Computational solid mechanics: variational formulation and high order approximation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
CRC Press
2015
|
| Schlagworte: | |
| Online-Zugang: | Klappentext Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xxvii, 647 pages illustrations 26 cm |
| ISBN: | 9781439860014 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV042158139 | ||
| 003 | DE-604 | ||
| 005 | 20160122 | ||
| 007 | t | ||
| 008 | 141029s2015 a||| |||| 00||| eng d | ||
| 015 | |a GBB168655 |2 dnb | ||
| 020 | |a 9781439860014 |c hbk |9 978-1-4398-6001-4 | ||
| 020 | |z 1439860017 |9 1439860017 | ||
| 035 | |a (OCoLC)896157907 | ||
| 035 | |a (DE-599)BVBBV042158139 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-29T |a DE-703 | ||
| 084 | |a UF 1200 |0 (DE-625)145559: |2 rvk | ||
| 100 | 1 | |a Bittencourt, Marco L. |d 1964- |e Verfasser |0 (DE-588)1068482737 |4 aut | |
| 245 | 1 | 0 | |a Computational solid mechanics |b variational formulation and high order approximation |c Marco L. Bittencourt |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press |c 2015 | |
| 300 | |a xxvii, 647 pages |b illustrations |c 26 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mechanics | |
| 650 | 0 | 7 | |a Festkörpermechanik |0 (DE-588)4129367-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Festkörpermechanik |0 (DE-588)4129367-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027597847&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027597847&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027597847 | ||
Datensatz im Suchindex
| _version_ | 1804152653978009600 |
|---|---|
| adam_text | Presents a Systematic Approach for Modeling Mechanical Models Using
Variational Formulation—Uses Real-World Examples and Applications of
Mechanical Models
Utilizing material developed in a classroom setting and tested over a 12-year
period, Computational Solid Mechanics: Variational Formulation and High
Order Approximation details an approach that establishes a logical sequence
for the treatment of any mechanical problem. Incorporating variational formulation
based on the principle of virtual work, this text considers various aspects of
mechanical models, explores analytical mechanics and their variational principles,
and presents model approximations using the finite element method. It introduces
the basics of mechanics for one-, two-, and three-dimensional models, emphasizes
the simplification aspects required in their formulation, and provides relevant
applications.
Introduces Approximation Concepts Gradually throughout the Chapters
Organized into ten chapters, this text provides a clear separation of formulation
and finite element approximation. It details standard procedures to formulate and
approximate models, while at the same time illustrating their application via
software. Chapter one provides a general introduction to variational formulation
and an overview of the mechanical models to be presented in the other chapters.
Chapter two uses the concepts on equilibrium that readers should have to intro-
duce basic notions on kinematics, duality, virtual work, and the PVW. Chapters
three to ten present mechanical models, approximation and applications to bars,
shafts, beams, beams with shear, general two- and three-dimensional beams,
solids, plane models, and generic torsion and plates.
Learn Theory Step by Step
In each chapter, the material profiles all aspects of a specific mechanical model,
and uses the same sequence of steps for all models. The steps include kinematics,
strain, rigid body deformation, internal loads, external loads, equilibrium, constitu-
tive equations, and structural design.
The text uses MATLAB® scripts to calculate analytic and approximated solutions
of the considered mechanical models.
Computational Solid Mechanics: Variational Formulation and High Order
Approximation presents mechanical models, their main hypotheses, and
applications, and is intended for graduate and undergraduate engineering
students taking courses in solid mechanics.
Contents,?
Chapter 1 INTRODUCTION.................................................... 1
1.1 Initial Aspects.................................................2
1.1.1 Objectives of Continuum Mechanics........................2
1.1.2 Definition of Bodies.....................................2
1.1.3 Analytic and Newtonian Formulations......................3
1.1.4 Formulation Methodology..................................5
1.2 Bars............................................................6
1.3 Shafts..........................................................8
1.4 Beams...........................................................8
1.5 Two-Dimensional Models.........................................10
1.6 Plates.........................................................10
1.7 Linear Elastic Solids..........................................11
Chapter 2 EQUILIBRIUM OF PARTICLES AND RIGID BODIES............................15
2.1 Introduction...................................................15
2.2 Diagrammatic Conventions.......................................15
2.2.1 Supports................................................15
2.2.2 Loadings.............................................. 16
2.3 Equilibrium of Particles.......................................17
2.4 Equilibrium of Rigid Bodies.................................. 19
2.5 Principle of Virtual Power (PVP)...............................24
2.6 Some Aspects about the Definition of Power.....................42
2.7 Final Comments.................................................42
2.8 Problems.......................................................43
Chapter 3 FORMULATION AND APPROXIMATION OF BARS.............................. 45
3.1 Introduction...................................................45
3.2 Kinematics............................................... 45
3.3 Strain Measure.................................................48
3.4 Rigid Actions..................................................50
3.5 Determination of Internal Loads................................50
3.6 Determination of External Loads................................53
3.7 Equilibrium....................................................54
3.8 Material Behavior............................................ 60
3.8.1 Experimental Traction and Compression Diagrams..........60
3.8.2 Poisson Ratio...........................................65
3.8.3 Hooke’s Law.............................................66
3.9 Application of the Constitutive Equation.......................67
3.10 Design and Verification........................................71
3.11 Bars Subjected to Temperature Changes..........................73
3.12 Volume and Area Strain Measures................................75
3.13 Singularity Functions for External Loading Representation .....77
3.14 Summary of the Variational Formulation of Bars.................94
3.15 Approximated Solution..........................................96
Vili
Contents
3.15.1 Analogy of the Approximated Solution with Vectors...........96
3.15.2 Collocation Method..........................................99
3.15.3 Weighted Residuals Method..................................101
3.15.4 Least Squares Method.......................................102
3.15.5 Galerkin Method............................................104
3.15.6 Finite Element Method (FEM)................................110
3.16 Analysis of Trusses............................................. 115
3.17 Final Comments.................................................. 121
3.18 Problems.........................................................121
Chapter 4 FORMULATION AND APPROXIMATION OF SHAFTS....................................127
4.1 Introduction......................................................127
4.2 Kinematics........................................................127
4.3 Strain Measure....................................................132
4.4 Rigid Actions..................................................... 136
4.5 Determination of Internal Loads...................................137
4.6 Determination of External Loads...................................139
4.7 Equilibrium......................................................140
4.8 Material Behavior.................................................146
4.9 Application of the Constitutive Equation..........................148
4.10 Design and Verification..........................................154
4.11 Singularity Functions for External Loading Representation........155
4.12 Summary of the Variational Formulation of Shafts.................165
4.13 Approximated Solution............................................167
4.14 Mathematical Aspects of the FEM..................................172
4.15 Local Coordinate Systems.........................................174
4.16 One-Dimensional Shape Functions..................................176
4.16.1 Nodal Basis................................................176
4.16.2 Modal Basis................................................181
4.16.3 Schur’s Complement.........................................183
4.16.4 Sparsity and Numerical Conditioning........................185
4.17 Mapping..........................................................187
4.18 Numerical Integration............................................193
4.19 Collocation Derivative...........................................196
4.20 Final Comments...................................................199
4.21 Problems.........................................................199
Chapter 5 FORMULATION AND APPROXIMATION OF BEAMS.....................................203
5.1 Introduction......................................................203
5.2 Kinematics........................................................204
5.3 Strain Measure....................................................207
5.4 Rigid Actions.....................................................209
5.5 Determination of Internal Loads...................................209
5.6 Determination of External Loads...................................212
5.7 Equilibrium.......................................................213
5.8 Application of the Constitutive Equation..........................222
5.9 Design and Verification...........................................229
5.10 Singularity Functions for External Loading Representation........230
5.11 Summary of the Variational Formulation for the Euler-Bernoulli Beam ... 255
5.12 Buckling of Columns............................................. 256
Contents ix
5.12Л Euler Column.............................................258
5.13 Approximated Solution...........................................263
5.14 High-Order Beam Element.........................................274
5.15 Mathematical Aspects of the FEM.................................280
5.16 Final Comments..................................................286
5.17 Problems........................................................286
Chapter 6 FORMULATION AND APPROXIMATION OF BEAM IN SHEAR..................291
6.1 Introduction....................................................291
6.2 Ki nematics.....................................................291
6.3 Strain Measure................................................ 294
6.4 Rigid Actions...................................................296
6.5 Determination of Internal Loads.................................296
6.6 Determination of External Loads.................................300
6.7 Equilibrium.....................................................300
6.8 Application of the Constitutive Equation........................302
6.9 Shear Stress Distribution.......................................314
6.9.1 Rectangular Cross-Section................................315
6.9.2 Circular Cross-Section...................................319
6.9.3 I-shaped Cross-Section...................................321
6.10 Design and Verification........................................327
6.11 Standardized Cross-Section Shapes...............................329
6.12 Shear Center....................................................331
6.13 Summary of the Variational Formulation of Beams with Shear......334
6.14 Energy Methods.................................................335
6.14.1 Strain Energy............................................336
6.14.2 Complementary Strain Energy..............................339
6.14.3 Complementary External Work..............................339
6.14.4 Principle of Energy Conservation.........................340
6.14.5 Method of Virtual Forces.................................342
6.15 Approximated Solution...........................................348
6.16 Mathematical Aspects of the FEM.................................356
6.17 Final Comments..................................................356
6.18 Problems........................................................357
Chapter 7 FORMULATION AND APPROXIMATION OF TWO/THREE-DIMENSIO-
NAL BEAMS............................................................359
7.1 Introduction....................................................359
7.2 TWo-Dimensional Beam............................................361
7.2.1 Kinematics...............................................361
7.2.2 Strain Measure...........................................363
7.2.3 Rigid Body Actions.......................................363
7.2.4 Determination of Internal Loads..........................364
7.2.5 Determination of External Loads........................ 365
7.2.6 Equilibrium..............................................367
7.2.7 Application of the Constitutive Equation.................368
7.2.8 Stress Distributions.....................................369
7.2.9 Design and Verification..................................372
7.3 Three-Dimensional Beam..........................................382
7.3.1 Kinematics...............................................382
x Contents
7.3.2 Strain Measure........................................ 386
7.3.3 Rigid Body Actions..........................................386
7.3.4 Determination of Internal Loads.............................387
7.3.5 Determination of External Loads.............................389
7.3.6 Equilibrium.................................................390
7.3.7 Application of the Constitutive Equation....................392
7.3.8 Stress Distributions........................................394
7.3.9 Design and Verification.....................................397
7.4 BeamLab Program.....................................................417
7.5 Summary of the Variational Formulation of Beams.....................418
7.6 Aproximated Solution................................................420
7.7 Final Comments......................................................433
7.8 Problems............................................................433
Chapter 8 FORMULATION AND APPROXIMATION OF SOLIDS.....................................439
8.1 Introduction.................................................... 439
8.2 Kinematics..........................................................439
8.3 Strain Measure......................................................440
8.4 Rigid Actions.......................................................446
8.5 Determination of Internal Loads.....................................447
8.6 Determination of External Loads.....................................450
8.7 Equilibrium.........................................................453
8.8 Generalized Hooke’s Law.............................................456
8.9 Application of the Constitutive Equation............................460
8.10 Formulation Employing Tensors......................................461
8.10.1 Body........................................................461
8.10.2 Vectors.....................................................462
8.10.3 Kinematics................................................ 464
8.10.4 Strain Measure..............................................464
8.10.5 Rigid Actions...............................................475
8.10.6 Determination of Internal Loads.............................477
8.10.7 Equilibrium............................................. 482
8.10.8 Application of the Constitutive Equation....................482
8.11 Verification of Linear Elastic Solids..............................484
8.11.1 Transformation of Vectors and Tensors.......................484
8.11.2 Eigenvalue Problem..........................................487
8.11.3 Principal Stresses and Principal Directions.................490
8.11.4 Principal Stresses for a Plane Stress Problem...............490
8.11.5 Mohr’s Circle............................................. 494
8.11.6 Maximum Shear Stress Theory (Tresca Criterion)..............498
8.11.7 Maximum Distortion Energy Theory (von Mises Criterion)......501
8.11.8 Rankine Criterion for Brittle Materials.....................503
8.11.9 Comparison of Tresca, von Mises, and Rankine Criteria.......504
8.12 Approximation of Linear Elastic Solids.............................505
8.12.1 Weak Form...................................................505
8.12.2 Shape Functions for Structured Elements.....................509
8.12.3 Shape Functions for Nonstructured Elements................ 523
8.12.4 Mapping................................................... 535
8.12.5 Surface Jacobian............................................540
8.13 Final Comments.....................................................544
xi
544
547
547
548
549
554
558
567
568
570
570
571
573
574
576
577
579
582
583
585
588
591
592
596
599
600
600
603
603
603
608
610
612
622
624
627
632
636
638
639
641
8.14 Problems
FORMULATION AND APPROXIMATION OF PLANE PROBLEMS ...
9.1 Plane Stress State...........................................
9.2 Plane Strain State............................................
9.3 Compatibility Equations.......................................
9.4 Analytical Solutions for Plane Problems in Linear Elasticity.
9.5 Analytical Solutions for Problems in Three-Dimensional Elasticity ..
9.6 Plane State Approximation....................................
9.7 (hp)2fem Program.............................................
9.8 Torsion of Generic Sections..................................
9.8.1 Kinematics............................................
9.8.2 Strain Measures.......................................
9.8.3 Rigid Actions.........................................
9.8.4 Determination of Internal Loads........................
9.8.5 Determination of External Loads and Equilibrium.......
9.8.6 Application of the Constitutive Equation...............
9.8.7 Shear Stress Distribution in Elliptical Cross-Section.
9.8.8 Analogy with Membranes................................
9.8.9 Summary of the Variational Formulation of Generic Torsion
9.8.10 Approximated Solution.................................
9.9 Multidimensional Numerical Integration.......................
9.10 Summary of the Variational Formulation of Mechanical Models..
9.10.1 External Power........................................
9.10.2 Internal Power........................................
9.10.3 Principle of Virtual Power (PVP)......................
9.11 Final Comments...............................................
9.12 Problems.....................................................
FORMULATION AND APPROXIMATION OF PLATES...........................
10.1 Introduction.................................................
10.2 Kinematics...................................................
10.3 Strain Measure...............................................
10.4 Rigid Actions................................................
10.5 Determination of Internal Loads..............................
10.6 Determination of External Loads and Equilibrium..............
10.7 Application of the Constitutive Equation.....................
10.8 Approximated Solution........................................
10.8.1 Plate Finite Elements.................................
10.8.2 High-Order Finite Element.............................
10.9 Problems.....................................................
|
| any_adam_object | 1 |
| author | Bittencourt, Marco L. 1964- |
| author_GND | (DE-588)1068482737 |
| author_facet | Bittencourt, Marco L. 1964- |
| author_role | aut |
| author_sort | Bittencourt, Marco L. 1964- |
| author_variant | m l b ml mlb |
| building | Verbundindex |
| bvnumber | BV042158139 |
| classification_rvk | UF 1200 |
| ctrlnum | (OCoLC)896157907 (DE-599)BVBBV042158139 |
| discipline | Physik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01748nam a2200373 c 4500</leader><controlfield tag="001">BV042158139</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160122 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">141029s2015 a||| |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">GBB168655</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781439860014</subfield><subfield code="c">hbk</subfield><subfield code="9">978-1-4398-6001-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">1439860017</subfield><subfield code="9">1439860017</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)896157907</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042158139</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-703</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UF 1200</subfield><subfield code="0">(DE-625)145559:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bittencourt, Marco L.</subfield><subfield code="d">1964-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1068482737</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Computational solid mechanics</subfield><subfield code="b">variational formulation and high order approximation</subfield><subfield code="c">Marco L. Bittencourt</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton, Fla. [u.a.]</subfield><subfield code="b">CRC Press</subfield><subfield code="c">2015</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xxvii, 647 pages</subfield><subfield code="b">illustrations</subfield><subfield code="c">26 cm</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="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mechanics</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Festkörpermechanik</subfield><subfield code="0">(DE-588)4129367-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Festkörpermechanik</subfield><subfield code="0">(DE-588)4129367-8</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">Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment</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=027597847&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Klappentext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment</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=027597847&sequence=000004&line_number=0002&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:BVB01-027597847</subfield></datafield></record></collection> |
| id | DE-604.BV042158139 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:14:08Z |
| institution | BVB |
| isbn | 9781439860014 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027597847 |
| oclc_num | 896157907 |
| open_access_boolean | |
| owner | DE-29T DE-703 |
| owner_facet | DE-29T DE-703 |
| physical | xxvii, 647 pages illustrations 26 cm |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Bittencourt, Marco L. 1964- Verfasser (DE-588)1068482737 aut Computational solid mechanics variational formulation and high order approximation Marco L. Bittencourt Boca Raton, Fla. [u.a.] CRC Press 2015 xxvii, 647 pages illustrations 26 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mechanics Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027597847&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027597847&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bittencourt, Marco L. 1964- Computational solid mechanics variational formulation and high order approximation Mechanics Festkörpermechanik (DE-588)4129367-8 gnd |
| subject_GND | (DE-588)4129367-8 |
| title | Computational solid mechanics variational formulation and high order approximation |
| title_auth | Computational solid mechanics variational formulation and high order approximation |
| title_exact_search | Computational solid mechanics variational formulation and high order approximation |
| title_full | Computational solid mechanics variational formulation and high order approximation Marco L. Bittencourt |
| title_fullStr | Computational solid mechanics variational formulation and high order approximation Marco L. Bittencourt |
| title_full_unstemmed | Computational solid mechanics variational formulation and high order approximation Marco L. Bittencourt |
| title_short | Computational solid mechanics |
| title_sort | computational solid mechanics variational formulation and high order approximation |
| title_sub | variational formulation and high order approximation |
| topic | Mechanics Festkörpermechanik (DE-588)4129367-8 gnd |
| topic_facet | Mechanics Festkörpermechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027597847&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027597847&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bittencourtmarcol computationalsolidmechanicsvariationalformulationandhighorderapproximation |