Programming the Finite Element Method (5th Edition)
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of this book, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new Fifth Edition offers ti...
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| Hlavní autoři: | , , |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Sussex
John Wiley & Sons
2013
Wiley John Wiley & Sons, Incorporated Wiley-Blackwell |
| Vydání: | 5 |
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| ISBN: | 1119973341, 9781119973348, 1118535928, 9781118535929, 9781118535912, 111853591X |
| On-line přístup: | Získat plný text |
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- Title Page Preface to Fifth Edition Table of Contents 1. Preliminaries: Computer Strategies 2. Spatial Discretisation by Finite Elements 3. Programming Finite Element Computations 4. Static Equilibrium of Structures 5. Static Equilibrium of Linear Elastic Solids 6. Material Non-Linearity 7. Steady State Flow 8. Transient Problems: First Order (Uncoupled) 9. Coupled Problems 10. Eigenvalue Problems 11. Forced Vibrations 12. Parallel Processing of Finite Element Analyses Appendices Author Index Subject Index
- 3.13.5 Explicit Methods and Other Storage-Saving Strategies -- References -- Chapter 4 Static Equilibrium of Structures -- 4.1 Introduction -- 4.2 Conclusions -- 4.3 Glossary of Variable Names -- 4.4 Exercises -- References -- Chapter 5 Static Equilibrium of Linear Elastic Solids -- 5.1 Introduction -- 5.2 Glossary of Variable Names -- 5.3 Exercises -- References -- Chapter 6 Material Non-linearity -- 6.1 Introduction -- 6.2 Stress-strain Behaviour -- 6.3 Stress Invariants -- 6.4 Failure Criteria -- 6.4.1 Von Mises -- 6.4.2 Mohr-Coulomb and Tresca -- 6.5 Generation of Body Loads -- 6.6 Viscoplasticity -- 6.7 Initial Stress -- 6.8 Corners on the Failure and Potential Surfaces -- 6.9 Elastoplastic Rate Integration -- 6.9.1 Forward Euler Method -- 6.9.2 Backward Euler Method -- 6.10 Tangent Stiffness Approaches -- 6.10.1 Inconsistent Tangent Matrix -- 6.10.2 Consistent Tangent Matrix -- 6.10.3 Convergence Criterion -- 6.11 The Geotechnical Processes of Embanking and Excavation -- 6.11.1 Embanking -- 6.11.2 Excavation -- 6.12 Undrained Analysis -- 6.13 Glossary of Variable Names -- 6.14 Exercises -- References -- Chapter 7 Steady State Flow -- 7.1 Introduction -- 7.2 Glossary of Variable Names -- 7.3 Exercises -- References -- Chapter 8 Transient Problems: First Order (Uncoupled) -- 8.1 Introduction -- 8.2 Comparison of Programs 8.4, 8.5, 8.6 and 8.7 -- 8.3 Glossary of Variable Names -- 8.4 Exercises -- References -- Chapter 9 Coupled Problems -- 9.1 Introduction -- 9.2 Glossary of Variable Names -- 9.3 Exercises -- References -- Chapter 10 Eigenvalue Problems -- 10.1 Introduction -- 10.2 Glossary of Variable Names -- 10.3 Exercises -- References -- Chapter 11 Forced Vibrations -- 11.1 Introduction -- 11.2 Glossary of Variable Names -- 11.3 Exercises -- References -- Chapter 12 Parallel Processing of Finite Element Analyses -- 12.1 Introduction
- 2.17.1 Steady State -- 2.17.2 Transient State -- 2.17.3 Convection -- 2.18 Further Coupled Equations: Biot Consolidation -- 2.19 Conclusions -- References -- Chapter 3 Programming Finite Element Computations -- 3.1 Introduction -- 3.2 Local Coordinates for Quadrilateral Elements -- 3.2.1 Numerical Integration for Quadrilaterals -- 3.2.2 Analytical Integration for Quadrilaterals -- 3.3 Local Coordinates for Triangular Elements -- 3.3.1 Numerical Integration for Triangles -- 3.3.2 Analytical Integration for Triangles -- 3.4 Multi-Element Assemblies -- 3.5 'Element-by-Element' Techniques -- 3.5.1 Conjugate Gradient Method for Linear Equation Systems -- 3.5.2 Preconditioning -- 3.5.3 Unsymmetric Systems -- 3.5.4 Symmetric Non-Positive Definite Equations -- 3.5.5 Eigenvalue Systems -- 3.6 Incorporation of Boundary Conditions -- 3.6.1 Convection Boundary Conditions -- 3.7 Programming using Building Blocks -- 3.7.1 Black Box Routines -- 3.7.2 Special Purpose Routines -- 3.7.3 Plane Elastic Analysis using Quadrilateral Elements -- 3.7.4 Plane Elastic Analysis using Triangular Elements -- 3.7.5 Axisymmetric Strain of Elastic Solids -- 3.7.6 Plane Steady Laminar Fluid Flow -- 3.7.7 Mass Matrix Formation -- 3.7.8 Higher-Order 2D Elements -- 3.7.9 Three-Dimensional Elements -- 3.7.10 Assembly of Elements -- 3.8 Solution of Equilibrium Equations -- 3.9 Evaluation of Eigenvalues and Eigenvectors -- 3.9.1 Jacobi Algorithm -- 3.9.2 Lanczos and Arnoldi Algorithms -- 3.10 Solution of First-Order Time-Dependent Problems -- 3.11 Solution of Coupled Navier-Stokes Problems -- 3.12 Solution of Coupled Transient Problems -- 3.12.1 Absolute Load Version -- 3.12.2 Incremental Load Version -- 3.13 Solution of Second-Order Time-Dependent Problems -- 3.13.1 Modal Superposition -- 3.13.2 Newmark or Crank-Nicolson Method -- 3.13.3 Wilson's Method -- 3.13.4 Complex Response
- 12.2 Differences between Parallel and Serial Programs -- 12.2.1 Parallel Libraries -- 12.2.2 Global Variables -- 12.2.3 MPI Library Routines -- 12.2.4 The _pp Appendage -- 12.2.5 Simple Test Problems -- 12.2.6 Reading and Writing -- 12.2.7 rest Instead of nf -- 12.2.8 Gathering and Scattering -- 12.2.9 Reindexing -- 12.2.10 Domain Composition -- 12.2.11 Third-party Mesh-partitioning Tools -- 12.2.12 Load Balancing -- 12.3 Graphics Processing Units -- 12.4 Cloud Computing -- 12.5 Conclusions -- 12.6 Glossary of Variable Names -- References -- Appendix A Equivalent Nodal Loads -- Appendix B Shape Functions and Element Node Numbering -- Appendix C Plastic Stress-Strain Matrices and Plastic Potential Derivatives -- Appendix D main Library Subprograms -- Appendix E geom Library Subroutines -- Appendix F Parallel Library Subroutines -- Appendix G External Subprograms -- Author Index -- Subject Index
- Cover -- Title Page -- Copyright -- Contents -- Preface to Fifth Edition -- Acknowledgements -- Chapter 1 Preliminaries: Computer Strategies -- 1.1 Introduction -- 1.2 Hardware -- 1.3 Memory Management -- 1.4 Vector Processors -- 1.5 Multi-core Processors -- 1.6 Co-processors -- 1.7 Parallel Processors -- 1.8 Applications Software -- 1.8.1 Compilers -- 1.8.2 Arithmetic -- 1.8.3 Conditions -- 1.8.4 Loops -- 1.9 Array Features -- 1.9.1 Dynamic Arrays -- 1.9.2 Broadcasting -- 1.9.3 Constructors -- 1.9.4 Vector Subscripts -- 1.9.5 Array Sections -- 1.9.6 Whole-array Manipulations -- 1.9.7 Intrinsic Procedures for Arrays -- 1.9.8 Modules -- 1.9.9 Subprogram Libraries -- 1.9.10 Structured Programming -- 1.10 Third-party Libraries -- 1.10.1 BLAS Libraries -- 1.10.2 Maths Libraries -- 1.10.3 User Subroutines -- 1.10.4 MPI Libraries -- 1.11 Visualisation -- 1.11.1 Starting ParaView -- 1.11.2 Display Restrained Nodes -- 1.11.3 Display Applied Loads -- 1.11.4 Display Deformed Mesh -- 1.12 Conclusions -- References -- Chapter 2 Spatial Discretisation by Finite Elements -- 2.1 Introduction -- 2.2 Rod Element -- 2.2.1 Rod Stiffness Matrix -- 2.2.2 Rod Mass Element -- 2.3 The Eigenvalue Equation -- 2.4 Beam Element -- 2.4.1 Beam Element Stiffness Matrix -- 2.4.2 Beam Element Mass Matrix -- 2.5 Beam with an Axial Force -- 2.6 Beam on an Elastic Foundation -- 2.7 General Remarks on the Discretisation Process -- 2.8 Alternative Derivation of Element Stiffness -- 2.9 Two-dimensional Elements: Plane Stress -- 2.10 Energy Approach and Plane Strain -- 2.10.1 Thermoelasticity -- 2.11 Plane Element Mass Matrix -- 2.12 Axisymmetric Stress and Strain -- 2.13 Three-dimensional Stress and Strain -- 2.14 Plate Bending Element -- 2.15 Summary of Element Equations for Solids -- 2.16 Flow of Fluids: Navier-Stokes Equations -- 2.17 Simplified Flow Equations