear elasticity. The techniques presented for solving parabolic problems are the Laplace transform and separation of variables, illustrated for problems of heat flow and soil mechanics. Hyperbolic problems of vibrating strings and bars, governed by the wave equation are solved by the method of characteristics as well as by Laplace transform. The method of characteristics for quasi-linear hyperbolic partial differential equations is illustrated for the case of a failing granular material, such as sand, underneath a strip footing. The Navier Stokes equations are derived and discussed in the final chapter as an illustration of a highly non-linear set of partial differential equations and the solutions are interpreted by illustrating the role of rotation (curl) in energy transfer of a fluid.
The Linearized Theory Of Elasticity
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Author : William S. Slaughter
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
The Linearized Theory Of Elasticity written by William S. Slaughter 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 2002 with Mathematics categories.
The mathematical framework behind the theory is developed in detail, with the assumptions behind the eventual linearization made clear, so that the reader will be adequately prepared for further studies in continuum mechanics, nonlinear elasticity, inelasticity, fracture mechanics and/or finite elements. Prior to linearization, configurations and general measure of strain and stress are discussed. A modern treatment of the theory of tensors and tensor calculus is used. General curvilinear coordinates are described in an appendix.
Complex Variable Function Solutions In The Mechanical Analysis Of Tunnels
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Author : Aizhong Lu
language : en
Publisher: Springer Nature
Release Date : 2025-03-03
Complex Variable Function Solutions In The Mechanical Analysis Of Tunnels written by Aizhong Lu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-03 with Science categories.
This book covers the mechanical problems of tunnels in traffic, hydraulic and mining engineering. By extending the complex variable method in mechanical analysis, it proposes accurate analytical solutions for tunnels. The solutions are further applied to the back analysis of tunnels, hole shape optimization, support design and estimation of tunnel stability. The considered rock characteristics involve elasticity, elastoplasticity, viscoelasticity and anisotropy, and various geometric conditions are included, such as circular/noncircular single/multiple tunnels with/without support at deep/shallow depths. Some original achievements are provided, including new mapping functions for complex regions, precise determination of the noncircular plastic zone around single/twin tunnels and related elastoplastic solutions and quantitative analysis of the interaction between rock and the support, which are new developments of theory and method in rock mechanics. The proposed analyticalsolutions are reliable tools to initially estimate the design parameters and achieve optimal design, providing guidance in the conceptual stage of the design process. They can clearly reveal the influences of parameters in functional form and provide a benchmark against which the overall correctness of numerical analyses can be assessed. This book summarizes the author's research achievements over more than 20 years. It is a valuable reference for professionals working in geotechnical engineering.
Elastic And Inelastic Stress Analysis
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Author : Irving H Shames
language : en
Publisher: CRC Press
Release Date : 1997-02-01
Elastic And Inelastic Stress Analysis written by Irving H Shames and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-01 with Science categories.
Presents certain key aspects of inelastic solid mechanics centered around viscoelasticity, creep, viscoplasticity, and plasticity. It is divided into three parts consisting of the fundamentals of elasticity, useful constitutive laws, and applications to simple structural members, providing extended treatment of basic problems in static structural mechanics, including elastic and inelastic effects. It contains worked-out examples and end-of-chapter problems.
The Linearized Theory Of Elasticity
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Author : William S. Slaughter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Linearized Theory Of Elasticity written by William S. Slaughter 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 2012-12-06 with Technology & Engineering categories.
This book is derived from notes used in teaching a first-year graduate-level course in elasticity in the Department of Mechanical Engineering at the University of Pittsburgh. This is a modern treatment of the linearized theory of elasticity, which is presented as a specialization of the general theory of continuum mechanics. It includes a comprehensive introduction to tensor analysis, a rigorous development of the governing field equations with an emphasis on recognizing the assumptions and approximations in herent in the linearized theory, specification of boundary conditions, and a survey of solution methods for important classes of problems. Two- and three-dimensional problems, torsion of noncircular cylinders, variational methods, and complex variable methods are covered. This book is intended as the text for a first-year graduate course in me chanical or civil engineering. Sufficient depth is provided such that the text can be used without a prerequisite course in continuum mechanics, and the material is presented in such a way as to prepare students for subsequent courses in nonlinear elasticity, inelasticity, and fracture mechanics. Alter natively, for a course that is preceded by a course in continuum mechanics, there is enough additional content for a full semester of linearized elasticity.
Theoretical Elasticity
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Author : Albert Edward Green
language : en
Publisher: Courier Corporation
Release Date : 1992-01-01
Theoretical Elasticity written by Albert Edward Green and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Technology & Engineering categories.
A valuable research tool in continuum mechanics for more that 50 years, this highly regarded engineering manual focuses on three important aspects of elasticity theory: finite elastic deformations, complex variable methods for two-dimensional problems for both isotropic and aeolotropic bodies, and shell theory. Additional topics include three-dimensional problems for isotropic and transversely isotropic bodies.