New mathematical approaches to the optimal design and material degradation of discrete and discretized structures:
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| Format: | Book |
| Language: | English |
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1999
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| Online Access: | Inhaltsverzeichnis |
| Item Description: | Erlangen-Nürnberg, Univ., Habil.-Schr., 2000 |
| Physical Description: | VIII, 256 S. Ill. |
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| 100 | 1 | |a Achtziger, Wolfgang |d 1965- |e Verfasser |0 (DE-588)141008148 |4 aut | |
| 245 | 1 | 0 | |a New mathematical approaches to the optimal design and material degradation of discrete and discretized structures |c by Wolfgang Achtziger |
| 264 | 1 | |c 1999 | |
| 300 | |a VIII, 256 S. |b Ill. | ||
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CONTENTS
*
I DESIGN OPTIMIZATION OF DISCRETE AND DISCRETIZED STRUCTURES TOWARDS
REALISTIC MODELLING AND CON
STRAINTS 1
1 INTRODUCTION, NOTATIONS, PRELIMINARIES. 1
1.1 A PERSONAL VIEW ON MATHEMATICS IN STRUCTURAL OPTIMIZATION. 1
1.2 GOAL AND PLOT OF CHAPTER. 2
1.3 LITERATURE AND SOME RECENT DEVELOPMENTS. 3
1.4 MODELLING, NOTATIONS, AND ASSUMPTIONS . 7
1.4.1 DISCRETE AND DISCRETIZED STRUCTURES. 7
1.4.2 SPECIAL CASE: TRUSS STRUCTURES, DYADIC ELEMENT STIFFNESS MATRICES.
11
1.5 MATHEMATICAL TOOLS. 14
2 AN INTRODUCTORY CASE STUDY . 16
2.1 FORMULATION IN MEMBER FORCES. 16
2.2 FORMULATION IN DISPLACEMENTS. 19
2.3 RELATIONS OF PROBLEMS. 21
2.4 COMPARISON OF THE APPROACHES IN PRACTICE. 22
2.5 PRACTICAL APPLICATIONS. 23
3 MAXIMUM STIFFNESS TOPOLOGY AND SIZING OPTIMIZATION SUBJECT TO MULTIPLE
LOADINGS AND GENERAL
DESIGN CONSTRAINTS. 29
3.1 INTRODUCTION: PROBLEM, ASSUMPTIONS, AND NOTATIONS. 29
3.1.1 GENERAL PROBLEM . 30
3.1.2 INTRODUCTION OF GENERAL CONSTRAINTS ON THE DESIGN VARIABLES . 34
3.1.3 RELATION TO THE MINIMIZATION OF WEIGHT . 36
3.1.4 PLOT OF SECTION, ANTI QUESTIONS TO BE ANSWERED. 37
3.2 STRUCTURES SATISFYING ELASTIC EQUILIBRIUM. 37
3.3 TRANSFORMATION OF MINIMAX COMPLIANCE. 39
3.4 CONVEXITY AND CONTINUITY OF MINIMAX COMPLIANCE. 41
3.5 EXISTENCE OF OPTIMAL STRUCTURES. 45
3.6 PERTURBATION OF LINEAR DESIGN CONSTRAINTS . 48
3.7 (SUB-)DIFFERENTIABILITY OF MINIMAX COMPLIANCE. 52
3.8 NUMERICAL APPROACHES AND SIMPLE TESTS. 54
3.8.1 BRIEF DISCUSSION ON NUMERICAL APPROACHES. 54
3.8.2 NUMERICAL TESTS USING NONSMOOTH OPTIMIZATION . . 56
4 TRUSS TOPOLOGY OPTIMIZATION WITH DIFFERENT MATERIAL PROPERTIES FOR
TENSION AND FOR COMPRESSION 59
4.1 INTRODUCTION TO THE PROBLEM. 59
4.2 STATEMENT OF THE PROBLEM. 62
4.3 REFORMULATION OF THE PROBLEM . 63
4.4 SIMPLE APPLICATIONS.-. 71
4.4.1 SIMPLE RELATIONSHIPS OF PRACTICAL PROBLEMS. 71
4.4.2 NUMERICAL EXAMPLES. 72
5 TRUSS TOPOLOGY OPTIMIZATION INCLUDING LOCAL BUCKLING CONDITIONS. 76
5.1 INTRODUCTION. 76
5.2 BASIC DEFINITIONS AND INTRODUCTION TO THE PROBLEM. 77
V
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/959910239
VI
5.2.1 GROUND STRUCTURES AND SIMPLE LOCAL BUCKLING. 78
5.2.2 ILLUSTRATION OF LOCAL STABILITY CONSTRAINTS IN A TOPOLOGY CONTEXT.
82
5.3 MODELLING OF TOPOLOGICAL LOCAL BUCKLING. 83
5.3.1 CHAINS, NODES, AND AN EXACT DEFINITION OF TOPOLOGICAL LOCAL
BUCKLING. 83
5.3.2 THE ACTIVE BUCKLING LENGTH, AND A FIRST PROBLEM STATEMENT . 87
5.3.3 THE SLENDERNESS CONDITION AND A WELL-POSED PROBLEM FORMULATION. 90
5.3.4 AN ALTERNATIVE FORMULATION IN TERMS OF CHAIN CONDITIONS. 93
5.4 REFORMULATION OF THE PROBLEM BY AN EXACT APPROXIMATION APPROACH. 96
5.5 A DESCENT ALGORITHM VIA LINEARIZATION AND SEQUENTIAL LINEAR
PROGRAMMING. 100
5.6 NEIGHBOUR-CONNECTED GROUND STRUCTURES. 104
5.7 NUMERICAL TESTS. 106
5.7.1 GENERAL EXPERIENCE. 106
5.7.2 A NUMERICAL EXAMPLE. 107
6 AN EXCURSION: GENERAL OPTIMIZATION SUBJECT TO VARIABLE-DEPENDENT
CONSTRAINT INDICES. 110
6.1 INTRODUCTION AND PROBLEM STATEMENT. ILL
6.2 EXISTENCE OF SOLUTIONS AND A PRACTICAL CONDITION. 114
6.3 A NUMERICAL APPROACH BY SUCCESSIVE APPROXIMATION. 117
6.3.1 FAILURE OF PENALTY AND BARRIER APPROACHES. 118
6.3.2 FAILURE OF STANDARD PERTURBATION APPROACH. 118
6.3.3 AN APPROPRIATE PERTURBATION APPROACH. 119
6.4 APPLICATION IN THE FRAMEWORK OF TRUSS TOPOLOGY OPTIMIZATION
INCLUDING TOPOLOGICAL
LOCAL BUCKLING CONSTRAINTS . 122
II COMPUTING EXTREMAL EFFECTS OF MATERIAL DEGRADATION IN DISCRETE AND
DISCRETIZED STRUCTURES 127
7 INTRODUCTION, NOTATIONS, PRELIMINARIES. 127
7.1 ON THE PROBLEM. 127
7.2 PLOT OF CHAPTER. 128
7.3 GENERAL MODELLING, NOTATIONS, AND ASSUMPTIONS. 129
7.4 MATHEMATICAL TOOLS. 131
8 THE LINEAR MODEL OF DEGRADATION. 140
8.1 MODELLING OF DEGRADATION BY LINEAR INTERPOLATION. 140
8.1.1 GENERAL DESCRIPTION. 140
8.1.2 INTERPRETATIONS. 144
8.1.2.1 REDUCTION OF STIFFNESS. 144
8.1.2.2 REMOVAL OF MATERIAL . 144
8.1.3 PROPERTIES OF COMPLIANCE AS A FUNCTION OF THE DEGRADATION FIELD.
145
8.2 THE MAXIMAL EFFECT OF DEGRADATION. 147
8.2.1 PROBLEM FORMULATION, EXISTENCE OF SOLUTIONS . 147
8.2.2 ANALYSIS OF DEGRADATION BEHAVIOUR. 148
8.2.2.1 FORMULATION IN POTENTIAL ENERGY. 149
8.2.2.2 THE DYADIC CASE: FORMULATION IN COMPLEMENTARY ENERGY. 152
8.2.3 MODELLING OF PROGRESSIVE DEGRADATION. 153
8.2.4 NUMERICAL TREATMENT. 154
8.2.4.1 A THEORETICAL COMBINATORIAL APPROACH. 155
8.2.4.2 A FINITE DESCENT METHOD. 156"
8.2.4.3 OPTIMIZATION IN THE DISPLACEMENTS. 160
8.2.5 NUMERICAL EXAMPLES: REDUCTION OF STIFFNESS. 160
8.2.6 NUMERICAL EXAMPLES: REMOVAL OF MATERIAL . 163
8.3 THE MINIMAL EFFECT OF DEGRADATION. 170
8.3.1 PROBLEM FORMULATION, EXISTENCE OF SOLUTIONS. 170
8.3.2 ANALYSIS OF DEGRADATION BEHAVIOUR. 172
8.3.2.1 FORMULATION IN POTENTIAL ENERGY. 172
8.3.2.2 THE DYADIC CASE: QP-FORMULATION IN POTENTIAL ENERGY. 176
VII
8.3.23 THE DYADIC CASE: FORMULATION IN COMPLEMENTARY ENERGY. 180
8.3.3 MODELLING OF PROGRESSIVE DEGRADATION.
184
8.3.4 NUMERICAL TREATMENT.
185
8.3.5 NUMERICAL EXAMPLES.
186
9 THE INVERSE MODEL OF DEGRADATION .
189
9.1 MODELLING OF DEGRADATION BY INVERSE LINEAR INTERPOLATION.; . 189
9.1.1 GENERAL DESCRIPTION.
189
9.1.2 INTERPRETATIONS.
191
9.1.2.1 REDUCTION OF STIFFNESS.
191
9.1.2.2 REMOVAL OF MATERIAL .\.
192
9.1.3 PROPERTIES OF COMPLIANCE AS A FUNCTION OF THE DEGRADATION FIELD.
192
9.2 THE MAXIMAL EFFECT OF DEGRADATION.
194
9.2.1 PROBLEM FORMULATION, EXISTENCE OF SOLUTIONS . 194
9.2.2 ANALYSIS OF DEGRADATION BEHAVIOUR. 195
9.2.2.1 FORMULATION IN POTENTIAL ENERGY. 195
9.2.2.2 THE DYADIC CASE: FORMULATION IN COMPLEMENTARY ENERGY.200
9.2.3 MODELLING OF PROGRESSIVE DEGRADATION.206
9.2.4 NUMERICAL TREATMENT. 207
9.2.5 NUMERICAL EXAMPLES . . . . .R\".208
9.3 THE MINIMAL EFFECT OF DEGRADATION.210
9.3.1 PROBLEM FORMULATION, EXISTENCE OF SOLUTIONS .210
9.3.2 ANALYSIS OF DEGRADATION BEHAVIOUR. 211
9.3.2.1 FORMULATION IN POTENTIAL ENERGY.211
93.2.2 THE DYADIC CASE: FORMULATION IN COMPLEMENTARY ENERGY.211
9.3.3 PROGRESSIVE DEGRADATION . 213
9.3.4 NUMERICAL TREATMENT. 213
10 RELATIONS OF DEGRADATION MODELS . 214
10.1 RELATIONS OF DEGRADATION FIELDS. 214
10.2 RELATIONS OF MODEL PROBLEMS . 216
10.3 RELATIONS OF THE SPECIFIC ENERGY FUNCTIONS. 217
10.4 NUMERICAL EXAMPLES. 224
11 OUTLOOK: SOME EXTENSIONS OF THE INVERSE STIFFNESS MODEL FOR MAXIMAL
DEGRADATION .226
11.1 GENERALIZATIONS FOR IHE DISCRETE CASE. 226
11.1.1 MODELS WITH DIFFERENT PROPERTIES IN TENSION AND IN
COMPRESSION.226
11.1.2 STAGES OF DEGRADATION. 227
11.1.3 PROGRESSIVE DEGRADATION WITH CHANGING LOADS.228
11.1.4 MULTIPLE LOADS.229
11.2 MODELS FOR CONTINUA.231
11.2.1 THE MAXIMAL EFFECT OF DEGRADATION. 231
11.2.2 MODELLING FOR A RANGE OF ANISOTROPIC DEGRADATION
POSSIBILITIES.232
11.2.3 MODELLING TO INCLUDE PREDICTION OF THE MATERIAL DEGRADATION
TENSOR.233
12 TOPOLOGY DESIGN AGAINST DEGRADATION.234
12.1 PROBLEM FORMULATION. 234
12.2 DESIGN FORMULATION IN POTENTIAL ENERGY. 238
12.3 OPTIMAL DEGRADATION FIELDS, OPTIMAL TOPOLOGY, EXISTENCE OF
SOLUTIONS.240
BIBLIOGRAPHY
247 |
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| spelling | Achtziger, Wolfgang 1965- Verfasser (DE-588)141008148 aut New mathematical approaches to the optimal design and material degradation of discrete and discretized structures by Wolfgang Achtziger 1999 VIII, 256 S. Ill. txt rdacontent n rdamedia nc rdacarrier Erlangen-Nürnberg, Univ., Habil.-Schr., 2000 (DE-588)4113937-9 Hochschulschrift gnd-content DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008913932&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | New mathematical approaches to the optimal design and material degradation of discrete and discretized structures |
| title_auth | New mathematical approaches to the optimal design and material degradation of discrete and discretized structures |
| title_exact_search | New mathematical approaches to the optimal design and material degradation of discrete and discretized structures |
| title_full | New mathematical approaches to the optimal design and material degradation of discrete and discretized structures by Wolfgang Achtziger |
| title_fullStr | New mathematical approaches to the optimal design and material degradation of discrete and discretized structures by Wolfgang Achtziger |
| title_full_unstemmed | New mathematical approaches to the optimal design and material degradation of discrete and discretized structures by Wolfgang Achtziger |
| title_short | New mathematical approaches to the optimal design and material degradation of discrete and discretized structures |
| title_sort | new mathematical approaches to the optimal design and material degradation of discrete and discretized structures |
| topic_facet | Hochschulschrift |
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