The mechanics of solids and structures: hierarchical modeling and the finite element solution
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Computational fluid and solid mechanics
|
| Subjects: | |
| Online Access: | http://deposit.dnb.de/cgi-bin/dokserv?id=2707361&prov=M&dok_var=1&dok_ext=htm Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 597 S. Ill., graph. Darst. |
| ISBN: | 9783540263319 |
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| 245 | 1 | 0 | |a The mechanics of solids and structures |b hierarchical modeling and the finite element solution |c Miguel Luiz Bucalem ; Klaus-Jürgen Bathe |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
1. MATHEMATICAL MODELS AND THE FINITE ELEMENT SOLUTION. HIER- ARCHICAL
MODELING 1
1.1 INTRODUCTORY REMARKS 1
1.2 MATHEMATICAL MODELS 2
1.2.1 A DEMONSTRATIVE PROBLEM - A CARABINER 3
1.2.2 THE CASE FOR HIERARCHICAL MODELING 6
1.2.3 DEMONSTRATIVE HIERARCHICAL MODELING EXAMPLE - A CARA- BINER 7
1.3 REMARKS ON THE HIERARCHICAL MODELING PROCESS 14
1.4 OUTLINE OF BOOK 17
2. FUNDAMENTAL STEPS IN STRUCTURAL MECHANICS 19
2.1 GENERAL CONDITIONS 19
2.1.1 MOTION OF A DEFORMABLE THREE-DIMENSIONAL BODY 19 2.1.2 PROPERLY
SUPPORTED BODIES 23
2.1.3 INTERNAL ACTIONS 24
2.1.4 ASSUMPTIONS FOR STATIC ANALYSIS 25
2.1.5 ASSUMPTIONS FOR A LINEAR STATIC ANALYSIS 25
2.1.6 SUMMARY 26
2.2 THE ANALYSIS OF TRUSS STRUCTURES - TO EXEMPLIFY GENERAL CON- CEPTS
OF ANALYSIS 27
2.2.1 MODEL ASSUMPTIONS 27
2.2.2 KINEMATIC CONDITIONS FOR A PROPERLY SUPPORTED TRUSS .. 28 2.2.3
EQUILIBRIUM CONDITIONS FOR A TRUSS MODEL 30
2.2.4 CONSTITUTIVE BEHAVIOR FOR A TRUSS BAR 34
2.2.5 COMPATIBILITY CONDITIONS FOR A TRUSS 35
2.2.6 STATICALLY DETERMINATE AND INDETERMINATE TRUSSES 40 2.3 MATRIX
DISPLACEMENT METHOD FOR TRUSSES 44
2.3.1 TRUSS BAR STIFFNESS MATRIX IN ITS LOCAL SYSTEM 45
2.3.2 SOLUTION OF A TWO-BAR TRUSS STRUCTURE USING THE MATRIX METHOD 47
2.3.3 STIFFNESS MATRIX OF AN ARBITRARILY ORIENTED TRUSS ELEMENT 52 2.3.4
SOLUTION OF THE THREE-BAR TRUSS STRUCTURE USING THE MA- TRIX METHOD 56
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/977063658
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
2.3.5 SYSTEMATIZATION OF THE MATRIX FORMULATION FOR TRUSS STRUCTURES 61
2.3.6 PRINCIPLE OF SUPERPOSITION 72
2.3.7 REMARKS ABOUT THE STRUCTURE STIFFNESS MATRIX 73 2.3.8 STRAIN
ENERGY OF A TRUSS STRUCTURE 73
2.3.9 PROPERLY SUPPORTED TRUSS STRUCTURES IN THE CONTEXT OF THE MATRIX
METHOD 76
2.4 MODELING CONSIDERATIONS FOR TRUSS STRUCTURES 80
3. THE LINEAR 3-D ELASTICITY MATHEMATICAL MODEL 83
3.1 THE ANALYSIS OF A STEEL SHEET PROBLEM 83
3.1.1 ONE-DIMENSIONAL CONDITIONS 84
3.1.2 TWO DIMENSIONAL CONDITIONS 91
3.2 DEFORMATIONS 95
3.2.1 DISPLACEMENT FIELD 96
3.2.2 NORMAL AND SHEAR STRAINS 99
3.2.3 FINITE AND INFINITESIMAL RIGID DEFORMATIONS 113 3.2.4 TECHNICAL OR
ENGINEERING NOTATION FOR THE STRAINS 119 3.2.5 DEFORMATION IN THE
VICINITY OF A POINT 120
3.3 STRESSES 124
3.3.1 CLASSICAL CONCEPT OF STRESS 126
3.3.2 CHARACTERIZATION OF THE STATE OF STRESS AT A POINT 128 3.3.3
DIFFERENTIAL EQUILIBRIUM EQUATIONS 136
3.3.4 PRINCIPAL STRESSES 139
3.3.5 PRINCIPAL STRAINS 148
3.3.6 INFINITESIMALLY SMALL DISPLACEMENTS 149
3.3.7 TECHNICAL OR ENGINEERING NOTATION FOR THE STRESSES 150 3.4
CONSTITUTIVE EQUATIONS 150
3.4.1 HOOKE S LAW FOR THREE-DIMENSIONAL ISOTROPIC MATERIAL CONDITIONS
151
3.4.2 RELATION BETWEEN G AND E, V 155
3.4.3 GENERALIZED HOOKE S LAW FOR AN ISOTROPIC MATERIAL IN MATRIX
NOTATION 158
3.5 FORMULATION OF THE LINEAR ELASTICITY PROBLEM 159
3.6 TORSION OF A PRISMATIC BAR 166
4. MATHEMATICAL MODELS USED IN ENGINEERING STRUCTURAL ANALY- SIS 179
4.1 PLANE ELASTICITY 179
4.1.1 THE PLANE STRAIN MODEL 179
4.1.2 THE PLANE STRESS MODEL 187
4.1.3 THE AXISYMMETRIC MODEL 197
4.2 BAR MODELS 208
4.2.1 PRISMATIC BAR SUBJECTED TO AXIAL LOADING 210
IMAGE 3
CONTENTS XI
4.2.2 PRISMATIC BAR SUBJECTED TO TRANSVERSE LOADING; THE BERNOULLI-EULER
BEAM MODEL 217
4.2.3 BAR MODELS OBTAINED BY AN ASSEMBLAGE OF BARS 239 4.2.4 MATRIX
DISPLACEMENT METHOD FOR FRAMES 245
4.2.5 BARS SUBJECTED TO 3-D ACTIONS 270
4.2.6 THIN WALLED BARS 274
4.2.7 CURVED BAR MODEL 286
4.2.8 THE TIMOSHENKO BEAM MODEL 301
4.3 PLATES IN BENDING 307
4.3.1 THE KIRCHHOFF PLATE BENDING MODEL 307
4.3.2 THE REISSNER-MINDLIN PLATE BENDING MODEL 320
4.4 SHELLS 327
4.4.1 GEOMETRICAL PRELIMINARIES 328
4.4.2 SHELL MATHEMATICAL MODELS 330
4.4.3 SHELLS OF REVOLUTION LOADED AXISYMMETRICALLY 335 4.4.4 REMARKS ON
SHELL MODELING OF ENGINEERING STRUCTURES .. 353 4.5 SUMMARY OF THE
MATHEMATICAL MODELS FOR STRUCTURAL MECHANICS354
5. THE PRINCIPLE OF VIRTUAL WORK 367
5.1 THE PRINCIPLE OF VIRTUAL WORK FOR THE BAR PROBLEM 367
5.2 THE PRINCIPLE OF VIRTUAL WORK IN 2-D AND 3-D ANALYSES 380 5.2.1 THE
PRINCIPLE OF VIRTUAL WORK FOR 3-D ELASTICITY 381 5.2.2 THE PRINCIPLE OF
VIRTUAL WORK FOR THE PLANE STRESS MODEL 385 5.2.3 THE PRINCIPLE OF
VIRTUAL WORK FOR THE PLANE STRAIN MODEL388 5.2.4 THE PRINCIPLE OF
VIRTUAL WORK FOR THE AXISYMMETRIC
MODEL 389
5.2.5 THE PRINCIPLE OF VIRTUAL WORK FOR THE BERNOULLI-EULER BEAM MODEL
389
5.3 STRAIN AND POTENTIAL ENERGY IN 3-D 390
5.3.1 STRAIN ENERGY 390
5.3.2 THE TOTAL POTENTIAL ENERGY 391
6. THE FINITE ELEMENT PROCESS OF SOLUTION 395
6.1 FINITE ELEMENT FORMULATION OF 1-D BAR PROBLEM 395
6.2 CONVERGENCE PROPERTIES OF 1-D FINITE ELEMENT SOLUTIONS 415 6.2.1
CONVERGENCE CONDITIONS 420
6.2.2 DISTANCES AND NORMS OF FUNCTIONS 421
6.2.3 CONVERGENCE PROPERTIES 423
6.2.4 SMOOTHNESS OF THE SOLUTION 433
6.2.5 THE H, P AND H - P FINITE ELEMENT METHODS 433
6.3 DISPLACEMENT-BASED FINITE ELEMENT FORMULATION FOR SOLIDS 434 6.3.1
DISCRETIZATION METHODOLOGY 434
6.3.2 EQUILIBRIUM PROPERTIES OF THE FINITE ELEMENT SOLUTIONS FOR 2-D 448
6.3.3 ISOPARAMETRIC FINITE ELEMENTS 451
IMAGE 4
XII CONTENTS
6.3.4 NUMERICAL INTEGRATION 456
6.3.5 DISPLACEMENT-BASED FINITE ELEMENT FORMULATIONS FOR 3- D SOLIDS 460
6.3.6 FRAMEWORK TO FORMULATE DISPLACEMENT-BASED FINITE EL- EMENTS 461
6.4 FINITE ELEMENTS FOR BEAMS, PLATES AND SHELLS 461
6.4.1 BERNOULLI-EULER BEAM FINITE ELEMENT 462
6.4.2 MATRIX AND FINITE ELEMENT STRUCTURAL ANALYSIS FOR FRAMES 464 6.4.3
PLATE AND SHELL FINITE ELEMENTS 468
6.4.4 BEAM FINITE ELEMENTS 473
6.5 EFFECTIVE FINITE ELEMENTS 476
6.5.1 CONVERGENCE OF DISPLACEMENT-BASED FINITE ELEMENT FOR- MULATIONS
AND THE EFFECTS OF LOCKING 476
6.5.2 LOCKING FOR THE 2-NODE TIMOSHENKO BEAM ELEMENT . . .. 479 6.5.3
LOCKING IN A GENERAL SETTING 485
6.6 FINITE ELEMENT MODELING TOOLS 489
6.6.1 COMBINING DIFFERENT TYPE OF ELEMENTS IN THE SAME MODEL489 6.6.2
CONSTRAINT EQUATIONS 490
6.6.3 RIGID LINKS 492
6.6.4 SPRING ELEMENTS 494
6.6.5 MODEL SYMMETRIES 495
6.6.6 SUBSTRUCTURES 497
6.6.7 CONNECTING DIFFERENT TYPE OF ELEMENTS 499
6.6.8 SKEW SYSTEMS 501
6.7 MESHING ISSUES AND ERROR ASSESSMENT 502
6.7.1 MESH GRADING 503
6.7.2 ELEMENT SHAPE 503
6.7.3 ERROR ESTIMATION AND ADAPTATIVE PROCEDURES 505 6.8 FINITE ELEMENT
MODEL CONSTRUCTION 509
6.9 A FINITE ELEMENT MODELING EXAMPLE 511
7. HIERARCHICAL MODELING EXAMPLES 519
7.1 BUILT-IN CANTILEVER SUBJECTED TO A TIP LOAD 519
7.1.1 BERNOULLI-EULER BEAM MODEL 520
7.1.2 TIMOSHENKO BEAM MODEL 521
7.1.3 PLANE STRESS SOLUTION 523
7.2 MACHINE TOOL JIG 540
7.2.1 BEAM MODEL 542
7.2.2 THE SHELL MODEL 545
7.2.3 THREE-DIMENSIONAL ELASTICITY MODEL 545
7.2.4 QUALITATIVE ANALYSIS 546
7.2.5 QUANTITATIVE ANALYSIS 549
7.3 MODELING OF A CARABINER 552
7.3.1 STRAIGHT BAR MODEL 552
7.3.2 CURVED BAR MODEL 553
IMAGE 5
CONTENTS XIII
7.3.3 THREE-DIMENSIONAL ELASTICITY MODEL 553
7.3.4 QUALITATIVE ANALYSIS 554
7.3.5 QUANTITATIVE ANALYSIS 555
8. MODELING FOR NONLINEAR ANALYSIS. AN APERGU 559
8.1 SOURCES OF NONLINEARITY 559
8.2 INCREMENTAL FORMULATION FOR NONLINEAR ANALYSIS 568 8.3 DETERMINATION
OF ULTIMATE LOADS LEADING TO STRUCTURAL COLLAPSE 578 8.4 MODELING
NONLINEAR PROBLEMS 587
REFERENCES 589
INDEX 593
|
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| author | Bucalem, Miguel Luiz Bathe, Klaus-Jürgen |
| author_facet | Bucalem, Miguel Luiz Bathe, Klaus-Jürgen |
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| discipline | Maschinenbau / Maschinenwesen |
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| id | DE-604.BV037350171 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:22:39Z |
| institution | BVB |
| isbn | 9783540263319 |
| language | English |
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| physical | XIII, 597 S. Ill., graph. Darst. |
| publishDate | 2011 |
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| publisher | Springer |
| record_format | marc |
| series2 | Computational fluid and solid mechanics |
| spelling | Bucalem, Miguel Luiz Verfasser aut The mechanics of solids and structures hierarchical modeling and the finite element solution Miguel Luiz Bucalem ; Klaus-Jürgen Bathe Berlin [u.a.] Springer 2011 XIII, 597 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computational fluid and solid mechanics Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Strukturmechanik (DE-588)4126904-4 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Strukturmechanik (DE-588)4126904-4 s Festkörpermechanik (DE-588)4129367-8 s Mathematisches Modell (DE-588)4114528-8 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Bathe, Klaus-Jürgen Verfasser aut http://deposit.dnb.de/cgi-bin/dokserv?id=2707361&prov=M&dok_var=1&dok_ext=htm text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2707361&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022503675&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bucalem, Miguel Luiz Bathe, Klaus-Jürgen The mechanics of solids and structures hierarchical modeling and the finite element solution Mathematisches Modell (DE-588)4114528-8 gnd Festkörpermechanik (DE-588)4129367-8 gnd Strukturmechanik (DE-588)4126904-4 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4129367-8 (DE-588)4126904-4 (DE-588)4017233-8 |
| title | The mechanics of solids and structures hierarchical modeling and the finite element solution |
| title_auth | The mechanics of solids and structures hierarchical modeling and the finite element solution |
| title_exact_search | The mechanics of solids and structures hierarchical modeling and the finite element solution |
| title_full | The mechanics of solids and structures hierarchical modeling and the finite element solution Miguel Luiz Bucalem ; Klaus-Jürgen Bathe |
| title_fullStr | The mechanics of solids and structures hierarchical modeling and the finite element solution Miguel Luiz Bucalem ; Klaus-Jürgen Bathe |
| title_full_unstemmed | The mechanics of solids and structures hierarchical modeling and the finite element solution Miguel Luiz Bucalem ; Klaus-Jürgen Bathe |
| title_short | The mechanics of solids and structures |
| title_sort | the mechanics of solids and structures hierarchical modeling and the finite element solution |
| title_sub | hierarchical modeling and the finite element solution |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Festkörpermechanik (DE-588)4129367-8 gnd Strukturmechanik (DE-588)4126904-4 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Mathematisches Modell Festkörpermechanik Strukturmechanik Finite-Elemente-Methode |
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