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Boundary element method fundamentals and applications
1040
Book reviews
The mathematical background for the asymptotic methods is given in chapter one and then in the succeeding chapters applied to determine effective properties of stiffness, of thermal expansion and to some extent of strength. These homogenized models are given special attention in relation to frames (beams), plates and shells. For these models also analytical results are listed. Readers with a traditional (although mathematically oriented) engineering background will have difficulties in following especially the development in the first chapter. It is striking that many important books on composites (authors as Jones, Tsai, Hahn) are not referenced and used in an effort to bridge the gap. Also it should be commented that the most important tool for calculating effective properties, i.e. the finite element method is not given any priority. However, much knowledge from extensive studies is contained in this book. Pauli Pedersen Lyngby Denmark
lr~bration of Discrete and Continuous Systems, by A.A. Shabana (Springer, Berlin, 1996). It is a pleasure to read this book. Designed for a one-semester graduate course the book gives an overview about the basic methods nowadays used in the examination of vibration problems of rigid and elastic multibody systems. Starting from the single degree of freedom oscillator the author successively increases the complexity of the underlying dynamic systems in order to finally arrive at the Finite Element approach for vibrating systems. On this route one meets the classical Newton-Euler equations for 3-dimensionai motion with special emphasis on planar and one-dimensional motion as well as Lagrange's equations and Hamiltons principle. At least at this point the aim of the book becomes clear: it is not intended to derive everything in detail but to present the main ideas and methods of the mechanics of oscillating systems in a reasonable manner by teaching also the corresponding technical terms, and to quickly proceed towards approximation methods of continuous systems. In this sense, Lagrange's equations are derived from particle systems, Linear systems are considered as far as they permit a representation via constant matrices not containing gyroscopical terms or circular forces, and continuous systems are assumed not to have zero-order forces accompanied by second-order changes in the displacements. In the chapters on continuous systems, classical Euler-Bemoulli and Rayleigh beam theory as well as approximation techniques such as Rayleigh's, Ritz's, and Galerkin's methods are discussed. From this point, the step to the Finite Element Method is easy to do. After a clear introduction and a discussion of several element types the arrangement and the calculation of the stiffness and the mass matrix is presented. The book closes with a chapter on the numerical analysis of eigenvalue problems, especially similarity and Householder transformations, the QR-decomposition, and the Jacobi iteration method, followed by an appendix on vector and matrix calculus. The author succeeded in writing an attractive and very homogeneous book for graduate students which teaches within 400 pages how to deal with oscillating discrete and continuous systems. Nearly one third of the book is devoted to examples and exercises which makes it very easy to follow the clearly and speedily presented theory. Ch. Gloeker Miinchen Germany
Boundary Element Method Fundamentals and Applications, by F. Paris, J. Canas (Oxford Science Publications, Oxford, 1997, 416 pp.). This is a textbook on the boundary element method intended for advanced graduate students in the fields of civil, mechanical and material science engineering. It can be used as a textbook for a first introductory
Book reviews
I:~l
course in boundary elements as it emphasizes fundamentals of the method and its applications in potential theory and linear elastostatics. The book is close to 400 pages long and consists of seven main chapters, four appendices describing in detail some mathematical derivations and the standard Gauss quadrature as well as'a diskette containing computer programs in Fortran for analysing two-dimensional problems in potential theory and elastostatics. The first chapter describes the mathematical background necessary for ~ e subsequent developments. Concepts like the delta function or the singular integrals are clearly stated and explained from the engineering point of view. Chapter two describes the integral formulation of potential theory problems in detail for two- and three-dimensions. Chapter three deals with the discretization and Solution approach based on the boundary element method, while chapter four describes its computer implementation in the framework of the program BETIS contained in the diskette accompanying the book. The last two chapters are restricted to two-dimensional problems and constant and linear elements because of the introductory character of the book. Entirely analogous things are covered in the next three chapters pertaining to elastostatics. More specifically, chapter five deals with the integral formulation, chapter six with the discretization and solution procedure by boundary elements and chapter seven with the computer implementation of the method as applied to two-dimensional elastostatic problems (program SERBA employing linear elements). The book is very well written by two experienced engineers, the first of them being one of the leading figures in the field. It is characterized by the following two features: the first is that the book is seN-contained and one does not really need to consult other references; the second is that it provides detailed derivations, which can easily be followed by engineers, and presents theorems and difficult concepts clearly stating all the underlying assumptions and their range of applicability. The computer implementation chapters are also very well written. In conclusion, the authors have succeeded in writing an excellent introductory textbook on the boundary element method, primarily intended for advanced graduate students studying for their M.S. or Ph.D. degrees. D.E. Beskos Patras Greece
Nonlinear Finite Element Analysis of Solids and Structures, Volume 2: Advanced Topics, by M.A. Crisfield (John Wiley, Chichester; ISBN: 0-471-95649-X). With the present book, M.A. Crisfield continues the well-established first volume "Non-linear Finite Element Analysis of Solids and Structures, Volume 1: Essentials". Whereas in the first text book, the fundamentals of continuum mechanics, finite elements and non-linear solution procedures are discussed, the second volume focuses on more advanced topics like large strain elasticity and plasticity, modern shell theory, ~ontaet algorithms and dynamics. Adopting an engineering rather than a mathematical approach, the author emphasizes in particular the numerical implementation. :In Chapter 10, the continuum mechanical background for algorithms in finite elasticity and pl~isticity is provided. In the following chapter, in preparation of later chapters in the book, the use of non-orthogonal coordinates is discussed. Chapter 12 extends Chapter 5 of Volume 1 on finite, element analysis on continua. Expressions for the internal force vector and the tangent stiffness matrix are derived. The author uses the Lagrangian formulation as well as the "Eulerian" approach, employing the Truesdell and the Janmann rate form. Chapter 13 is devoted to hyperelasticity. Various concepts, using invariants or alternatively the principal stretches directly, are discussed in detail. In Chapter 14, the author continues Chapter 6 of Volume 1, here introducing pressure-sensitive yield criteria and yield functions with corners for small-strain plasticity. At the
Book reviews
The mathematical background for the asymptotic methods is given in chapter one and then in the succeeding chapters applied to determine effective properties of stiffness, of thermal expansion and to some extent of strength. These homogenized models are given special attention in relation to frames (beams), plates and shells. For these models also analytical results are listed. Readers with a traditional (although mathematically oriented) engineering background will have difficulties in following especially the development in the first chapter. It is striking that many important books on composites (authors as Jones, Tsai, Hahn) are not referenced and used in an effort to bridge the gap. Also it should be commented that the most important tool for calculating effective properties, i.e. the finite element method is not given any priority. However, much knowledge from extensive studies is contained in this book. Pauli Pedersen Lyngby Denmark
lr~bration of Discrete and Continuous Systems, by A.A. Shabana (Springer, Berlin, 1996). It is a pleasure to read this book. Designed for a one-semester graduate course the book gives an overview about the basic methods nowadays used in the examination of vibration problems of rigid and elastic multibody systems. Starting from the single degree of freedom oscillator the author successively increases the complexity of the underlying dynamic systems in order to finally arrive at the Finite Element approach for vibrating systems. On this route one meets the classical Newton-Euler equations for 3-dimensionai motion with special emphasis on planar and one-dimensional motion as well as Lagrange's equations and Hamiltons principle. At least at this point the aim of the book becomes clear: it is not intended to derive everything in detail but to present the main ideas and methods of the mechanics of oscillating systems in a reasonable manner by teaching also the corresponding technical terms, and to quickly proceed towards approximation methods of continuous systems. In this sense, Lagrange's equations are derived from particle systems, Linear systems are considered as far as they permit a representation via constant matrices not containing gyroscopical terms or circular forces, and continuous systems are assumed not to have zero-order forces accompanied by second-order changes in the displacements. In the chapters on continuous systems, classical Euler-Bemoulli and Rayleigh beam theory as well as approximation techniques such as Rayleigh's, Ritz's, and Galerkin's methods are discussed. From this point, the step to the Finite Element Method is easy to do. After a clear introduction and a discussion of several element types the arrangement and the calculation of the stiffness and the mass matrix is presented. The book closes with a chapter on the numerical analysis of eigenvalue problems, especially similarity and Householder transformations, the QR-decomposition, and the Jacobi iteration method, followed by an appendix on vector and matrix calculus. The author succeeded in writing an attractive and very homogeneous book for graduate students which teaches within 400 pages how to deal with oscillating discrete and continuous systems. Nearly one third of the book is devoted to examples and exercises which makes it very easy to follow the clearly and speedily presented theory. Ch. Gloeker Miinchen Germany
Boundary Element Method Fundamentals and Applications, by F. Paris, J. Canas (Oxford Science Publications, Oxford, 1997, 416 pp.). This is a textbook on the boundary element method intended for advanced graduate students in the fields of civil, mechanical and material science engineering. It can be used as a textbook for a first introductory
Book reviews
I:~l
course in boundary elements as it emphasizes fundamentals of the method and its applications in potential theory and linear elastostatics. The book is close to 400 pages long and consists of seven main chapters, four appendices describing in detail some mathematical derivations and the standard Gauss quadrature as well as'a diskette containing computer programs in Fortran for analysing two-dimensional problems in potential theory and elastostatics. The first chapter describes the mathematical background necessary for ~ e subsequent developments. Concepts like the delta function or the singular integrals are clearly stated and explained from the engineering point of view. Chapter two describes the integral formulation of potential theory problems in detail for two- and three-dimensions. Chapter three deals with the discretization and Solution approach based on the boundary element method, while chapter four describes its computer implementation in the framework of the program BETIS contained in the diskette accompanying the book. The last two chapters are restricted to two-dimensional problems and constant and linear elements because of the introductory character of the book. Entirely analogous things are covered in the next three chapters pertaining to elastostatics. More specifically, chapter five deals with the integral formulation, chapter six with the discretization and solution procedure by boundary elements and chapter seven with the computer implementation of the method as applied to two-dimensional elastostatic problems (program SERBA employing linear elements). The book is very well written by two experienced engineers, the first of them being one of the leading figures in the field. It is characterized by the following two features: the first is that the book is seN-contained and one does not really need to consult other references; the second is that it provides detailed derivations, which can easily be followed by engineers, and presents theorems and difficult concepts clearly stating all the underlying assumptions and their range of applicability. The computer implementation chapters are also very well written. In conclusion, the authors have succeeded in writing an excellent introductory textbook on the boundary element method, primarily intended for advanced graduate students studying for their M.S. or Ph.D. degrees. D.E. Beskos Patras Greece
Nonlinear Finite Element Analysis of Solids and Structures, Volume 2: Advanced Topics, by M.A. Crisfield (John Wiley, Chichester; ISBN: 0-471-95649-X). With the present book, M.A. Crisfield continues the well-established first volume "Non-linear Finite Element Analysis of Solids and Structures, Volume 1: Essentials". Whereas in the first text book, the fundamentals of continuum mechanics, finite elements and non-linear solution procedures are discussed, the second volume focuses on more advanced topics like large strain elasticity and plasticity, modern shell theory, ~ontaet algorithms and dynamics. Adopting an engineering rather than a mathematical approach, the author emphasizes in particular the numerical implementation. :In Chapter 10, the continuum mechanical background for algorithms in finite elasticity and pl~isticity is provided. In the following chapter, in preparation of later chapters in the book, the use of non-orthogonal coordinates is discussed. Chapter 12 extends Chapter 5 of Volume 1 on finite, element analysis on continua. Expressions for the internal force vector and the tangent stiffness matrix are derived. The author uses the Lagrangian formulation as well as the "Eulerian" approach, employing the Truesdell and the Janmann rate form. Chapter 13 is devoted to hyperelasticity. Various concepts, using invariants or alternatively the principal stretches directly, are discussed in detail. In Chapter 14, the author continues Chapter 6 of Volume 1, here introducing pressure-sensitive yield criteria and yield functions with corners for small-strain plasticity. At the