Finite elements using maple: a symbolic programming approach
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Engineering online library
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 325 S. graph. Darst. 1 CD-ROM |
| ISBN: | 3540429867 |
Staff View
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Record in the Search Index
| _version_ | 1804129024895614976 |
|---|---|
| adam_text | A. PORTELA * A. CHARAFI FINITE ELEMENTS USING MAPLE A SYMBOLIC
PROGRAMMING APPROACH SPRINGER CONTENTS 1. INTRODUCTION TO MAPLE 1 1.1
BASICS 1 1.2 ENTERING COMMANDS 1 1.3 FUNDAMENTAL DATA TYPES 3 1.4
MATHEMATICAL FUNCTIONS 3 1.5 NAMES 4 1.6 BASIC TYPES OF MAPLE OBJECTS 5
1.6.1 SEQUENCES 5 1.6.2 LISTS 6 1.6.3 SETS 6 1.6.4 ARRAYS 7 1.6.5 TABLES
7 1.6.6 STRINGS 8 1.7 EVALUATION RULES 8 1.7.1 LEVELS OF EVALUATION 8
1.7.2 LAST-NAME EVALUATION 9 1.7.3 ONE-LEVEL EVALUATION 9 1.7.4 SPECIAL
EVALUATION RULES 10 1.7.5 DELAYED EVALUATION 10 1.8 ALGEBRAIC EQUATIONS
11 1.9 DIFFERENTIATION AND INTEGRATION 12 1.10 SOLVING DIFFERENTIAL
EQUATIONS 14 1.11 EXPRESSION MANIPULATION 15 1.12 BASIC PROGRAMMING
CONSTRUCTS 16 1.13 FUNCTIONS, PROCEDURES AND MODULES 16 1.14 MAPLE S
ORGANIZATION 19 1.15 LINEAR ALGEBRA COMPUTATIONS 20 1.16 GRAPHICS 31
1.17 PLOTTER: PACKAGE FOR FINITE ELEMENT GRAPHICS 34 1.17.1 EXAMPLE 39
1.17.2 EXAMPLE 41 1.17.3 EXAMPLE 42 XII CONTENTS 2. COMPUTATIONAL
MECHANICS 45 2.1 INTRODUCTION 45 2.2 MATHEMATICAL MODELLING OF PHYSICAL
SYSTEMS 45 2.3 CONTINUOUS MODELS 47 2.3.1 EQUILIBRIUM 47 2.3.2
PROPAGATION 49 2.3.3 DIFFUSION 51 2.4 MATHEMATICAL ANALYSIS 52 2.5
APPROXIMATION METHODS 52 2.6 DISCRETE MODELS 55 2.7 STRUCTURAL MODELS 56
3. APPROXIMATION METHODS 59 3.1 INTRODUCTION 59 3.2 RESIDUAIS 60 3.3
WEIGHTED-RESIDUAL EQUATION 61 3.3.1 EXAMPLE 61 3.4 APPROXIMATION
FUNCTIONS 62 3.5 ADMISSIBILITY CONDITIONS 62 3.5.1 EXAMPLE 63 3.6 GLOBAL
INDIRECT DISCRETIZATION 64 3.6.1 SATISFACTION OF BOUNDARY CONDITIONS 65
3.6.2 DOMAIN METHODS OF APPROXIMATION 66 3.6.3 GALERKIN METHOD 66 3.6.4
LEAST SQUARES METHOD 67 3.6.5 MOMENTS METHOD 67 3.6.6 COLLOCATION METHOD
68 3.6.7 EXAMPLE 70 3.6.8 EXAMPLE 82 3.7 INTEGRATION BY PARTS 84 3.7.1
STRONG, WEAK AND TRANSPOSED FORMS 84 3.7.2 ONE-DIMENSIONAL CASE 85 3.7.3
EXAMPLE 85 3.7.4 HIGHER-DIMENSIONAL CASES 86 3.7.5 EXAMPLE 88 3.8 LOCAL
DIRECT DISCRETIZATION 88 3.8.1 NODES AND LOCAL REGIONS 89 3.8.2
SATISFACTION OF BOUNDARY CONDITIONS 89 3.8.3 FINITE DIFFERENCE METHOD 90
3.8.4 FINITE ELEMENT METHOD 93 3.8.5 BOUNDARY ELEMENT METHOD 96 3.8.6
EXAMPLE 98 3.8.7 EXAMPLE 113 3.8.8 EXAMPLE 132 CONTENTS XIII 4.
INTERPOLATION 135 4.1 INTRODUCTION 135 4.2 GLOBALLY DEFINED FUNCTIONS
136 4.2.1 POLYNOMIAL BASES 136 4.2.2 EXAMPLE 137 4.2.3 EXAMPLE 138 4.2.4
CONCLUSIONS 142 4.3 PIECEWISELY DEFINED FUNCTIONS 143 4.3.1 SPLINE
INTERPOLATION 143 4.3.2 FINITE ELEMENT INTERPOLATION 144 4.4 FINITE
ELEMENT GENERALIZED COORDINATES 145 4.4.1 CONVERGENCE CONDITIONS 145
4.4.2 GEOMETRIE ISOTROPY 146 4.4.3 FINITE ELEMENT FAMILIES 146 4.5
FINITE ELEMENT SHAPE FUNCTIONS 148 4.5.1 NATURAL COORDINATES 150 4.5.2
CURVILINEAR COORDINATES 156 4.5.3 EXAMPLE 157 4.6 PARAMETRIC FINITE
ELEMENTS 161 4.7 ISOPARAMETRIC FINITE ELEMENTS 162 4.7.1 CONVERGENCE
CONDITIONS 162 4.7.2 EVALUATION OF ELEMENT EQUATIONS 164 4.7.3 NUMERICAL
INTEGRATION 166 4.8 LINEAR TRIANGULAER ISOPARAMETRIC ELEMENT 168 4.8.1
EXAMPLE 169 4.8.2 EXAMPLE 171 4.8.3 EXAMPLE 174 4.8.4 EXAMPLE 176 5. THE
FINITE ELEMENT METHOD 179 5.1 INTRODUCTION 179 5.2 STEADY-STATE MODELS
WITH SCALAR VARIABLE 179 5.2.1 CONTINUOUS MODEL 180 5.2.2 WEIGHTED
RESIDUAL GALERKIN APPROXIMATION 183 5.2.3 DISCRETE MODEL 185 5.3 FINITE
ELEMENT MESH 186 5.3.1 LINEAR TRIANGULAER ISOPARAMETRIC ELEMENT 187 5.3.2
TOTAL POTENTIAL ENERGY 188 5.3.3 INTERNAL POTENTIAL ENERGY DENSITY 188
5.3.4 MESH TOPOLOGY 189 5.4 LOCAL FINITE ELEMENT EQUATIONS 190 5.5
GLOBAL FINITE ELEMENT EQUATIONS 192 5.6 EXACT BOUNDARY CONDITIONS 193
5.7 SOLUTION OF THE SYSTEM OF EQUATIONS 194 5.8 COMPUTATION OF
DERIVATIVES 194 XIV CONTENTS 5.9 FINITE ELEMENT PRE- AND POST-
PROCESSING 196 5.10 CGTJFEM: PACKAGE FOR FINITE ELEMENT ANALYSIS 197
5.10.1 DATA PREPARATION 197 5.11 EXAMPLE 198 5.12 EXAMPLE 208 5.13
EXAMPLE 213 5.14 EXAMPLE 217 6. FLUID MECHANICS APPLICATIONS 223 6.1
INTRODUCTION 223 6.2 CONTINUOUS MODELS OF FLUID FLOW 223 6.2.1
INCOMPRESSIBLE FLUIDS 223 6.2.2 INVISCID FLUIDS 224 6.2.3 IRROTATIONAL
FLOWS 224 6.2.4 STEADY-STATE FLOWS 224 6.2.5 BERNOULLI S ENERGY
CONSERVATION 225 6.2.6 VELOCITY POTENTIAL 226 6.2.7 STREAM FUNCTION 226
6.3 CONFINED FLOWS 227 6.4 UNCONFINED FLOWS 228 6.5 GROUNDWATER FLOWS
229 6.5.1 DARCY S HYPOTHESIS 229 6.5.2 DUPUIT S HYPOTHESIS 231 6.6
EXAMPLE 232 6.6.1 FLOW UNDER A DAM 232 6.6.2 PROBLEM S SOLUTION 233 6.7
EXAMPLE 240 6.7.1 FLOW IN AN UNCONFINED AQUIFER 240 6.7.2 PROBLEM S
SOLUTION 241 7. SOLID MECHANICS APPLICATIONS 251 7.1 INTRODUCTION 251
7.2 CONTINUOUS MODELS 251 7.3 FUNDAMENTAL CONTINUOUS MODEL: ELASTICITY
THEORY 252 7.3.1 STRAIN-DISPLACEMENT EQUATIONS 253 7.3.2 EQUILIBRIUM
EQUATIONS 253 7.3.3 STRESS-STRAIN EQUATIONS 254 7.3.4 BOUNDARY
CONDITIONS 254 7.3.5 ELASTIC FIELDS 255 7.3.6 THE WORK THEOREM 256 7.3.7
THEOREM OF VIRTUAL DISPLACEMENTS 256 7.3.8 THEOREM OF TOTAL POTENTIAL
ENERGY 256 7.4 FINITE ELEMENT MODEL 257 7.4.1 WEIGHTED RESIDUAL EQUATION
257 7.4.2 THEOREM OF WORK 258 CONTENTS XV 7.4.3 THEOREM OF VIRTUAL
DISPLACEMENTS 259 7.4.4 DISCRETIZATION 259 7.5 MESH TOPOLOGY 261 7.5.1
TOTAL STRAIN ENERGY 261 7.5.2 DISTRIBUTION OF THE STRAIN ENERGY DENSITY
262 7.6 CONSTRAINED DISPLACEMENTS 262 7.7 APPLICATION OF THE FINITE
ELEMENT MODEL 264 7.8 THREE-DIMENSIONAL EQUILIBRIUM STATES 265 7.8.1
CONSTANT-STRAIN TETRAHEDRON ELEMENT 265 7.9 TWO-DIMENSIONAL EQUILIBRIUM
STATES 267 7.9.1 PLANE STRESS AND PLANE STRAIN 267 7.9.2 ASYMPTOTIC
MODEL: PLANE ELASTICITY 269 7.9.3 CONSTANT-STRAIN TRIANGULAER
ISOPARAMETRIC ELEMENT.... 270 7.9.4 CST_FEM: PACKAGE FOR FINITE ELEMENT
ANALYSIS 273 7.9.5 DATA PREPARATION 274 7.9.6 EXAMPLE 275 7.9.7 EXAMPLE
281 7.9.8 EXAMPLE 284 7.9.9 EXAMPLE 292 7.10 ONE-DIMENSIONAL EQUILIBRIUM
STATES 302 7.10.1 ASYMPTOTIC MODEL: THEORY OF BARS 303 7.10.2 TRUSS
ELEMENT 312 7.10.3 SKEW ELEMENTS 314 7.10.4 BEAM ELEMENT 315 7.11
FURTHER STUDY 318 A. THE COMPANION CD-ROM 319 REFERENCES 321 INDEX 323
|
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| indexdate | 2024-07-09T18:58:34Z |
| institution | BVB |
| isbn | 3540429867 |
| language | English |
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| physical | XV, 325 S. graph. Darst. 1 CD-ROM |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
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| spelling | Portela, Artur Verfasser aut Finite elements using maple a symbolic programming approach A. Portela ; A. Charafi Berlin [u.a.] Springer 2002 XV, 325 S. graph. Darst. 1 CD-ROM txt rdacontent n rdamedia nc rdacarrier Engineering online library Maple (Computer file) Datenverarbeitung Engineering mathematics Data processing Maple Programm (DE-588)4209397-1 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s Maple Programm (DE-588)4209397-1 s DE-604 Charafi, Abdellatif Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009698191&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Portela, Artur Charafi, Abdellatif Finite elements using maple a symbolic programming approach Maple (Computer file) Datenverarbeitung Engineering mathematics Data processing Maple Programm (DE-588)4209397-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4209397-1 (DE-588)4017233-8 |
| title | Finite elements using maple a symbolic programming approach |
| title_auth | Finite elements using maple a symbolic programming approach |
| title_exact_search | Finite elements using maple a symbolic programming approach |
| title_full | Finite elements using maple a symbolic programming approach A. Portela ; A. Charafi |
| title_fullStr | Finite elements using maple a symbolic programming approach A. Portela ; A. Charafi |
| title_full_unstemmed | Finite elements using maple a symbolic programming approach A. Portela ; A. Charafi |
| title_short | Finite elements using maple |
| title_sort | finite elements using maple a symbolic programming approach |
| title_sub | a symbolic programming approach |
| topic | Maple (Computer file) Datenverarbeitung Engineering mathematics Data processing Maple Programm (DE-588)4209397-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Maple (Computer file) Datenverarbeitung Engineering mathematics Data processing Maple Programm Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009698191&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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