Differential quadrature and its application in engineering:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2000
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 324 - 335 |
| Physical Description: | XVI, 340 S. graph. Darst. |
| ISBN: | 1852332093 |
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| 245 | 1 | 0 | |a Differential quadrature and its application in engineering |c Chang Shu |
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Record in the Search Index
| _version_ | 1804127772746973184 |
|---|---|
| adam_text | CHANG SHU DIFFERENTIAL QUADRATURE AND ITS APPLICATION IN ENGINEERING
SPRINGER TABLE OF CONTENTS 1 MATHEMATICAL FUNDAMENTALS OF DIFFERENTIAL
QUADRATURE METHOD: LINEAR VECTOR SPACE ANALYSIS AND FUNCTION
APPROXIMATION 1 1.1 INTRODUCTION 1 1.2 DERIVATIVE APPROXIMATION BY
DIFFERENTIAL QUADRATURE (DQ) METHOD 3 1.2.1 INTEGRAL QUADRATURE 4 1.2.2
DIFFERENTIAL QUADRATURE 5 1.3 ANALYSIS OF A LINEAR VECTOR SPACE 6 1.3.1
DEFINITION OF A LINEAR VECTOR SPACE 6 1.3.2 PROPERTIES OF A LINEAR
VECTOR SPACE 8 1.4 SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS (PDES) AND
FUNCTION APPROXIMATION 11 1.4.1 TWO BASIC TYPES OF SOLUTION FOR PDES 11
1.4.2 HIGH ORDER POLYNOMIAL APPROXIMATION 13 1.4.3 FOURIER SERIES
EXPANSION 18 1.4.3.1 GENERAL FUNCTION 18 1.4.3.2 EVEN FUNCTION 21
1.4.3.3 ODD FUNCTION 23 2 POLYNOMIAL-BASED DIFFERENTIAL QUADRATURE (PDQ)
25 2.1 INTRODUCTION 25 2.2 COMPUTATION OF WEIGHTING COEFFICIENTS FOR THE
FIRST ORDER DERIVATIVE 26 2.2.1 BELLMAN S APPROACHES 26 2.2.2 QUAN AND
CHANG S APPROACH 28 2.2.3 SHU S GENERAL APPROACH 29 2.3 COMPUTATION OF
WEIGHTING COEFFICIENTS FOR THE SECOND AND HIGHER ORDER DERIVATIVES 32
2.3.1 WEIGHTING COEFFICIENTS OF THE SECOND ORDER DERIVATIVE 32 2.3.2
SHU S RECURRENCE FORMULATION FOR HIGHER ORDER DERIVATIVES 34 2.3.3
MATRIX MULTIPLICATION APPROACH 36 2.4 ERROR ANALYSIS 38 2.4.1 THE
FUNCTION APPROXIMATION 38 2.4.2 THE DERIVATIVE APPROXIMATION 40
DIFFERENTIAL QUADRATURE AND ITS APPLICATION IN ENGINEERING 2.5
RELATIONSHIP BETWEEN PDQ AND OTHER APPROACHES 44 2.5.1 RELATIONSHIP
BETWEEN PDQ AND FINITE DIFFERENCE SCHEME 44 2.5.1.1 GENERATION OF FINITE
DIFFERENCE SCHEME 44 2.5.1.2 RELATIONSHIP BETWEEN PDQ AND HIGHEST ORDER
FINITE DIFFERENCE SCHEME 48 2.5.2 RELATIONSHIP BETWEEN PDQ AND CHEBYSHEV
COLLOCATION METHOD 52 2.6 EXTENSION TO THE MULTI-DIMENSIONAL CASE 55
2.6.1 DIRECT EXTENSION FOR REGULAR DOMAIN 55 2.6.2 DIFFERENTIAL CUBATURE
METHOD 60 2.7 SPECIFIC RESULTS FOR TYPICAL GRID POINT DISTRIBUTIONS 62
2.7.1 UNIFORM GRID 62 2.7.2 CHEBYSHEV-GAUSS-LOBATTO GRID 63 2.7.3
COORDINATES OF GRID POINTS CHOSEN AS THE ROOTS OF CHEBYSHEV POLYNOMIAL
64 2.8 GENERATION OF LOW ORDER FINITE DIFFERENCE SCHEMES BY PDQ 65
FOURIER EXPANSION-BASED DIFFERENTIAL QUADRATURE (FDQ) 69 3.1
INTRODUCTION 69 3.2 COSINE EXPANSION-BASED DIFFERENTIAL QUADRATURE (CDQ)
FOR EVEN FUNCTIONS 70 3.3 SINE EXPANSION-BASED DIFFERENTIAL QUADRATURE
(SDQ) FOR ODD FUNCTIONS 81 3.4 FOURIER EXPANSION-BASED DIFFERENTIAL
QUADRATURE (FDQ) FOR ANY GENERAL FUNCTION 86 3.5 SOME PROPERTIES OF
FOURIER EXPANSION-BASED DIFFERENTIAL QUADRATURE 91 SOME PROPERTIES OF DQ
WEIGHTING COEFFICIENT MATRICES 95 4.1 INTRODUCTION 95 4.2 DETERMINANT
AND RANK OF DQ WEIGHTING COEFFICIENT MATRICES 96 4.2.1 DEFINITION AND
PROPERTIES OF DETERMINANT AND RANK 96 4.2.2 DETERMINANT AND RANK OF DQ
WEIGHTING COEFFICIENT MATRICES 98 4.3 STRUCTURES AND PROPERTIES OF DQ
WEIGHTING COEFFICIENT MATRICES 100 4.3.1 DEFINITION OF CENTROSYMMETRIC
AND SKEW CENTROSYMMETRIC MATRICES 101 4.3.2 PROPERTIES OF
CENTROSYMMETRIC AND SKEW CENTROSYMMETRIC MATRICES 102 4.3.2.1 PROPERTIES
OF CENTROSYMMETRIC MATRICES 102 TABLE OF CONTENTS XIII 4.3.2.2
PROPERTIES OF SKEW CENTROSYMMETRIC MATRICES 105 4.3.3 STRUCTURES OF DQ
WEIGHTING COEFFICIENT MATRICES 107 4.3.3.1 STRUCTURE OF FIRST ORDER DQ
WEIGHTING COEFFICIENT MATRIX 107 4.3.3.2 STRUCTURES OF HIGHER ORDER DQ
WEIGHTING COEFFICIENT MATRICES 109 4.4 EFFECT OF GRID POINT DISTRIBUTION
ON EIGENVALUES OF DQ DISCRETIZATION MATRICES 110 4.4.1 STABILITY OF
ORDINARY DIFFERENTIAL EQUATIONS ILL 4.4.2 EIGENVALUES OF SOME SPECIFIC
DQ DISCRETIZATION MATRICES 112 4.4.2.1 THE CONVECTION OPERATOR 112
4.4.2.2 THE DIFFUSION OPERATOR 117 4.4.2.3 THE CONVECTION-DIFFUSION
OPERATOR 119 4.5 EFFECT OF GRID POINT DISTRIBUTION ON MAGNITUDE OF DQ
WEIGHTING COEFFICIENTS 120 5 SOLUTION TECHNIQUES FOR DQ RESULTANT
EQUATIONS 12 3 5.1 INTRODUCTION 123 5.2 SOLUTION TECHNIQUES FOR DQ
ORDINARY DIFFERENTIAL EQUATIONS 124 5.3 SOLUTION TECHNIQUES FOR DQ
ALGEBRAIC EQUATIONS 128 5.3.1 DIRECT METHODS 130 5.3.2 ITERATIVE METHODS
134 5.3.2.1 ITERATIVE METHODS FOR CONVENTIONAL SYSTEM 134 5.3.2.2
ITERATIVE METHODS FOR LYAPUNOV SYSTEM 137 5.4 IMPLEMENTATION OF BOUNDARY
CONDITIONS 140 5.5 SAMPLE APPLICATIONS OF DQ METHOD 143 5.5.1 BURGERS
EQUATION 143 5.5.2 TWO-DIMENSIONAL POISSON EQUATION 145 5.5.3 HELMHOLTZ
EIGENVALUE PROBLEM 148 6 APPLICATION OF DIFFERENTIAL QUADRATURE METHOD
TO SOLVE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS 153 6.1 INTRODUCTION 153
6.2 GOVERNING EQUATIONS 154 6.2.1 DIMENSIONAL FORM 154 6.2.2
NON-DIMENSIONAL FORM 157 6.2.3 VORTICITY-STREAM FUNCTION FORMULATION 159
6.3 SOLUTION OF VORTICITY-STREAM FUNCTION FORMULATION 160 6.3.1
DISCRETIZATION OF GOVERNING EQUATIONS 160 6.3.2 IMPLEMENTATION OF
BOUNDARY CONDITIONS 161 X1V DIFFERENTIAL QUADRATURE AND ITS APPLICATION
IN ENGINEERING 6.3.2.1 IMPLEMENTATION OF BOUNDARY CONDITION FOR
VORTICITY 162 6.3.2.2 IMPLEMENTATION OF BOUNDARY CONDITION FOR STREAM
FUNCTION 162 6.3.2.3 IMPLEMENTATION OF BOUNDARY CONDITION FOR
TEMPERATURE 167 6.3.3 SOLUTION PROCEDURES 168 6.3.4 SOME NUMERICAL
EXAMPLES 170 6.3.4.1 THE FLOW PAST A CIRCULAR CYLINDER 170 6.3.4.2 THE
NATURAL CONVECTION IN A CONCENTRIC ANNULUS 172 6.4 SOLUTION OF
INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN PRIMITIVE VARIABLE FORM 175
6.4.1 INTRODUCTION 175 6.4.2 PRESSURE CORRECTION METHOD 176 6.4.3 TWO
APPROACHES TO SPECIFY BOUNDARY CONDITION FOR P AND TO ENFORCE
CONTINUITY CONDITION ON THE BOUNDARY 178 6.4.3.1 APPROACH 1 178 6.4.3.2
APPROACH 2 180 6.4.4 COMPUTATIONAL SEQUENCE 181 6.4.5 SAMPLE APPLICATION
AND COMMENTS ON THE TWO APPROACHES.. 182 6.4.5.1 IMPORTANCE OF ENFORCING
CONTINUITY CONDITION ON THE BOUNDARY 182 6.4.5.2 COMMENTS ON PERFORMANCE
OF TWO APPROACHES 184 7 APPLICATION OF DIFFERENTIAL QUADRATURE METHOD TO
STRUCTURAL AND VIBRATION ANALYSIS 186 7.1 INTRODUCTION 186 7.2
DIFFERENTIAL QUADRATURE ANALYSIS OF BEAMS 188 7.2.1 GOVERNING EQUATIONS
AND BOUNDARY CONDITIONS 188 7.2.2 NUMERICAL DISCRETIZATION 189 7.2.3
IMPLEMENTATION OF BOUNDARY CONDITIONS 190 7.2.3.1 THE 8-TECHNIQUE 190
7.2.3.2 MODIFICATION OF WEIGHTING COEFFICIENT MATRICES 191 7.2.3.3
DIRECT SUBSTITUTION OF BOUNDARY CONDITIONS INTO DISCRETE GOVERNING
EQUATIONS 194 7.2.4 NUMERICAL EXAMPLE: FREE VIBRATION ANALYSIS OF A
UNIFORM BEAM 196 7.3 DIFFERENTIAL QUADRATURE ANALYSIS OF THIN PLATES 197
7.3.1 GOVERNING EQUATIONS AND BOUNDARY CONDITIONS 197 7.3.2 NUMERICAL
DISCRETIZATION 199 TABLE OF CONTENTS XV 7.3.3 IMPLEMENTATION OF BOUNDARY
CONDITIONS 200 7.3.3.1 THE 5-TECHNIQUE 200 7.3.3.2 MODIFICATION OF
WEIGHTING COEFFICIENT MATRICES 201 7.3.3.3 DIRECT SUBSTITUTION OF
BOUNDARY CONDITIONS INTO DISCRETE GOVERNING EQUATIONS 202 7.3.3.4
GENERAL APPROACH 205 7.3.4 NUMERICAL EXAMPLE: FREE VIBRATION ANALYSIS OF
SQUARE PLATES 207 7.4 DIFFERENTIAL QUADRATURE ANALYSIS OF SHELLS 209
7.4.1 GOVERNING EQUATIONS AND BOUNDARY CONDITIONS 209 7.4.2 NUMERICAL
DISCRETIZATION 218 7.4.3 IMPLEMENTATION OF BOUNDARY CONDITIONS 219 7.4.4
NUMERICAL EXAMPLE: FREE VIBRATION ANALYSIS OF A COMPOSITE LAMINATED
CONICAL SHELL 222 8 MISCELLANEOUS APPLICATIONS OF DIFFERENTIAL
QUADRATURE METHOD 224 8.1 INTRODUCTION 224 8.2 APPLICATION TO HEAT
TRANSFER 224 8.3 APPLICATION TO CHEMICAL REACTOR 228 8.4 APPLICATION TO
LUBRICATION PROBLEMS 232 8.5 APPLICATION TO WAVEGUIDE ANALYSIS 235 8.6
SOLUTION OF THE HELMHOLTZ EQUATION 239 8.7 EFFECT OF MESH POINT
DISTRIBUTION ON ACCURACY OF DQ RESULTS 242 9 APPLICATION OF DIFFERENTIAL
QUADRATURE TO COMPLEX PROBLEMS 245 9.1 INTRODUCTION 245 9.2 MULTI-DOMAIN
DQ METHOD 245 9.2.1 TOPOLOGY OF INTERFACE 246 9.2.1.1 PATCHED INTERFACE
246 9.2.1.2 OVERLAPPED INTERFACE 248 9.2.2 MULTI-DOMAIN DQ APPLICATION
IN FLUID MECHANICS 249 9.2.3 MULTI-DOMAIN DQ APPLICATION IN SOLID
MECHANICS 251 9.2.4 MULTI-DOMAIN DQ APPLICATION IN WAVEGUIDE ANALYSIS
252 9.3 DQ APPLICATION IN CURVILINEAR COORDINATE SYSTEM 254 9.3.1
COORDINATE TRANSFORMATION 254 9.3.2 DQ SIMULATION OF INCOMPRESSIBLE
FLOWS IN IRREGULAR DOMAINS 256 9.3.3 DQ VIBRATION ANALYSIS OF IRREGULAR
PLATES 260 9.3.3.1 PARTIAL TRANSFORMATION 260 XV1 DIFFERENTIAL
QUADRATURE AND ITS APPLICATION IN ENGINEERING 9.3.3.2 COMPLETE
TRANSFORMATION 261 9.3.3.3 IMPLEMENTATION OF BOUNDARY CONDITIONS 262
9.3.3.4 SAMPLE APPLICATION 264 9.4 DIFFERENTIAL CUBATURE METHOD FOR
COMPLEX PROBLEMS 266 10 GENERALIZED INTEGRAL QUADRATURE (GIQ) AND ITS
APPLICATION TO SOLVE BOUNDARY LAYER EQUATIONS 267 10.1 INTRODUCTION 267
10.2 GENERALIZED INTEGRAL QUADRATURE (GIQ) 268 10.2.1 ONE-DIMENSIONAL
GENERALIZED INTEGRAL QUADRATURE 268 10.2.2 ERROR ANALYSIS 271 10.2.3
EXTENSION TO MULTI-DIMENSIONAL CASES 272 10.2.4 SAMPLE APPLICATION OF
GIQ METHOD 273 10.3 DQ-GIQ ALGORITHM TO SOLVE BOUNDARY LAYER EQUATIONS
275 10.3.1 STREAM FUNCTION AS DEPENDENT VARIABLE 275 10.3.2 PRIMITIVE
VARIABLES AS DEPENDENT VARIABLES 277 10.4 STEADY BOUNDARY LAYER
SOLUTIONS 279 10.4.1 ONE-DIMENSIONAL CASE 279 10.4.2 TWO-DIMENSIONAL
CASE 280 10.4.3 THREE-DIMENSIONAL CASE 281 10.5 UNSTEADY BOUNDARY LAYER
SOLUTIONS 285 APPENDICES A. A FORTRAN PROGRAM FOR SIMULATION OF NATURAL
CONVECTION IN A SQUARE CAVITY 288 B. A FORTRAN PROGRAM FOR VIBRATION
ANALYSIS OF RECTANGULAR PLATES 305 C. A FORTRAN PROGRAM FOR L-SHAPED
WAVEGUIDE ANALYSIS BY MULTI-DOMAIN DQ METHOD 315 REFERENCES 324 INDEX
336
|
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| id | DE-604.BV013074411 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:38:40Z |
| institution | BVB |
| isbn | 1852332093 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008908124 |
| oclc_num | 633626779 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-91G DE-BY-TUM |
| owner_facet | DE-824 DE-703 DE-91G DE-BY-TUM |
| physical | XVI, 340 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| spelling | Shu, Chang 1962- Verfasser (DE-588)121362493 aut Differential quadrature and its application in engineering Chang Shu London [u.a.] Springer 2000 XVI, 340 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 324 - 335 Technik (DE-588)4059205-4 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Technik (DE-588)4059205-4 s DE-604 Numerisches Verfahren (DE-588)4128130-5 s HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008908124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shu, Chang 1962- Differential quadrature and its application in engineering Technik (DE-588)4059205-4 gnd Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4059205-4 (DE-588)4012249-9 (DE-588)4128130-5 |
| title | Differential quadrature and its application in engineering |
| title_auth | Differential quadrature and its application in engineering |
| title_exact_search | Differential quadrature and its application in engineering |
| title_full | Differential quadrature and its application in engineering Chang Shu |
| title_fullStr | Differential quadrature and its application in engineering Chang Shu |
| title_full_unstemmed | Differential quadrature and its application in engineering Chang Shu |
| title_short | Differential quadrature and its application in engineering |
| title_sort | differential quadrature and its application in engineering |
| topic | Technik (DE-588)4059205-4 gnd Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Technik Differentialgleichung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008908124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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