Matrix and finite element displacement analysis of structures:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Pr.
1984
|
| Schriftenreihe: | The Oxford engineering science series.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 565 S. graph. Darst. |
| ISBN: | 019856211X |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV004109482 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 901009s1984 d||| |||| 00||| eng d | ||
| 020 | |a 019856211X |9 0-19-856211-X | ||
| 035 | |a (OCoLC)9622575 | ||
| 035 | |a (DE-599)BVBBV004109482 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-706 |a DE-83 | ||
| 050 | 0 | |a TA347.D4 | |
| 082 | 0 | |a 624.1/7/015129434 |2 19 | |
| 082 | 0 | |a 624.1/71/015129434 |2 19 | |
| 100 | 1 | |a Dawe, D. J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Matrix and finite element displacement analysis of structures |
| 264 | 1 | |a Oxford |b Clarendon Pr. |c 1984 | |
| 300 | |a XVIII, 565 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a The Oxford engineering science series. | |
| 650 | 4 | |a Constructions, Théorie des - Méthodes des matrices | |
| 650 | 4 | |a Éléments finis, Méthode des | |
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Structural analysis (Engineering) |x Matrix methods | |
| 650 | 0 | 7 | |a Tragwerk |0 (DE-588)4060592-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Tragwerk |0 (DE-588)4060592-9 |D s |
| 689 | 0 | 1 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002564368&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-002564368 | ||
Datensatz im Suchindex
| _version_ | 1804118327207919616 |
|---|---|
| adam_text | CONTENTS
1 GENERAL INTRODUCTION AND STRUCTURAL
PRELIMINARIES 1
11A few historical remarks 1
1 2 Matrix methods of analysis of skeletal structures 2
1 3 The finite-element method 5
1 4 Commonality of matrix and finite-element methods 11
1 5 Some basic considerations of structural analysis 11
151 General remarks 11
152 Linear structures: superposition 12
153 Elasticity, equilibrium, and compatability 13
154 Boundary conditions 16
155 Comments 16
156 Work 17
157 Reciprocal theorems 18
1 6 Determinate and indeterminate structures 19
1 7 Methods of analysis 21
1 8 Displacement method: stiffness relationships 26
1 9 Brief remarks on co-ordinate systems used in the book 27
2 THE MATRIX DISPLACEMENT APPROACH 30
2 1 Introduction 30
2 2 Stiffness matrix of a bar element subjected to axial force 31
2 3 Bar structure stiffness matrix 33
2 4 Application of zero-displacement boundary conditions
and problem solution 36
2 5 Remarks on the solution procedure 38
2 6 Some properties of stiffness matrices 39
2 7 Stiffness matrix of a bar element subjected to torsion 40
2 8 Stiffness matrix of a beam element 42
2 9 Assembly of the structure stiffness matrix by the direct
stiffness method 49
2 10 Symmetrical geometry 61
2 11 Further remarks on prescribed displacements 67
Problems 71
3 MATRIX DISPLACEMENT ANALYSIS OF PLANAR
FRAMES WITH JOINT LOADS 74
3 1 Introduction 74
3 2 Definitions and conventions for planar frames 75
XIV CONTENTS
3 3 Planar pin-jointed frames 78
3 4 Planar rigid-jointed frames 88
3 5 Non-standard planar frames 97
3 6 Neglect of axial strain in the analysis of planar rigid-
jointed frames 101
3 7 Inclined supports 105
3 8 Form of structure stiffness matrix: bandwidth 110
Problems 112
4 OTHER KINDS OF LOADING AND OTHER KINDS
OF FRAME 119
4 1 Introduction 119
4 2 Representation of loading between joints 120
4 3 Effects of temperature change and lack of fit 127
4 4 The grillage 138
4 5 Ball-jointed space frames 146
4 6 Rigid-jointed space frames 152
Bibliography 161
Problems 161
5 VIRTUAL DISPLACEMENTS, POTENTIAL ENERGY,
AND THE RAYLEIGH-RITZ METHOD 166
5 1 Introduction 166
5 2 Strain energy of one-dimensional systems 167
521 Axially loaded bar 167
522 Torsionally loaded bar 171
523 Bending of beams 172
5 3 Principle of virtual displacements 173
5 4 Principle of minimum potential energy 178
5 5 The Rayleigh-Ritz method 184
5 6 Approximate solutions by the principle of virtual displace
ments 203
Bibliography 208
Problems 208
6 ONE-DIMENSIONAL FINITE ELEMENTS 211
6 1 Introduction 211
6 2 Stiffness matrix for the basic bar element 212
6 3 Stiffness matrix for the basic beam element 217
6 4 Comments on the basic bar and beam elements 221
641 Summary of the results of Sections 6 2 and 6 3 221
642 The exact nature of the basic bar and beam ele
ments 222
CONTENTS xv
6 5 Representation of distributed loading 223
6 6 The assembly process within the PMPE approach 227
6 7 Element stresses 232
6 8 Requirements for element displacement fields 236
6 9 Shape functions and interpolation polynomials 240
6 10 Refined one-dimensional elements 246
6 11 Static condensation 253
6 12 Inclusion of initial strain effects 254
Problems 260
7 INTRODUCTION TO TWO- AND THREE-DIMEN
SIONAL ANALYSIS 263
7 1 Introduction 263
7 2 Equations from three-dimensional elasticity theory 263
721 Stresses: equilibrium equations 263
722 Displacements and strains: strain-displacement re
lationships 265
723 Stress-strain relations (constitutive equations) 267
724 Compatibility conditions 269
725 Boundary conditions 269
726 Comments 271
7 3 Potential energy for the continuum: the general finite-
element formulation 271
7 4 Plane stress and plane strain 276
7 5 Bodies of revolution with axisymmetric loading 279
7 6 Plate bending 280
References 288
8 SOME FINITE ELEMENTS FOR PLANAR ANALYSIS 290
8 1 Introduction 290
8 2 Requirements for element displacement fields 292
8 3 Triangular elements for plane stress or strain 294
831 The constant strain triangle: displacement field,
stiffness matrix, and stress matrix 294
832 The constant strain triangle: consistent load col
umn matrix 299
833 The linear strain triangle 309
834 Other triangular elements 312
835 Comments on the triangular elements 315
836 Numerical studies using the constant strain triangle
and linear strain triangle 317
8 4 Rectangular elements 322
841 The basic rectangular element 322
XVI CONTENTS
842 Higher-order rectangular elements: Lagrange ele
ment family 330
References 333
Problems 334
9 SOME FINITE ELEMENTS FOR THREE-DIMEN
SIONAL AND AXISYMMETRIC ANALYSIS 338
9 1 Introduction 338
9 2 Requirements for element displacement fields in three-
dimensional analysis 339
9 3 Tetrahedral elements 340
931 The basic (constant strain) tetrahedron 340
932 Higher-order tetrahedra 345
9 4 Rectangular hexahedral elements 348
941 The basic rectangular hexadron 348
942 Higher-order rectangular hexahedra: the Lagrange
element family 352
9 5 Numerical results using three-dimensional elements 353
9 6 The basic element for the analysis of axisymmetric bodies 355
9 7 Applications of the basic axisymmetric element 361
9 8 Further remarks on the analysis of axisymmetric bodies 361
References 363
Problems 364
10 MORE-ADVANCED CONCEPTS IN THE FORMULA
TION OF TWO- AND THREE-DIMENSIONAL
ELASTICITY ELEMENTS 366
10 1 Introduction 366
10 2 Natural co-ordinates 367
10 2 1 Length co-ordinates 367
10 2 2 Area or triangular co-ordinates 372
10 2 3 Volume or tetrahedral co-ordinates 378
10 3 Serendipity rectangles and hexahedra 379
10 3 1 Rectangles 379
10 3 2 Rectangular hexahedra 384
10 4 The isoparametric concept 387
10 41A linear quadrilateral element 387
10 4 2 Other isoparametric (and related) elements 393
10 4 3 Properties of isoparametric elements 397
10 4 4 Numerical integration 399
10 4 5 Numerical applications using the eight-node
curvilinear quadrilateral 404
References 407
Problems 408
CONTENTS xvii
11 FINITE ELEMENTS FOR PLATE BENDING ANALY
SIS 410
11 1 Introduction 410
11 2 Requirements for element displacement fields and ele
ment formulation 411
11 3 A 12-degree-of-freedom rectangular element (Rl) 415
11 4 Other rectangular elements 428
11 4 1 An invalid conforming element (R2) 428
11 4 2 An improved non-conforming 12-degree-of-
freedom element (R3) 429
11 4 3 Compatibility and twist 431
11 4 4 Elements based on the use of extra nodal free
doms (R4) 432
11 4 5 An element based on the sub-region approach
(R5) 434
11 5 Numerical results for rectangular elements 436
11 6 Elements of more general shape 438
11 7 Triangular elements 438
11 7 1 Non-conforming elements using basic freedoms
only 439
11 7 2 Conforming elements based on sub-region or
related approach 442
11 7 3 Conforming elements using higher-order de
grees of freedom 443
11 8 Numerical results for triangular elements 449
11 9 Alternative philosophies in the generation of plate finite
elements 452
11 10 Remarks on shell analysis 456
References 460
Problems 462
12 VIBRATION AND BUCKLING THE EIGENVALUE
PROBLEM 463
12 1 Introduction 463
12 2 Free undamped vibration of a spring-mass system 464
12 3 Finite-element formulation of the free vibration
problem 469
12 4 Lateral vibration of beams 472
12 5 Vibration of bars and frameworks 480
12 6 Lateral vibration of plates 486
12 7 Lumped mass matrices 493
12 8 Eigenvalue economization 497
12 9 Buckling of a strut 504
12 10 Buckling of struts using the FEM 508
CONTENTS
12 11 Buckling of plates 514
References 519
Problems 521
APPENDIX A MATRIX ALGEBRA AND THE SOLUTION
OF EQUATIONS 525
APPENDIX B USE OF THE PRINCIPLE OF VIRTUAL
DISPLACEMENTS IN THE FINITE-
ELEMENT METHOD 542
SOLUTIONS TO PROBLEMS 546
AUTHOR INDEX 559
xviii
SUBJECT INDEX 561
|
| any_adam_object | 1 |
| author | Dawe, D. J. |
| author_facet | Dawe, D. J. |
| author_role | aut |
| author_sort | Dawe, D. J. |
| author_variant | d j d dj djd |
| building | Verbundindex |
| bvnumber | BV004109482 |
| callnumber-first | T - Technology |
| callnumber-label | TA347 |
| callnumber-raw | TA347.D4 |
| callnumber-search | TA347.D4 |
| callnumber-sort | TA 3347 D4 |
| callnumber-subject | TA - General and Civil Engineering |
| ctrlnum | (OCoLC)9622575 (DE-599)BVBBV004109482 |
| dewey-full | 624.1/7/015129434 624.1/71/015129434 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 624 - Civil engineering |
| dewey-raw | 624.1/7/015129434 624.1/71/015129434 |
| dewey-search | 624.1/7/015129434 624.1/71/015129434 |
| dewey-sort | 3624.1 17 815129434 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Bauingenieurwesen |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01611nam a2200421 c 4500</leader><controlfield tag="001">BV004109482</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">901009s1984 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">019856211X</subfield><subfield code="9">0-19-856211-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)9622575</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV004109482</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">TA347.D4</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">624.1/7/015129434</subfield><subfield code="2">19</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">624.1/71/015129434</subfield><subfield code="2">19</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dawe, D. J.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Matrix and finite element displacement analysis of structures</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford</subfield><subfield code="b">Clarendon Pr.</subfield><subfield code="c">1984</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 565 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">The Oxford engineering science series.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Constructions, Théorie des - Méthodes des matrices</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Éléments finis, Méthode des</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Finite element method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Structural analysis (Engineering)</subfield><subfield code="x">Matrix methods</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Tragwerk</subfield><subfield code="0">(DE-588)4060592-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Finite-Elemente-Methode</subfield><subfield code="0">(DE-588)4017233-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Tragwerk</subfield><subfield code="0">(DE-588)4060592-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Finite-Elemente-Methode</subfield><subfield code="0">(DE-588)4017233-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002564368&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-002564368</subfield></datafield></record></collection> |
| id | DE-604.BV004109482 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:08:32Z |
| institution | BVB |
| isbn | 019856211X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002564368 |
| oclc_num | 9622575 |
| open_access_boolean | |
| owner | DE-706 DE-83 |
| owner_facet | DE-706 DE-83 |
| physical | XVIII, 565 S. graph. Darst. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Clarendon Pr. |
| record_format | marc |
| series2 | The Oxford engineering science series. |
| spelling | Dawe, D. J. Verfasser aut Matrix and finite element displacement analysis of structures Oxford Clarendon Pr. 1984 XVIII, 565 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Oxford engineering science series. Constructions, Théorie des - Méthodes des matrices Éléments finis, Méthode des Finite element method Structural analysis (Engineering) Matrix methods Tragwerk (DE-588)4060592-9 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Tragwerk (DE-588)4060592-9 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002564368&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dawe, D. J. Matrix and finite element displacement analysis of structures Constructions, Théorie des - Méthodes des matrices Éléments finis, Méthode des Finite element method Structural analysis (Engineering) Matrix methods Tragwerk (DE-588)4060592-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4060592-9 (DE-588)4017233-8 |
| title | Matrix and finite element displacement analysis of structures |
| title_auth | Matrix and finite element displacement analysis of structures |
| title_exact_search | Matrix and finite element displacement analysis of structures |
| title_full | Matrix and finite element displacement analysis of structures |
| title_fullStr | Matrix and finite element displacement analysis of structures |
| title_full_unstemmed | Matrix and finite element displacement analysis of structures |
| title_short | Matrix and finite element displacement analysis of structures |
| title_sort | matrix and finite element displacement analysis of structures |
| topic | Constructions, Théorie des - Méthodes des matrices Éléments finis, Méthode des Finite element method Structural analysis (Engineering) Matrix methods Tragwerk (DE-588)4060592-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Constructions, Théorie des - Méthodes des matrices Éléments finis, Méthode des Finite element method Structural analysis (Engineering) Matrix methods Tragwerk Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002564368&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dawedj matrixandfiniteelementdisplacementanalysisofstructures |