Finite element approximation for optimal shape, material and topology design:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester ; New York ; Brisbane ; Toronto ; Singapore
John Wiley and Sons
[1996]
|
| Edition: | second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 1. Aufl. u.d.T.: Haslinger, Jaroslav: Finite element method for optimal shape design |
| Physical Description: | xiii, 423 Seiten Diagramme |
| ISBN: | 0471958506 |
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MARC
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| 245 | 1 | 0 | |a Finite element approximation for optimal shape, material and topology design |c J. Haslinger ; P. Neittaanmaki |
| 250 | |a second edition | ||
| 264 | 1 | |a Chichester ; New York ; Brisbane ; Toronto ; Singapore |b John Wiley and Sons |c [1996] | |
| 264 | 4 | |c © 1996 | |
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Record in the Search Index
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| adam_text | Contents
1 Preliminaries 1
1.1 Basic notation 1
1.2 Basic concepts of real analysis 2
1.3 Classification of domains 4
1.4 Green s formula 4
1.5 Preliminaries from functional analysis 6
1.6 Uniform extension property 10
1.7 Elliptic variational inequalities 12
1.8 Approximation of elliptic variational inequalities 24
1.9 Approximation by the finite element method 25
2 Abstract setting of the optimal shape design problem and its
approximation 29
2.1 The continuous case 29
2.2 Approximation of (P) 34
2.3 Examples 36
3 Optimal shape design of systems governed by a unilateral
boundary value state problem — the scalar case 53
3.1 Existence result 53
3.2 Penalty approach to the solution of (P) 62
4 Approximation of the optimal shape design problems by
finite elements — the scalar case 66
5 Numerical realization of optimal shape design problems
associated with a unilateral boundary value problem — the
scalar case 75
5.1 Setting the continuous problem 75
vi FINITE ELEMENT APPROXIMATION FOR OPTIMAL SHAPE DESIGN
5.2 Discretization of settled optimal shape design problems by FEM 77
5.3 Converting settled optimal shape design problems to non linear
programming problems 79
5.4 Design sensitivity analysis algebraic approach 82
5.5 Design sensitivity analysis material derivative method 88
5.6 A procedure for solving optimal shape design problems by applying
non linear programming software 99
6 Shape optimization in unilateral boundary value problems
with a flux cost functional 104
6.1 Setting the problem 104
6.2 Approximation of (P) 106
6.3 Design sensitivity analysis 113
6.3.1 Design sensitivity analysis material derivative approach .... 113
6.3.2 Design sensitivity analysis algebraic approach 115
7 Optimal shape design in contact problems — the elastic case
118
7.1 Introduction to elasticity 118
7.2 Variational formulation of contact problems 121
7.3 Setting the optimal shape problem. The existence result 122
7.4 Finite element approximation of the optimal shape design problem
(P) 131
7.5 Numerical realization of optimal shape design problems for elastic
bodies in contact 138
7.5.1 Converting a settled optimal shape design problem to a non linear
programming problem 138
7.5.2 Sensitivity analysis algebraic approach 141
7.5.3 Sensitivity analysis material derivatives approach 143
7.6 Reciprocal energy as objective functional in contact shape optimiza¬
tion 155
7.6.1 Setting the problem. The existence result 155
7.6.2 Approximation of (P) 163
7.7 Shape optimization in contact problems with friction 169
7.7.1 The optimal shape design problem with given friction 169
7.7.2 Discretization of (P). Discrete design sensitivity analysis 172
7.7.3 Optimal shape design with Coulomb s law of friction and normal
compliance 184
7.8 Examples 186
8 Shape optimization of materially non linear bodies in contact
192
8.1 Shape optimization in the deformation theory of plasticity ... 192
CONTENTS vii
8.1.1 Variational formulation in the deformation theory of plasticity 192
8.1.2 Formulation of the optimal shape design problem. Existence of a
solution 195
8.1.3 Approximation of (P) 202
8.1.4 Numerical realization 206
8.2 Shape optimization of elastic perfectly plastic bodies in contact 209
8.2.1 Variational formulation of the contact problem for an elastic perfectly
plastic body 209
8.2.2 Formulation of the optimal shape design problem. Existence of a
solution 213
8.2.3 Numerical realization of (P) 219
9 Shape optimization in problems with inner obstacles . 230
9.1 The packaging problem 230
9.1.1 Setting the problem. The existence result 232
9.1.2 Penalty method for the approximation of (P) 236
9.1.3 FE approximation of the penalized problem (Pe) 238
9.1.4 Design sensitivity analysis 243
9.1.5 Regularization of state inequality 246
9.1.6 Numerical results 248
9.2 Identification of the incidence set 251
9.2.1 Setting the problem. The existence result 251
9.2.2 Approximation of (P£). Numerical realization 256
10 State constrained optimal control problems and their
approximations 262
10.1 Setting the problem. The existence result 263
10.2 Examples 266
10.3 Approximation of (P) 270
10.4 The penalty method for solving state constrained optimal control
problems 275
10.5 Numerical realization of model examples based on the penalty
approach 277
11 Optimum composite material design 288
11.1 Setting the problem. The existence result 288
11.2 Approximation of (P). Convergence analysis 292
11.3 Sensitivity analysis 296
11.4 Numerical studies of the Gg closure sets 300
11.5 Examples 305
12 Topology optimization in unilateral problems 311
12.1 Setting the problem 311
viii FINITE ELEMENT APPROXIMATION FOR OPTIMAL SHAPE DESIGN
12.2 Approximation of (P). Convergence results 315
12.3 A particular finite element approximation 320
13 Fictitious domain based approaches in shape optimization
328
13.1 Fictitious domain approach based on distributed controls .... 328
13.1.1 Fictitious domain approach for the numerical realization of state
problems 329
13.1.2 The fictitious domain approach in shape optimization 330
13.1.3 Analysis of (P£) x 332
13.1.4 The approximation of (P£) 339
13.2 The Lagrange multiplier technique in fictitious domain methods 345
13.2.1 Formulation of the problem 345
13.2.2 Approximation of (P) 349
13.3 Practical aspects of fictitious domain based approaches in shape
optimization 354
Appendix I: Survey of the methods for non smooth optimization
374
AI.l Subgradient methods 375
AI.1.1 Original subgradient method 375
AI.l.2 Variable metric methods 376
AI.2 Bundle methods 377
AI.2.1 e steepest descent method 378
AI.2.2 Generalized cutting plane method 380
AI.2.3 Proximal bundle and bundle trust region methods 381
AI.2.4 Tilted proximal bundle method 381
AI.2.5 Translated proximal bundle method 382
AI.2.6 Variable metric proximal bundle method 383
AI.2.7 Proximal level bundle method 383
Appendix II: Design sensitivity analysis for stiffness and mass
matrices and for force vectors 385
AII.l Material derivatives 385
AII.2 Sensitivity analysis for M, A and F 387
All.3 Design sensitivity analysis with a parametrized FE grid 391
All.4 Algebraic sensitivity analysis based on the isoparametric technique
394
Appendix III: Differentiation of min max functions 401
Appendix IV: Genetic algorithms 403
CONTENTS ix
Bibliography 409
Subject index 421
|
| any_adam_object | 1 |
| author | Haslinger, Jaroslav Neittaanmäki, Pekka 1951- |
| author_GND | (DE-588)113331002 (DE-588)132647702 |
| author_facet | Haslinger, Jaroslav Neittaanmäki, Pekka 1951- |
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| author_sort | Haslinger, Jaroslav |
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| dewey-search | 620/.0042 |
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| discipline | Mathematik Maschinenbau |
| edition | second edition |
| format | Book |
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| id | DE-604.BV010766435 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:58:30Z |
| institution | BVB |
| isbn | 0471958506 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007189323 |
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| physical | xiii, 423 Seiten Diagramme |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | John Wiley and Sons |
| record_format | marc |
| spelling | Haslinger, Jaroslav (DE-588)113331002 aut Finite element approximation for optimal shape, material and topology design J. Haslinger ; P. Neittaanmaki second edition Chichester ; New York ; Brisbane ; Toronto ; Singapore John Wiley and Sons [1996] © 1996 xiii, 423 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier 1. Aufl. u.d.T.: Haslinger, Jaroslav: Finite element method for optimal shape design Ciencias da engenharia larpcal Ingenieurwissenschaften Mathematisches Modell Engineering Mathematical models Finite element method Optimierung (DE-588)4043664-0 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Formgebung (DE-588)4113598-2 gnd rswk-swf Optimierung (DE-588)4043664-0 s Formgebung (DE-588)4113598-2 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Neittaanmäki, Pekka 1951- (DE-588)132647702 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007189323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Haslinger, Jaroslav Neittaanmäki, Pekka 1951- Finite element approximation for optimal shape, material and topology design Ciencias da engenharia larpcal Ingenieurwissenschaften Mathematisches Modell Engineering Mathematical models Finite element method Optimierung (DE-588)4043664-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Formgebung (DE-588)4113598-2 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4017233-8 (DE-588)4113598-2 |
| title | Finite element approximation for optimal shape, material and topology design |
| title_auth | Finite element approximation for optimal shape, material and topology design |
| title_exact_search | Finite element approximation for optimal shape, material and topology design |
| title_full | Finite element approximation for optimal shape, material and topology design J. Haslinger ; P. Neittaanmaki |
| title_fullStr | Finite element approximation for optimal shape, material and topology design J. Haslinger ; P. Neittaanmaki |
| title_full_unstemmed | Finite element approximation for optimal shape, material and topology design J. Haslinger ; P. Neittaanmaki |
| title_short | Finite element approximation for optimal shape, material and topology design |
| title_sort | finite element approximation for optimal shape material and topology design |
| topic | Ciencias da engenharia larpcal Ingenieurwissenschaften Mathematisches Modell Engineering Mathematical models Finite element method Optimierung (DE-588)4043664-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Formgebung (DE-588)4113598-2 gnd |
| topic_facet | Ciencias da engenharia Ingenieurwissenschaften Mathematisches Modell Engineering Mathematical models Finite element method Optimierung Finite-Elemente-Methode Formgebung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007189323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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