The Scaled Boundary Finite Element Method
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The Scaled Boundary Finite Element Method
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Author : John P. Wolf
language : en
Publisher: John Wiley & Sons
Release Date : 2003-03-14
The Scaled Boundary Finite Element Method written by John P. Wolf and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-14 with Technology & Engineering categories.
A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.
The Scaled Boundary Finite Element Method
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Author : Chongmin Song
language : en
Publisher: John Wiley & Sons
Release Date : 2018-09-04
The Scaled Boundary Finite Element Method written by Chongmin Song and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-04 with Science categories.
An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.
The Finite Element Method Theory Implementation And Applications
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Author : Mats G. Larson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-13
The Finite Element Method Theory Implementation And Applications written by Mats G. Larson 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 2013-01-13 with Computers categories.
This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Finite Element And Boundary Element Applications In Quantum Mechanics
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Author : L. Ramdas Ram-Mohan
language : en
Publisher: Oxford University Press, USA
Release Date : 2002
Finite Element And Boundary Element Applications In Quantum Mechanics written by L. Ramdas Ram-Mohan and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book introduces the finite element and boundary element methods (FEM and BEM) for applications to quantum mechanical systems. A discretization of the action integral with finite elements, followed by application of variational principles, brings a very general approach to the solution of Schroedinger's equation for physical systems in arbitrary geometries with complex mixed boundary conditions. The variational approach is a common thread through the book and is used for the improvement of solutions to spectroscopic accuracy, to adaptively improve finite element meshs, to develop a time-dependent theory, and also to generate the solution of large sparse matrix eigenvalue problems. A thorough introduction to BEM is given using the modelling of surface plasmons, quantum electron waveguides, and quantum scattering as illustrative examples. The book should be useful to graduate students and researchers in basic quantum theory, quantum semiconductor modeling, computational physics, mathematics and chemistry
The Finite Element Method
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Author : Bofang Zhu
language : en
Publisher: John Wiley & Sons
Release Date : 2018-06-13
The Finite Element Method written by Bofang Zhu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-13 with Mathematics categories.
A comprehensive review of the Finite Element Method (FEM), this book provides the fundamentals together with a wide range of applications in civil, mechanical and aeronautical engineering. It addresses both the theoretical and numerical implementation aspects of the FEM, providing examples in several important topics such as solid mechanics, fluid mechanics and heat transfer, appealing to a wide range of engineering disciplines. Written by a renowned author and academician with the Chinese Academy of Engineering, The Finite Element Method would appeal to researchers looking to understand how the fundamentals of the FEM can be applied in other disciplines. Researchers and graduate students studying hydraulic, mechanical and civil engineering will find it a practical reference text.
Finite Element Modelling Of Unbounded Media
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Author : John P. Wolf
language : en
Publisher:
Release Date : 1996-08-16
Finite Element Modelling Of Unbounded Media written by John P. Wolf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-16 with Mathematics categories.
Dynamic unbounded medium-structure interactions occur in many fields of engineering and physical science, such as wave propagation in soil-structure and fluid-structure interactions, acoustics and electromagnetism and as diffusion in heat conduction and consolidation. This book presents three novel concepts, based on the finite-element methodology, to model the unbounded medium: The consistent infinitesimal finite-element cell method, a boundary finite-element procedure, requires the discretization of the structure-medium interface only and is exact in the finite-element sense. It is applied to unbounded media governed by the hyperbolic, parabolic and elliptic differential equations. The damping-solvent extraction method permits the analysis of a bounded medium only. The doubly-asymptotic multi-directional transmitting boundary is exact for the low- and high-frequency limits at preselected wave propagation directions. All concepts are explained using simple examples that the reader can follow step by step. A computer program of the consistent infinitesimal finite-element cell method available on disk analyses two- and three-dimensional unbounded and bounded media for the scalar and vector wave equations and the diffusion equation in the frequency and time domains.
Solving Pdes In Python
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Author : Hans Petter Langtangen
language : en
Publisher: Springer
Release Date : 2017-03-21
Solving Pdes In Python written by Hans Petter Langtangen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-21 with Computers categories.
This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.
The Finite Element Method For Three Dimensional Thermomechanical Applications
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Author : Guido Dhondt
language : en
Publisher: John Wiley & Sons
Release Date : 2004
The Finite Element Method For Three Dimensional Thermomechanical Applications written by Guido Dhondt and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
1. Displacements, strain, stress and energy -- 2. Linear mechanical applications -- 3. Geometric nonlinear effects -- 4. Hyperelastic materials -- 5. Infinitesimal strain plasticity -- 6. Finite strain elastoplasticity -- 7. Heat transfer.
The Scaled Boundary Finite Element Method
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Author : Chongmin Song
language : en
Publisher: John Wiley & Sons
Release Date : 2018-06-19
The Scaled Boundary Finite Element Method written by Chongmin Song and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-19 with Science categories.
An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.