Free material optimization: mathematical analysis and numerical solution
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Berlin
dissertation.de
2001
|
| Edition: | Als Ms. gedr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Erlangen-Nürnberg, Univ., Diss., 2001. - Enth. Zsfassung in dt. Sprache |
| Physical Description: | XXIV, 163 S. graph. Darst. |
| ISBN: | 3898253104 |
Staff View
MARC
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| 100 | 1 | |a Werner, Ralf |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Free material optimization |b mathematical analysis and numerical solution |c von Ralf Werner |
| 250 | |a Als Ms. gedr. | ||
| 264 | 1 | |a Berlin |b dissertation.de |c 2001 | |
| 300 | |a XXIV, 163 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 500 | |a Zugl.: Erlangen-Nürnberg, Univ., Diss., 2001. - Enth. Zsfassung in dt. Sprache | ||
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Record in the Search Index
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|---|---|
| adam_text |
CONTENTS
1.
INTRODUCTION
TO
MATERIAL
OPTIMIZATION
.
1
1.1
MOTIVATION
.
2
1.2
ELASTICITY
THEORY
.
4
1.2.1
THE
CLASSICAL
FORMULATION
.
4
1.2.2
THE
WEAK
FORMULATION
.
11
1.2.3
THE
VARIATIONAL
FORMULATION
.
13
1.3
FORMULATION
OF
THE
OPTIMIZATION
PROBLEM
.
14
1.3.1
MOTIVATION
.
14
1.3.2
SHORT
OVERVIEW
.
16
1.3.3
THE
FREE
MATERIAL
DESIGN
PROBLEM
.
20
2.
REFORMULATIONS
OF
THE
DESIGN
PROBLEMS
.
25
2.1
PRELIMINARIES
.
25
2.1.1
STANDARD
ASSUMPTIONS
.
25
2.1.2
REFORMULATION
OF
COMPLIANCE
.
26
2.1.3
ILL-POSEDNESS
OF
THE
DESIGN
PROBLEMS
.
27
2.2
REFORMULATIONS
OF
THE
DESIGN
PROBLEMS
.
28
2.2.1
THE
SINGLE
LOAD
CASE
(MO5)
.
28
2.2.2
THE
MULTIPLE
LOAD
CASE
(MO
M
)
.
29
2.2.3
THE
VARIABLE
THICKNESS
SHEET
PROBLEM
(VTS§)
.
29
2.3
TECHNICAL
PREPARATIONS
.
29
2.3.1
SOME
FIRST
CONTINUITY
RESULTS
.
30
2.3.2
SOME
FURTHER
TECHNICAL
DETAILS
.
32
3.
EXISTENCE
OF
OPTIMAL
MATERIAL
.
37
3.1
A
FIRST
APPROACH
.
38
3.2
THE
SADDLE
POINT
APPROACH
.
39
3.2.1
EXISTENCE
OF
OPTIMAL
MATERIAL
.
40
XIV
CONTENTS
3.2.2
RELATIONSHIP
BETWEEN
(MOS)
AND
(VTS§)
.
41
3.2.3
CONSEQUENCES
.
44
3.2.4
FURTHER
RESULTS
.
46
3.2.5
COMPARISON
TO
PREVIOUS
RESULTS
.
48
3.3
EXISTENCE
VIA
DUALITY
THEORY
.
48
3.3.1
EQUIVALENT
FORMULATION
OF
(MO#)
.
49
3.3.2
THE
PRIMAL
PROBLEM
(MOS
T
P)
.
54
3.3.3
PRIMAL
AND
DUAL
SOLVABILITY
OF
(MOG,P)
.
57
3.3.4
EXPLOITING
THE
COMPLEMENTARY
SLACKNESS
CONDITION
66
4.
COMPUTATIONAL
TREATMENT
.
69
4.1
A
FINITE
ELEMENT
APPROACH
.
70
4.1.1
PROBLEM
SETTING
.
70
4.1.2
CONVERGENCE
THEORY
.
72
4.1.3
APPLICATION
TO
(MO$P)
.
79
4.1.4
FURTHER
DISCRETIZED
FORMULATIONS
.
90
4.1.5
CONCLUSION
.
92
4.2
NUMERICAL
IMPLEMENTATION
AND
SOFTWARE
REALIZATION
.
.
93
4.2.1
DESCRIPTION
OF
THE
SOFTWARE
PACKAGE
M
OPED
.
.
96
4.2.2
DESCRIPTION
OF
THE
SOFTWARE
PACKAGE
VIRES
.
97
4.2.3
THE
VISUALIZATION
PROBLEM
.
98
4.2.4
NUMERICAL
SOLUTION
OF
(VTSG
P)
-
THE
PBM
METHODL03
4.3
NUMERICAL
EXAMPLES
.
108
4.3.1
THE
MBB
BEAM
.
110
4.3.2
OPTIMIZATION
OF
A
BRIDGE
.
112
4.3.3
THE
PEDAL
OF
A
BIKE
.
115
4.3.4
CONCLUSION
.
115
5.
THE
MULTIPLE
LOAD
CASE
.
119
5.1
THE
SADDLE
POINT
APPROACH
.
120
5.2
DUALITY
APPROACH
.
123
5.2.1
PRELIMINARIES
.
123
5.2.2
APPLICATION
TO
THE
MULTIPLE
LOAD
FORMULATION
.
.
127
5.2.3
CONCEPTUAL
ALGORITHM
.
129
5.2.4
OUTLOOK
.
132
5.3
DISCRETIZATION
APPROACHES
.
133
CONTENTS
XV
APPENDIX
135
A.
SADDLE
POINT
THEORY
.
137
A.L
PROBLEM
SETTING
.
137
A.2
EXISTENCE
OF
SADDLE
POINTS
.
139
A.
2.1
STANDARD
THEORY
.
139
A.
2.2
GENERALIZED
VERSION
.
140
A.
3
CHARACTERIZATION
OF
SADDLE
POINTS
.
141
B.
LAGRANGE
DUALITY
THEORY
.
143
B.L
LINK
TO
SADDLE
POINT
THEORY
.
144
B.2
EXISTENCE
OF
PRIMAL
AND
DUAL
SOLUTIONS
.
145
B.2.1
EXISTENCE
OF
PRIMAL
SOLUTIONS
.
145
B.2.2
RELATIONSHIP
BETWEEN
PRIMAL
AND
DUAL
PROBLEM
.
146
B.2.
3
EXISTENCE
OF
DUAL
SOLUTIONS
.
146
B.3
THEOREM
OF
KARUSH,
KUHN
AND
TUCKER
.
148
C.
MISCELLANEOUS
.
149
C.L
SEMIDEFINITE
PROGRAMMING
.
149
C.2
BASICS
FROM
FUNCTIONAL
ANALYSIS
.
150
C.2.1
WEAK
LOWER
SEMICONTINUITY
WITH
RESPECT
TO
A
CONE
151
C.2.
2
KORN
'
S
INEQUALITY
ON
EQUIVALENT
NORMS
.
152 |
| any_adam_object | 1 |
| author | Werner, Ralf |
| author_facet | Werner, Ralf |
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| bvnumber | BV013883712 |
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| discipline | Mathematik |
| edition | Als Ms. gedr. |
| format | Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV013883712 |
| illustrated | Illustrated |
| indexdate | 2024-08-23T00:44:04Z |
| institution | BVB |
| isbn | 3898253104 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009498529 |
| oclc_num | 76254488 |
| open_access_boolean | |
| owner | DE-29 DE-29T DE-703 DE-706 |
| owner_facet | DE-29 DE-29T DE-703 DE-706 |
| physical | XXIV, 163 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | dissertation.de |
| record_format | marc |
| spelling | Werner, Ralf Verfasser aut Free material optimization mathematical analysis and numerical solution von Ralf Werner Als Ms. gedr. Berlin dissertation.de 2001 XXIV, 163 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zugl.: Erlangen-Nürnberg, Univ., Diss., 2001. - Enth. Zsfassung in dt. Sprache Semidefinite Optimierung (DE-588)4663806-4 gnd rswk-swf Dualitätstheorie (DE-588)4150801-4 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Strukturoptimierung (DE-588)4183811-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Strukturoptimierung (DE-588)4183811-7 s Dualitätstheorie (DE-588)4150801-4 s Semidefinite Optimierung (DE-588)4663806-4 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009498529&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Werner, Ralf Free material optimization mathematical analysis and numerical solution Semidefinite Optimierung (DE-588)4663806-4 gnd Dualitätstheorie (DE-588)4150801-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Strukturoptimierung (DE-588)4183811-7 gnd |
| subject_GND | (DE-588)4663806-4 (DE-588)4150801-4 (DE-588)4128130-5 (DE-588)4183811-7 (DE-588)4113937-9 |
| title | Free material optimization mathematical analysis and numerical solution |
| title_auth | Free material optimization mathematical analysis and numerical solution |
| title_exact_search | Free material optimization mathematical analysis and numerical solution |
| title_full | Free material optimization mathematical analysis and numerical solution von Ralf Werner |
| title_fullStr | Free material optimization mathematical analysis and numerical solution von Ralf Werner |
| title_full_unstemmed | Free material optimization mathematical analysis and numerical solution von Ralf Werner |
| title_short | Free material optimization |
| title_sort | free material optimization mathematical analysis and numerical solution |
| title_sub | mathematical analysis and numerical solution |
| topic | Semidefinite Optimierung (DE-588)4663806-4 gnd Dualitätstheorie (DE-588)4150801-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Strukturoptimierung (DE-588)4183811-7 gnd |
| topic_facet | Semidefinite Optimierung Dualitätstheorie Numerisches Verfahren Strukturoptimierung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009498529&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wernerralf freematerialoptimizationmathematicalanalysisandnumericalsolution |