Holdings: The finite element method

The finite element method: a practical course

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Bibliographic Details
Main Authors:	Liu, Gui-Rong (Author), Quek, S. S. (Author)
Format:	Book
Language:	English
Published:	Amsterdam [u.a.] Elsevier u.a. 2014
Edition:	2. ed.
Subjects:	Finite element method Finite-Elemente-Methode
Online Access:	Inhaltsverzeichnis
Physical Description:	XXI, 433 Seiten Diagramme, Illustrationen
ISBN:	9780080983561 0080983561

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adam_text	Contents Biography ............................................................................................................................................. vii Preface to the First Edition ................................................................................................................xvii CHAPTER 1 Computational Modeling ..............................................................1 1.1 Introduction ..................................................................................................................1 1.2 Physical Problems in Engineering ................................................................................4 1.3 Computational Modeling Using FEM ..........................................................................4 1.3.1 Modeling of the Geometry .................................................................................5 1.3.2 Meshing .............................................................................................................6 1.3.3 Material or Medium Properties ..........................................................................8 1.3.4 Boundary, Initial, and Loading Conditions ........................................................8 1.4 Solution Procedure .......................................................................................................8 1.4.1 Discrete System Equations ................................................................................8 1.4.2 Equation Sol vers ................................................................................................9 1.5 Results Visualization ..................................................................................................10 CHAPTER 2 Briefing on Mechanics for Solids and Structures .........................13 2.1 Introduction ................................................................................................................14 2.2 Equations for Three-Dimensional Solids ...................................................................16 2.2.1 Stress and Strain ...............................................................................................16 2.2.2 Constitutive Equations .....................................................................................18 2.2.3 Dynamic Equilibrium Equations .....................................................................19 2.2.4 Boundary Conditions .......................................................................................21 2.3 Equations for Two-Dimensional Solids .....................................................................22 2.3.1 Stress and Strain ...............................................................................................22 2.3.2 Constitutive Equations .....................................................................................24 2.3.3 Dynamic Equilibrium Equations .....................................................................25 2.4 Equations for Truss Members ....................................................................................26 2.4.1 Stress and Strain ...............................................................................................27 2.4.2 Constitutive Equations .....................................................................................27 2.4.3 Dynamic Equilibrium Equations .....................................................................27 2.5 Equations for Beams ..................................................................................................30 2.5.1 Stress and Strain ...............................................................................................30 2.5.2 Constitutive Equations .....................................................................................31 2.5.3 Moments and Shear Forces ..............................................................................31 2.5.4 Dynamic Equilibrium Equations .....................................................................33 IX Contents 2.6 Equations for Plates ...................................................................................................34 2.6.1 Stress and Strain ...............................................................................................35 2.6.2 Constitutive Equations .....................................................................................36 2.6.3 Moments and Shear Forces ..............................................................................36 2.6.4 Dynamic Equilibrium Equations .....................................................................38 2.6.5 Reissner-Mindlin Plate ....................................................................................38 2.7 Remarks .....................................................................................................................40 2.8 Review Questions ......................................................................................................40 CHAPTER 3 Fundamentals for Finite Element Method .....................................43 3.1 Introduction ................................................................................................................44 3.2 Strong and Weak Forms: Problem Formulation ........................................................44 3.3 Hamilton s Principle: A Weak Formulation ...............................................................45 3.3.1 Hamilton s Principle ........................................................................................45 3.3.2 Minimum Total Potential Energy Principle .....................................................47 3.4 FEM Procedure ..........................................................................................................47 3.4.1 Domain Discretization .....................................................................................47 3.4.2 Displacement Interpolation ..............................................................................49 3.4.3 Standard Procedure for Constructing Shape Functions ...................................50 3.4.4 Properties of the Shape Functions ...................................................................54 3.4.5 Formulation of Finite Element Equations in Local Coordinate System ..........63 3.4.6 Coordinate Transformation ..............................................................................67 3.4.7 Assembly of Global FE Equation ....................................................................68 3.4.8 Imposition of Displacement Constraints ..........................................................69 3.4.9 Solving the Global FE Equation ......................................................................69 3.5 Static Analysis ...........................................................................................................69 3.6 Analysis of Free Vibration (Eigenvalue Analysis) .....................................................69 3.7 Transient Response ....................................................................................................71 3.7.1 Central Difference Algorithm ..........................................................................72 3.7.2 Newmark s Method (Newmark, 1959)............................................................75 3.8 Remarks .....................................................................................................................76 3.8.1 Summary of Shape Function Properties ..........................................................76 3.8.2 Sufficient Requirements for FEM Shape Functions ........................................76 3.8.3 Recap of FEM Procedure .................................................................................77 3.9 Review Questions ......................................................................................................78 CHAPTER 4 FEM for Trusses .........................................................................81 4.1 Introduction ................................................................................................................81 4.2 FEM Equations ..........................................................................................................82 4.2.1 Shape Function Construction ...........................................................................82 Contents xi 4.2.2 Strain Matrix....................................................................................................85 4.2.3 Element Matrices in the Local Coordinate System .........................................86 4.2.4 Element Matrices in the Global Coordinate System ........................................87 4.2.5 Boundary Conditions .......................................................................................91 4.2.6 Recovering Stress and Strain ...........................................................................92 4.3 Worked Examples ......................................................................................................92 4.3.1 Properties of the FEM ......................................................................................94 4.4 High Order One-Dimensional Elements ..................................................................103 4.5 Review Questions ....................................................................................................105 CHAPTER 5 FEM for Beams ........................................................................111 5.1 Introduction .............................................................................................................. Ill 5.2 FEM Equations ........................................................................................................112 5.2.1 Shape Function Construction .........................................................................112 5.2.2 Strain Matrix ..................................................................................................115 5.2.3 Element Matrices ...........................................................................................116 5.3 Remarks ...................................................................................................................118 5.4 Worked Examples ....................................................................................................118 5.5 Case Study: Resonant Frequencies of Micro-Resonant Transducer ........................122 5.5.1 Modeling ........................................................................................................123 5.5.2 ABAQUS Input File .......................................................................................124 5.5.3 Solution Process .............................................................................................127 5.5.4 Results and Discussion ..................................................................................128 5.5.5 Comparison with ANSYS ..............................................................................130 5.6 Review Questions ....................................................................................................132 CHAPTER 6 FEM for Frames .......................................................................135 6.1 Introduction ..............................................................................................................135 6.2 FEM Equations for Planar Frames ..........................................................................137 6.2.1 The Idea of Superposition ..............................................................................137 6.2.2 Equations in the Local Coordinate System ....................................................137 6.2.3 Equations in the Global Coordinate System ..................................................140 6.3 FEM Equations for Space Frames ...........................................................................142 6.3.1 Equations in the Local Coordinate System ....................................................142 6.3.2 Equations in the Global Coordinate System ..................................................144 6.4 Remarks ...................................................................................................................149 6.5 Case Study: Finite Element Analysis of a Bicycle Frame .......................................150 6.5.1 Modeling ........................................................................................................151 6.5.2 ABAQUS Input File .......................................................................................152 6.5.3 Solution Processes .........................................................................................154 xii Contents 6.5.4 Results and Discussion ..................................................................................155 6.6 Review Questions ....................................................................................................157 CHAPTER 7 FEM for Two-Dimensional Solids ...............................................161 7.1 Introduction ..............................................................................................................162 7.2 Linear Triangular Elements .....................................................................................164 7.2.1 Field Variable Interpolation ...........................................................................164 7.2.2 Shape Function Construction .........................................................................166 7.2.3 Area Coordinates ............................................................................................170 7.2.4 Strain Matrix ..................................................................................................172 7.2.5 Element Matrices ...........................................................................................174 7.3 Linear Rectangular Elements ...................................................................................176 7.3.1 Shape Function Construction .........................................................................176 7.3.2 Strain Matrix ..................................................................................................179 7.3.3 Element Matrices ...........................................................................................179 7.3.4 Gauss Integration ...........................................................................................180 7.4 Linear Quadrilateral Elements .................................................................................183 7.4.1 Coordinate Mapping ......................................................................................183 7.4.2 Strain Matrix ..................................................................................................186 7.4.3 Element Matrices ...........................................................................................187 7.4.4 Remarks .........................................................................................................188 7.5 Elements for Axisymmetric Structures ....................................................................188 7.6 Higher Order Elements — Triangular Element Family .............................................191 7.6.1 General Formulation of Shape Functions ......................................................191 7.6.2 Quadratic Triangular Elements ......................................................................193 7.6.3 Cubic Triangular Elements ............................................................................194 7.7 Rectangular Elements ..............................................................................................195 7.7.1 Lagrange Type Elements ................................................................................195 7.7.2 Serendipity Type Elements ............................................................................196 7.8 Elements with Curved Edges ...................................................................................200 7.9 Comments on Gauss Integration ..............................................................................201 7.10 Case Study: Side Drive Micro-Motor ......................................................................201 7.10.1 Modeling ......................................................................................................203 7.10.2 ABAQUS Input File .....................................................................................204 7.10.3 Solution Process ..........................................................................................207 7.10.4 Results and Discussion ................................................................................208 7.11 Review Questions ....................................................................................................211 CHAPTER 8 FEM for Plates and Shells ........................................................219 8.1 Introduction ..............................................................................................................219 8.2 Plate Elements .........................................................................................................220 Contents xiii 8.2.1 Shape Functions .............................................................................................224 8.2.2 Element Matrices ...........................................................................................225 8.2.3 Higher Order Elements ..................................................................................227 8.3 Shell Elements .........................................................................................................227 8.3.1 The Idea of Superposition ..............................................................................228 8.3.2 Elements in the Local Coordinate System .....................................................228 8.3.3 Elements in the Global Coordinate System ...................................................232 8.4 Remarks ...................................................................................................................233 8.5 Case Study: Natural Frequencies of the Micro-Motor ............................................233 8.5.1 Modeling ........................................................................................................233 8.5.2 ABAQUS Input File .......................................................................................234 8.5.3 Solution Process .............................................................................................236 8.5.4 Results and Discussion ..................................................................................237 8.6 Case Study: Transient Analysis of a Micro-Motor ..................................................240 8.6.1 Modeling ........................................................................................................241 8.6.2 ABAQUS Input File .......................................................................................242 8.6.3 Solution Process .............................................................................................244 8.6.4 Results and Discussion ..................................................................................245 8.7 Review Questions ....................................................................................................247 CHAPTER 9 FEM for 3D Solid Elements .......................................................249 9.1 Introduction ..............................................................................................................249 9.2 Tetrahedron Element ................................................................................................250 9.2.1 Strain Matrix ..................................................................................................250 9.2.2 Element Matrices ...........................................................................................256 9.3 Hexahedron Element ................................................................................................261 9.3.1 Strain Matrix ..................................................................................................261 9.3.2 Element Matrices ...........................................................................................266 9.3.3 Using Tetrahedrons to form Hexahedrons .....................................................269 9.4 Higher Order Elements ............................................................................................269 9.4.1 Tetrahedron Elements ....................................................................................269 9.4.2 Brick Elements ...............................................................................................272 9.5 Elements with Curved Surfaces ...............................................................................277 9.6 Case Study: Stress and Strain Analysis of a Quantum Dot Heterostructure .................................................................................................277 9.6.1 Modeling ........................................................................................................279 9.6.2 ABAQUS Input File .......................................................................................282 9.6.3 Solution Process .............................................................................................284 9.6.4 Results and Discussion ..................................................................................285 9.7 Review Questions ....................................................................................................286 xiv Contents CHAPTER 10 Special Purpose Elements........................................................289 10.1 Introduction ..............................................................................................................289 10.2 Crack Tip Elements..................................................................................................289 10.3 Methods for Infinite Domains ..................................................................................293 10.3.1 Infinite Elements Formulated by Mapping ..................................................294 10.3.2 Gradual Damping Elements .........................................................................297 10.3.3 Coupling of FEM and the Boundary Element Method ................................297 Î0.3.4 Coupling of FEM and the Strip Element Method ........................................298 10.4 Finite Strip Elements ...............................................................................................298 10.5 Strip Element Method ..............................................................................................298 10.6 Meshfree Methods ...................................................................................................299 10.7 S-FEM ......................................................................................................................299 CHAPTER 11 Modeling Techniques ...............................................................301 11.1 Introduction ..............................................................................................................302 11.2 CPU Time Estimation ..............................................................................................303 11.3 Geometry Modeling .................................................................................................304 11.4 Meshing ...................................................................................................................306 11.4.1 Mesh Density ...............................................................................................306 11.4.2 Element Distortion .......................................................................................307 11.5 Mesh Compatibility .................................................................................................310 11.5.1 Different Order of Elements ........................................................................310 11.5.2 Straddling Elements .....................................................................................312 11.6 Use of Symmetry .....................................................................................................313 11.6.1 Mirror Symmetry or Plane Symmetry .........................................................314 11.6.2 Axial Symmetry ...........................................................................................318 11.6.3 Cyclic Symmetry .........................................................................................321 11.6.4 Repetitive Symmetry ...................................................................................322 11.7 Modeling of Offsets .................................................................................................322 11.7.1 Methods for Modeling Offsets .....................................................................322 11.7.2 Creation of MPC Equations for Offsets .......................................................325 11.8 Modeling of Supports ..............................................................................................328 11.9 Modeling of Joints ...................................................................................................328 11.10 Other Applications of MPC Equations ....................................................................332 11.10.1 Modeling of Symmetric Boundary Conditions .........................................332 11.10.2 Enforcement of Mesh Compatibility .........................................................334 11.10.3 Modeling of Constraints by Rigid Body Attachment ................................335 11.11 implementation of MPC Equations .........................................................................336 11.11.1 Lagrange Multiplier Method .....................................................................338 Contents xv 11.11.2 Penalty Method.......................................................................................... 338 11.12 Review Questions ....................................................................................................339 CHAPTER 12 FEM for Heat Transfer Problems ...............................................347 12.1 Field Problems .........................................................................................................348 12. 12. 12. 12. 12. 12. 12. .1 Heat Transfer in a Two-Dimensional Fin ....................................................348 .2 Heat Transfer in a Long Two-Dimensional Body ........................................349 .3 Heat Transfer in a One-Dimensional Fin .....................................................350 .4 Heat Transfer Across a Composite Wall ......................................................351 .5 Torsionai Deformation of a Bar ...................................................................352 .6 Ideal Irrotational Fluid Flow........................................................................ 353 1.7 Acoustic Problems .......................................................................................353 12.2 Weighted Residual Approach for FEM ....................................................................354 12.3 ID Heat Transfer Problem .......................................................................................355 12.3.1 One-Dimensional Fin ..................................................................................355 12.3.2 Direct Assembly Procedure .........................................................................361 12.3.3 Worked Example ..........................................................................................362 12.3.4 Remarks .......................................................................................................364 12.3.5 Composite Wall ............................................................................................365 12.3.6 Worked Example ..........................................................................................366 12.4 2D Heat Transfer Problem .......................................................................................370 12.4.1 Element Equations .......................................................................................370 12.4.2 Triangular Elements .....................................................................................373 12.4.3 Rectangular Elements ..................................................................................375 12.4.4 Boundary Conditions and Vector bw ...........................................................377 12.4.5 Point Heat Source or Sink ...........................................................................384 12.5 Summary ..................................................................................................................386 12.6 Case Study: Temperature Distribution of Heated Road Surface .............................386 12.6.1 Modeling ......................................................................................................387 12.6.2 ABAQUS Input File .....................................................................................388 12.6.3 Results and Discussion ................................................................................390 12.7 Review Questions ....................................................................................................390 CHAPTER 13 Using FEM Software Packages .................................................397 13.1 Introduction ..............................................................................................................397 13.2 Basic Building Block: Keywords and Data Lines ...................................................399 13.3 Using Sets ................................................................................................................400 13.4 ABAQUS Input Syntax Rules ..................................................................................401 13.4.1 Keyword Lines .............................................................................................401 xvi Contents 13.4.2 Data Lines ....................................................................................................401 13.4.3 Lables ...........................................................................................................402 13.5 Defining a Finite Element Model in ABAQUS ........................................................402 13.5.1 Model Data ..................................................................................................403 13.5.2 History Data .................................................................................................404 13.5.3 An Example of a Cantilever Beam Problem ................................................405 13.6 General Procedures ..................................................................................................411 13.7 Remarks (Example Using a GUI: ANSYS) .............................................................414 References ...................................................................................................423 Index ............................................................................................................425
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spelling	Liu, Gui-Rong Verfasser (DE-588)1056146923 aut The finite element method a practical course G.R. Liu ; S.S. Quek 2. ed. Amsterdam [u.a.] Elsevier u.a. 2014 XXI, 433 Seiten Diagramme, Illustrationen txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (pages 423-424) and index Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Quek, S. S. Verfasser (DE-588)1117713903 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026880794&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Liu, Gui-Rong Quek, S. S. The finite element method a practical course Includes bibliographical references (pages 423-424) and index Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd
subject_GND	(DE-588)4017233-8
title	The finite element method a practical course
title_auth	The finite element method a practical course
title_exact_search	The finite element method a practical course
title_full	The finite element method a practical course G.R. Liu ; S.S. Quek
title_fullStr	The finite element method a practical course G.R. Liu ; S.S. Quek
title_full_unstemmed	The finite element method a practical course G.R. Liu ; S.S. Quek
title_short	The finite element method
title_sort	the finite element method a practical course
title_sub	a practical course
topic	Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd
topic_facet	Finite element method Finite-Elemente-Methode
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026880794&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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