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The Scaled Boundary Finite Element Method

The Scaled Boundary Finite Element Method

Autorzy
Wydawnictwo John Wiley & Sons
Data wydania 01/08/2018
Wydanie Pierwsze
Liczba stron 504
Forma publikacji książka w twardej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
Język angielski
ISBN 9781119388159
Kategorie Analiza numeryczna, Inżynieria mechaniczna i materiałowa
532.14 PLN (z VAT)
$136.83 / €122.44 / £113.40 /
Produkt na zamówienie
Przesyłka w 3-4 tygodnie
Ilość
Do schowka

Opis książki

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 Scaled Boundary Finite Element Method

Spis treści

Preface xv


Acknowledgements xix


About the Companion Website xxi


1 Introduction 1


1.1 Numerical Modelling 1


1.2 Overview of the Scaled Boundary Finite Element Method 6


1.3 Features and Example Applications of the Scaled Boundary Finite Element Method 10


1.3.1 Linear Elastic Fracture Mechanics: Crack Terminating at Material Interface 11


1.3.2 Automatic Mesh Generation Based on Quadtree/Octree 13


1.3.3 Treatment of Non-matching Meshes 14


1.3.4 Crack Propagation 17


1.3.5 Adaptive Analysis 17


1.3.6 TransientWave Scattering in an Alluvial Basin 19


1.3.7 Automatic Image-based Analysis 19


1.3.7.1 Two-dimensional Elastoplastic Analysis of Cast Iron 20


1.3.7.2 Three-dimensional Concrete Specimen 22


1.3.8 Automatic Analysis of STL Models 24


1.4 Summary 26


Part I Basic Concepts and MATLAB Implementation of the Scaled Boundary Finite Element Method in Two Dimensions 27


2 Basic Formulations of the Scaled Boundary Finite Element Method 31


2.1 Introduction 31


2.2 Modelling of Geometry in Scaled Boundary Coordinates 31


2.2.1 S-domains: Scaling Requirement on Geometry, Scaling Centre and Scaling of Boundary 31


2.2.2 S-elements: Boundary Discretization of S-domains 37


2.2.3 Scaled Boundary Transformation 40


2.2.3.1 Scaled Boundary Coordinates 40


2.2.3.2 Coordinate Transformation of Partial Derivatives 42


2.2.3.3 Geometrical Properties in Scaled Boundary Coordinates 44


2.3 Governing Equations of Linear Elasticity in Scaled Boundary Coordinates 50


2.4 Semi-analytical Representation of Displacement and Strain Fields 51


2.5 Derivation of the Scaled Boundary Finite Element Equation by the Virtual Work Principle 53


2.5.1 Virtual Displacement and Strain Fields in Scaled Boundary Coordinates 54


2.5.2 Nodal Force Functions 54


2.5.3 The Scaled Boundary Finite Element Equation 55


2.6 Computer Program Platypus: Coefficient Matrices of an S-element 63


2.6.1 Element Coefficient Matrices of a 2-node Line Element 63


2.6.2 Assembly of Coefficient Matrices of an S-element 67


3 Solution of the Scaled Boundary Finite Element Equation by Eigenvalue Decomposition 73


3.1 Solution Procedure for the Scaled Boundary Finite Element Equations in Displacement 73


3.2 Pre-conditioning of Eigenvalue Problems 77


3.3 Computer Program Platypus: Solution of the Scaled Boundary Finite Element Equation of a Bounded S-element by the Eigenvalue Method 78


3.4 Assembly of S-elements and Solution of Global System of Equations 84


3.4.1 Assembly of S-elements 84


3.4.2 Surface Tractions 85


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