Finite element implementation:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Blackwell Science
1996
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 362 S. graph. Darst. |
| ISBN: | 063203937X |
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MARC
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| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Blackwell Science |c 1996 | |
| 300 | |a XVII, 362 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | IMAGE 1
FINITE
ELEMENT IMPLEMENTATION
Y. K. CHEUNG S. H. LO A. Y. T. LEUNG THE UNIVERSITY OF HONG KONG
B
BLACKWELL SCIENCE
IMAGE 2
CONTENTS
PREFACE XI
FACILE PROGRAM DISKS XIII
NOTATION XV
PART I
1 INTRODUCTION 1
1.1 THE FINITE ELEMENT METHOD 1
1.2 BRIEF HISTORICAL BACKGROUND 2
1.3 SCOPE OF APPLICATIONS AND IMPORTANT CHARACTERISTICS 2
1.4 FINITE ELEMENT PROCEDURE 4
1.5 FINITE ELEMENT DISCRETIZATION 4
1.6 DISPLACEMENT FUNCTIONS 6
1.7 A SIMPLE EXAMPLE 8
1.8 ENERGY APPROACH 10
1.9 A BRIEF REVIEW OF THE CHAPTERS 12
1.10 INDICIAL NOTATION 13
1.11 REFERENCES TO CHAPTER 1 18
2 TWO-DIMENSIONAL AND AXISYMMETRIC PROBLEMS 21
2.1 INTRODUCTION 21
2.2 PLANE STRESS AND PLANE STRAIN 22
2.2.1 LINEAR ELASTICITY 22
2.2.2 ELEMENT STIFFHESS MATRIX AND ELEMENT FORCE VECTORS 23
2.2.3 6-NODE ISOPARAMETRIC TRIANGULAER ELEMENT T6 26
2.2.4 6-NODE SUBPARAMETRIC TRIANGULAER ELEMENT 27
2.2.5 8-NODE ISOPARAMETRIC QUADRILATERAL ELEMENT Q8 30
2.2.6 8-NODE RECTANGULAR ELEMENT 31
2.2.7 NUMERICAL INTEGRATION FOR ISOPARAMETRIC T6 AND Q8 ELEMENTS 32
2.2.8 EXAMPLES 35
2.3 AXISYMMETRIC STRESS ANALYSIS 40
2.3.1 TRANSVERSELY ISOTROPIC MATERIAL 40
2.3.2 ELEMENT STIFFNESS MATRIX 42
2.3.3 ELEMENT NODAL FORCE VECTORS 43
2.3.4 EVALUATION OF ELEMENT STRESSES 44
2.3.5 EXAMPLES 44
IMAGE 3
CONTENTS
2.4 STEADY-STATE FIELD PROBLEMS (2D) 2.4.1 ELEMENT STIFFNESS MATRIX AND
ELEMENT FORCE VECTORS 2.4.2 6-NODE SUBPARAMETRIC TRIANGULAER ELEMENT
2.4.3 8-NODE SUBPARAMETRIC RECTANGULAR ELEMENT 2.4.4 NUMERICAL
INTEGRATION FOR T6 AND Q8 ELEMENTS 2.4.5 EXAMPLES 2.5 INFINITE DOMAIN
AND INFINITE ELEMENT
2.5.1 EXAMPLE 2.6 REFERENCES TO CHAPTER 2
3 THREE-DIMENSIONAL PROBLEMS 3.1 INTRODUCTION 3.2 THREE-DIMENSIONAL
ISOPARAMETRIC ELEMENTS 3.2.1 10-NODE ISOPARAMETRIC TETRAHEDRON ELEMENT
T10
3.2.2 20-NODE ISOPARAMETRIC HEXAHEDRON ELEMENT H20 3.2.3 15-NODE
ISOPARAMETRIC PENTAHEDRON ELEMENT P15 3.3 NUMERICAL INTEGRATION IN THREE
DIMENSIONS 3.3.1 TRANSFORMATION OF DIFFERENTIAL OPERATOR (3D)
3.3.2 TRANSFORMATION OF INTEGRAL (3D) 3.3.3 NUMERICAL INTEGRATION (3D)
3.3.4 SURFACE INTEGRAL (3D)
3.3.5 ELEMENT NODAL FORCES DUE TO A PRESSURE LOAD 3.4 STEADY-STATE FIELD
PROBLEMS 3.4.1 THE GENERAL QUASI-HARMONIC EQUATION
3.4.2 WEAK FORM OF GENERAL QUASI-HARMONIC EQUATION 3.4.3 GALERKIN
FORMULATION 3.4.4 FINITE ELEMENT DISCRETIZATION 3.4.5 CONDUCTIVITY
MATRIX K 3.4.6 ELEMENT STIFFNESS MATRIX AND ELEMENT FORCE VECTORS 3.4.7
EXAMPLES 3.5 THREE-DIMENSIONAL ELASTICITY PROBLEMS
3.5.1 PRINCIPLE OF VIRTUAL WORK 3.5.2 GALERKIN FORMULATION 3.5.3 LINEAR
ELASTICITY 3.5.4 STIFFNESS MATRIX, DISPLACEMENT VECTOR AND FORCE VECTORS
3.5.5 ELEMENT STIFFNESS MATRIX AND ELEMENT FORCE VECTORS 3.5.6 ISOTROPIE
MATERIAL 3.5.7 EXAMPLES 3.6 REFERENCES TO CHAPTER 3
4 PLATE AND SHELL ELEMENTS 4.1 INTRODUCTION TO PLATE ELEMENTS 4.2
REISSNER-MINDLIN PLATE ELEMENT 4.2.1 THEORY
4.2.2 STRAIN-DISPLACEMENT RELATIONSHIP 4.2.3 CONSTITUTIVE EQUATION 4.2.4
VIRTUAL WORK EQUATION 4.2.5 FINITE ELEMENT STIFFNESS MATRIX AND LOAD
VECTOR
IMAGE 4
CONTENTS VUE
4.2.6 ISOTROPIE PLATE 97
4.2.7 CONVERGENCE CRITERION FOR REISSNER-MINDLIN PLATE ELEMENT 98 4.2.8
BOUNDARY CONDITIONS 98
4.2.9 SHEAR LOCKING 99
4.2.10 UNIFORM/SELECTIVE REDUCED INTEGRATION 100
4.2.11 EQUIVALENCE OF REDUCED INTEGRATION AND MIXED 101
FORMULATION
4.2.12 RANK DEFICIENCY 101
4.3 SIMPLE PLATE BENDING ELEMENTS WITH STRAIGHT EDGES 101
4.3.1 A CORRECT RANK 4-NODE QUADRILATERAL ELEMENT, SSI 101
4.3.2 THE LINEAR TRIANGULAER ELEMENT, T 103
4.3.3 THE DISCRETE KIRCHHOFF APPROACH 103
4.4 SOME DISCUSSION ON PLATE BENDING ELEMENTS 105
4.5 PLATE BENDING ELEMENT L9P 106
4.6 INTRODUCTION TO SHELL ELEMENTS 109
4.7 A DEGENERATED SHELL ELEMENT 109
4.7.1 GEOMETRICAL DEFINITION OF THE ELEMENT 109
4.7.2 LAMINAR COORDINATE SYSTEM 110
4.7.3 FIBRE COORDINATE SYSTEM 111
4.7.4 DISPLACEMENT FIELD 112
4.7.5 CONSTITUTIVE EQUATION 112
4.7.6 STRAIN-DISPLACEMENT RELATIONSHIP 114
4.7.7 ELEMENT STIFFNESS MATRIX 115
4.7.8 ELEMENT FORCE VECTORS 116
4.7.9 FIBRE NUMERICAL INTEGRATION 118
4.7.10 STRESS RESULTANTS 118
4.7.11 CURVED SHELL ELEMENTS 119
4.8 A SHELL AS AN ASSEMBLY OF HAT ELEMENTS 120
4.9 DEGENERATED SHELL ELEMENT L9S 122
4.10 REFERENCES TO CHAPTER 4 123
PARTII
SUBSTRUCTURES, SYMMETRY AND PERIODICITY 129
5.1 INTRODUCTION 129
5.2 SUBSTRUCTURING 129
5.3 SYMMETRY 133
5.4 PERIODIC STRUETURES 142
5.4.1 PERIODIC BOUNDARY CONDITIONS 142
5.4.2 GENERAL BOUNDARY CONDITIONS 143
5.4.3 SOLUTION PROCEDURE 148
5.4.4 APPLICATION TO METHOD OF SUBSTRUCTURING 150
5.5 NUMERICAL EXAMPLES 152
5.6 REFERENCES TO CHAPTER 5 155
THE TWO LEVEL FINITE ELEMENT METHOD 157
6.1 INTRODUCTION 157
6.2 BUILDING FRAMES 159
IMAGE 5
VUE1 CONTENTS
6.2.1 LOCAL DISTRIBUTION FACTORS 6.2.2 GLOBAL DISTRIBUTION FACTORS 6.2.3
MIXING FACTORS 6.2.4 COMPUTATIONAL ASPECTS 6.2.5 NUMERICAL EXAMPLES 6.3
PLATE SUBJECT TO CONCENTRATED LOADS
6.3.1 FORMULATION 6.3.2 GLOBAL INTERPOLATING FUNCTIONS 6.3.3
TRANSFORMATION 6.3.4 STRESS EVALUATION 6.3.5 NUMERICAL EXAMPLES 6.4 2D
CRACK PROBLEMS
6.4.1 FORMULATION 6.4.2 GLOBAL INTERPOLATING FUNCTIONS 6.4.3
TRANSFORMATION 6.4.4 EVALUATION OF STRESS INTENSITY FACTOR 6.4.5
NUMERICAL EXAMPLES 6.5 LAMINATED THICK RECTANGULAR PLATES
6.5.1 GLOBAL FUNCTIONS 6.5.2 NUMERICAL EXAMPLES: STATIC ANALYSIS 6.5.3
NUMERICAL EXAMPLES: VIBRATION AND BUCKLING ANALYSIS 6.5.4 CONCLUSIONS
6.6 REFERENCES TO CHAPTER 6
FINITE ELEMENT MESH GENERATION 7.1 INTRODUCTION 7.2 MESH GENERATION ON
PLANAR DOMAINS 7.2.1 INTRODUCTION
7.2.2 COORDINATE TRANSFORMATION 7.2.3 AUTOMATIC MESH GENERATION FOR
ARBITRARY PLANAR DOMAINS 7.2.4 GENERATION OF QUADRILATERAL ELEMENTS 7.3
MESH GENERATION OVER CURVED SURFACES
7.3.1 INTRODUCTION 7.3.2 TRANSFORMATION OF DEVELOPABLE SURFACES 7.3.3
SURFACE OF REVOLUTION 7.3.4 SPHERICAL SURFACE 7.3.5 ARBITRARY SURFACES
7.3.6 TRIANGULATION OF ARBITRARY CURVED SURFACES 7.3.7 EXAMPLES
7.3.8 DISCUSSIONS ON MESH GENERATION OVER SURFACES 7.4 MESH GENERATION
FOR VOLUMES (3D) 7.4.1 INTRODUCTION 7.4.2 THE EXISTING METHODS
7.4.3 3D DELAUNAY TRIANGULATION 7.4.4 3D TRIANGULATION BASED ON THE
ADVANCING FRONT TECHNIQUE 7.5 REFERENCES TO CHAPTER 7
IMAGE 6
CONTENTS
IX
PART III
IMPLEMENTATION 265
8.1 INTRODUCTION 265
8.2 OPTIMIZATION OF MATRIX PROFILE 267
8.2.1 INTRODUCTION 267
8.2.2 NODE RENUMBERING PROGRAM RENUM 268
8.2.3 EXAMPLE 270
8.3 SOLUTION OF A SYSTEM OF LINEAR EQUATIONS 276
8.3.1 INTRODUCTION 276
8.3.2 MATRIX DECOMPOSITION 277
8.3.3 SKYLINE STORAGE SCHEME AND COLUMN REDUCTION 280
8.3.4 USING OUT-OF-CORE MEMORY 282
8.3.5 PROGRAM FOR MATRIX DECOMPOSITION AND SOLUTION OF UNKNOWNS 284
8.4 ASSEMBLY OF SYSTEM STIFFNESS MATRIX 287
8.4.1 PROCEDURE OF THE ASSEMBLY PROCESS 288
8.4.2 AN EXAMPLE OF THE ASSEMBLY PROCESS 288
8.4.3 MATRIX ASSEMBLY INVOLVING OUT-OF-CORE STORAGE 290
8.5 BOUNDARY AND LOADING CONDITIONS 292
8.5.1 INTRODUCTION OF DISPLACEMENT BOUNDARY CONDITIONS 292
8.5.2 EXAMPLE: IMPOSING BOUNDARY CONDITIONS BY DIFFERENT METHODS 293
8.5.3 TRANSFORMATION OF VARIABLES 294
8.5.4 EXAMPLE: ROTATION OF A REFERENCE SYSTEM AT A NODE 294
8.5.5 LINEAR CONSTRAINTS BETWEEN VARIABLES 295
8.5.6 EXAMPLE: LINEAR CONSTRAINTS BETWEEN VARIABLES 296
8.5.7 INTRODUCTION OF SPECIFIED VALUES TO VARIABLES 296
8.5.8 FORMING THE SYSTEM RIGHT-HAND SIDE FORCE VECTOR 296
8.6 FINITE DEMENT PROGRAM FACILE 297
8.6.1 INTRODUCTION 297
8.6.2 TYPES OF PROBLEMS AND FINITE ELEMENTS SUPPORTED BY FACILE 298
8.6.3 PROGRAM STRUCTURE OF FACILE 298
8.6.4 VARIABLES USED IN FACILE 301
8.6.5 INPUT DATA FOR PROGRAM FACILE 304
8.6.6 SAMPLE RUNS 307
8.6.7 PROGRAM LISTING 318
8.7 REFERENCES TO CHAPTER 8 358
INDEX 359
|
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| physical | XVII, 362 S. graph. Darst. |
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| spelling | Cheung, Yau K. Verfasser aut Finite element implementation Y. K. Cheung ; S. H. Lo ; A. Y. T. Leung 1. publ. Oxford [u.a.] Blackwell Science 1996 XVII, 362 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Elementos e diferencas finitos larpcal Finite element method Implementierung Informatik (DE-588)4026663-1 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Implementierung Informatik (DE-588)4026663-1 s Lo, S. H. Verfasser aut Leung, Andrew Y. T. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009110836&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cheung, Yau K. Lo, S. H. Leung, Andrew Y. T. Finite element implementation Elementos e diferencas finitos larpcal Finite element method Implementierung Informatik (DE-588)4026663-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4026663-1 (DE-588)4017233-8 |
| title | Finite element implementation |
| title_auth | Finite element implementation |
| title_exact_search | Finite element implementation |
| title_full | Finite element implementation Y. K. Cheung ; S. H. Lo ; A. Y. T. Leung |
| title_fullStr | Finite element implementation Y. K. Cheung ; S. H. Lo ; A. Y. T. Leung |
| title_full_unstemmed | Finite element implementation Y. K. Cheung ; S. H. Lo ; A. Y. T. Leung |
| title_short | Finite element implementation |
| title_sort | finite element implementation |
| topic | Elementos e diferencas finitos larpcal Finite element method Implementierung Informatik (DE-588)4026663-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Elementos e diferencas finitos Finite element method Implementierung Informatik Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009110836&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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