Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | German |
| Published: |
Augsburg
Wissner
1997
|
| Series: | Augsburger mathematisch-naturwissenschaftliche Schriften
15 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | III, 131 S. graph. Darst. |
| ISBN: | 3896390619 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV011281653 | ||
| 003 | DE-604 | ||
| 005 | 19971021 | ||
| 007 | t | ||
| 008 | 970325s1997 gw d||| m||| 00||| ger d | ||
| 016 | 7 | |a 950016977 |2 DE-101 | |
| 020 | |a 3896390619 |9 3-89639-061-9 | ||
| 035 | |a (OCoLC)40293091 | ||
| 035 | |a (DE-599)BVBBV011281653 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-384 |a DE-12 |a DE-37 |a DE-91 |a DE-739 |a DE-188 |a DE-706 | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a MTA 090d |2 stub | ||
| 084 | |a MAT 674d |2 stub | ||
| 100 | 1 | |a Bader, Harald |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements |c Harald Bader |
| 264 | 1 | |a Augsburg |b Wissner |c 1997 | |
| 300 | |a III, 131 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Augsburger mathematisch-naturwissenschaftliche Schriften |v 15 | |
| 502 | |a Zugl.: Augsburg, Univ., Diss., 1996 | ||
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Mechanik |0 (DE-588)4042095-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Adaptive Schrittweite |0 (DE-588)4311119-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elastoplastische Deformation |0 (DE-588)4306794-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Strukturmechanik |0 (DE-588)4126904-4 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Strukturmechanik |0 (DE-588)4126904-4 |D s |
| 689 | 0 | 1 | |a Nichtlineare Mechanik |0 (DE-588)4042095-4 |D s |
| 689 | 0 | 2 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Elastoplastische Deformation |0 (DE-588)4306794-3 |D s |
| 689 | 1 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 1 | 2 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
| 689 | 1 | 3 | |a Adaptive Schrittweite |0 (DE-588)4311119-1 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Augsburger mathematisch-naturwissenschaftliche Schriften |v 15 |w (DE-604)BV009824413 |9 15 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007576416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007576416 | |
Record in the Search Index
| _version_ | 1807594173789896704 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
1
2
THE
ELASTO-PLASTIC
BOUNDARY
VALUE
PROBLEM
4
2.1
EQUILIBRIUM
EQUATIONS
AND
CONSTITUENT
LAWS
.
4
2.1.1
CLASSICAL
FORMULATION
.
4
2.1.2
HENCKY
'
S
LAW
.
9
2.2
EXISTENCE
AND
UNIQUENESS
OF
SOLUTIONS
.
10
2.2.1
VARIATIONAL
PRINCIPLES
.
10
2.2.2
DEFORMATION
THEORY
.
:
.
.
.
12
2.2.3
FLOW
THEORY
.
18
2.3
THE
INCREMENTAL
EQUATION
OF
MOTION
.
20
2.3.1
INCREMENTATION
.
20
2.3.2
STRESS
AND
STRAIN
MEASURES
.
21
2.3.3
INCREMENTAL
PROCEDURES
.
23
3
FINITE
ELEMENT
DISCRETIZATION
28
3.1
CONFORMING
FINITE
ELEMENT
METHODS
.
28
3.1.1
TRIANGULATION
.
28
3.1.2
FINITE
ELEMENTS
.
29
3.1.3
FINITE
ELEMENT
SPACES
.
32
3.2
NONCONFORMING
FINITE
ELEMENT
METHODS
.
33
II
CONTENTS
3.2.1
ISOPARAMETRIC
FINITE
ELEMENTS
.
33
3.2.2
NUMERICAL
INTEGRATION
.
35
3.3
APPROXIMATION
OF
THE
INCREMENTAL
EQUATIONS
.
37
4
NUMERICAL
SOLUTION
PROCEDURES
43
4.1
GENERAL
SOLUTION
PROCEDURES
FOR
NONLINEAR
PROBLEMS
.
44
4.1.1
NEWTON
'
S
METHOD
.
44
4.1.2
CONTINUATION
METHOD
.
46
4.1.3
CONSTRAINT
EQUATIONS
.
.
48
4.2
NUMERICAL
ALGORITHMS
.
51
4.2.1
THE
ARC-LENGTH
METHOD
.
51
4.2.2
COMPUTATIONAL
ASPECTS
.
53
4.2.3
TERMINATION
CRITERIA
.
57
5
AUTOMATIC
STEP-LENGTH
ADAPTATION
61
5.1
INVARIANCE
PRINCIPLES
.
61
5.1.1
AFFINE
INVARIANCE
.
61
5.1.2
AFFINE
INVARIANT
THEOREMS
.
62
5.2
LOCAL
NEWTON
METHODS
.
64
5.2.1
LOCAL
EXACT
NEWTON
METHODS
.
64
5.2.2
LOCAL
INEXACT
NEWTON
METHODS
.
66
5.3
GLOBALIZATION
CONCEPTS
.
68
5.3.1
GLOBAL
NEWTON
METHODS
.
68
5.3.2
GLOBAL
INEXACT
NEWTON
METHODS
.
73
5.3.3
CONTINUATION
METHODS
.
75
5.4
COMPUTATIONAL
ASPECTS
.
79
5.4.1
EXACT
SOLUTION
OF
EQUATIONS
.
79
5.4.2
INEXACT
SOLUTION
OF
EQUATIONS
.
83
CONTENTS
III
6
SOLUTION
OF
THE
LINEAR
SYSTEMS
OF
EQUATIONS
89
6.1
GENERAL
PROPERTIES
OF
ITERATIVE
PROCEDURES
.
90
6.2
CONJUGATE
GRADIENT
METHODS
.
92
6.2.1
GRADIENT
METHODS
.
93
6.2.2
CONJUGATE
SEARCH
DIRECTIONS
.
94
6.2.3
PRECONDITIONING
.
96
6.3
DOMAIN
DECOMPOSITION
METHODS
.
99
7
NUMERICAL
EXAMPLES
104
7.1
NECKING
OF
A
CYLINDRICAL
BAR
.
105
7.2
SPHERICAL
CAP
UNDER
GRAVITY
LOAD
.
112
8
CONCLUSION
122
BIBLIOGRAPHY
124
BIBLIOGRAPHY
124 |
| any_adam_object | 1 |
| author | Bader, Harald |
| author_facet | Bader, Harald |
| author_role | aut |
| author_sort | Bader, Harald |
| author_variant | h b hb |
| building | Verbundindex |
| bvnumber | BV011281653 |
| classification_rvk | SK 950 |
| classification_tum | MTA 090d MAT 674d |
| ctrlnum | (OCoLC)40293091 (DE-599)BVBBV011281653 |
| discipline | Physik Mathematik |
| format | Thesis Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV011281653</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19971021</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">970325s1997 gw d||| m||| 00||| ger d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">950016977</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3896390619</subfield><subfield code="9">3-89639-061-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)40293091</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011281653</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">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-37</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MTA 090d</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 674d</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bader, Harald</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements</subfield><subfield code="c">Harald Bader</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Augsburg</subfield><subfield code="b">Wissner</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">III, 131 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="1" ind2=" "><subfield code="a">Augsburger mathematisch-naturwissenschaftliche Schriften</subfield><subfield code="v">15</subfield></datafield><datafield tag="502" ind1=" " ind2=" "><subfield code="a">Zugl.: Augsburg, Univ., Diss., 1996</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Randwertproblem</subfield><subfield code="0">(DE-588)4048395-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Mechanik</subfield><subfield code="0">(DE-588)4042095-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Adaptive Schrittweite</subfield><subfield code="0">(DE-588)4311119-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Elastoplastische Deformation</subfield><subfield code="0">(DE-588)4306794-3</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="650" ind1="0" ind2="7"><subfield code="a">Strukturmechanik</subfield><subfield code="0">(DE-588)4126904-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Strukturmechanik</subfield><subfield code="0">(DE-588)4126904-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Nichtlineare Mechanik</subfield><subfield code="0">(DE-588)4042095-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><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="689" ind1="1" ind2="0"><subfield code="a">Elastoplastische Deformation</subfield><subfield code="0">(DE-588)4306794-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Randwertproblem</subfield><subfield code="0">(DE-588)4048395-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="2"><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="1" ind2="3"><subfield code="a">Adaptive Schrittweite</subfield><subfield code="0">(DE-588)4311119-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Augsburger mathematisch-naturwissenschaftliche Schriften</subfield><subfield code="v">15</subfield><subfield code="w">(DE-604)BV009824413</subfield><subfield code="9">15</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB 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=007576416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007576416</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV011281653 |
| illustrated | Illustrated |
| indexdate | 2024-08-17T00:55:35Z |
| institution | BVB |
| isbn | 3896390619 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007576416 |
| oclc_num | 40293091 |
| open_access_boolean | |
| owner | DE-384 DE-12 DE-37 DE-91 DE-BY-TUM DE-739 DE-188 DE-706 |
| owner_facet | DE-384 DE-12 DE-37 DE-91 DE-BY-TUM DE-739 DE-188 DE-706 |
| physical | III, 131 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Wissner |
| record_format | marc |
| series | Augsburger mathematisch-naturwissenschaftliche Schriften |
| series2 | Augsburger mathematisch-naturwissenschaftliche Schriften |
| spelling | Bader, Harald Verfasser aut Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements Harald Bader Augsburg Wissner 1997 III, 131 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Augsburger mathematisch-naturwissenschaftliche Schriften 15 Zugl.: Augsburg, Univ., Diss., 1996 Randwertproblem (DE-588)4048395-2 gnd rswk-swf Nichtlineare Mechanik (DE-588)4042095-4 gnd rswk-swf Adaptive Schrittweite (DE-588)4311119-1 gnd rswk-swf Elastoplastische Deformation (DE-588)4306794-3 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Strukturmechanik (DE-588)4126904-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Strukturmechanik (DE-588)4126904-4 s Nichtlineare Mechanik (DE-588)4042095-4 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Elastoplastische Deformation (DE-588)4306794-3 s Randwertproblem (DE-588)4048395-2 s Adaptive Schrittweite (DE-588)4311119-1 s Augsburger mathematisch-naturwissenschaftliche Schriften 15 (DE-604)BV009824413 15 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007576416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bader, Harald Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements Augsburger mathematisch-naturwissenschaftliche Schriften Randwertproblem (DE-588)4048395-2 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd Adaptive Schrittweite (DE-588)4311119-1 gnd Elastoplastische Deformation (DE-588)4306794-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Strukturmechanik (DE-588)4126904-4 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4042095-4 (DE-588)4311119-1 (DE-588)4306794-3 (DE-588)4017233-8 (DE-588)4126904-4 (DE-588)4113937-9 |
| title | Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements |
| title_auth | Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements |
| title_exact_search | Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements |
| title_full | Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements Harald Bader |
| title_fullStr | Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements Harald Bader |
| title_full_unstemmed | Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements Harald Bader |
| title_short | Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements |
| title_sort | automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements |
| topic | Randwertproblem (DE-588)4048395-2 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd Adaptive Schrittweite (DE-588)4311119-1 gnd Elastoplastische Deformation (DE-588)4306794-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Strukturmechanik (DE-588)4126904-4 gnd |
| topic_facet | Randwertproblem Nichtlineare Mechanik Adaptive Schrittweite Elastoplastische Deformation Finite-Elemente-Methode Strukturmechanik Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007576416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009824413 |
| work_keys_str_mv | AT baderharald automaticsteplengthadaptionforthenumericalsolutionofnonlinearmechanicalproblemsdiscretizedbyfiniteelements |