Introduction to shape optimization: theory, approximation, and computation
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Soc. for Industrial and Applied Mathematics
2003
|
| Schriftenreihe: | Advances in design and control
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XVIII, 273 S. graph. Darst. |
| ISBN: | 0898715369 |
Internformat
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| 245 | 1 | 0 | |a Introduction to shape optimization |b theory, approximation, and computation |c J. Haslinger ; R. A. E. Mäkinen |
| 264 | 1 | |a Philadelphia, Pa. |b Soc. for Industrial and Applied Mathematics |c 2003 | |
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Datensatz im Suchindex
| _version_ | 1804129803415060480 |
|---|---|
| adam_text | Contents
Preface
ix
Notation
xiii
Introduction
xvii
Part I Mathematical Aspects of Sizing and Shape Optimization
1
1
Why the Mathematical Analysis Is Important
3
Problems
..................................... 12
2
A Mathematical Introduction to Sizing and Shape Optimization
13
2.1
Thickness optimization of an elastic beam: Existence and
convergence analysis
.......................... 13
2.2
A model optimal shape design problem
................. 24
2.3
Abstract setting of sizing optimization problems: Existence and
convergence results
........................... 38
2.4
Abstract setting of optimal shape design problems and their
approximations
............................. 45
2.5
Applications of the abstract results
................... 50
2.5.1
Thickness optimization of an elastic unilaterally
supported beam
...................... 50
2.5.2
Shape optimization with Neumann boundary value
state problems
....................... 53
2.5.3
Shape optimization for state problems involving mixed
boundary conditions
.................... 61
2.5.4
Shape optimization of systems governed by
variational inequalities
................... 64
2.5.5
Shape optimization in linear elasticity and contact
problems
.......................... 71
2.5.6
Shape optimization in fluid mechanics
.......... 83
Problems
..................................... 93
v
vi
Contents
Part II Computational Aspects of Sizing and Shape Optimization
97
3
Sensitivity Analysis
99
3.1
Algebraic sensitivity analysis
...................... 99
3.2
Sensitivity analysis in thickness optimization
.............. 107
3.3
Sensitivity analysis in shape optimization
................ 109
3.3.1
The material derivative approach in the continuous setting
109
3.3.2
Isoparametric approach for discrete problems
....... 119
Problems
..................................... 125
4
Numerical Minimization Methods
129
4.1
Gradient methods for unconstrained optimization
...........129
4.1.1
Newton s method
.....................131
4.1.2
Quasi-Newton
methods
..................131
4.1.3
Ensuring convergence
...................133
4.2
Methods for constrained optimization
..................134
4.2.1
Sequential quadratic programming methods
.......136
4.2.2
Available sequential quadratic programming software
. . 138
4.3
On optimization methods using function values only
..........139
4.3.1
Modified controlled random search algorithm
.......140
4.3.2
Genetic algorithms
.....................141
4.4
On multiobjective optimization methods
................144
4.4.1
Setting of the problem
...................145
4.4.2
Solving multiobjective optimization problems by
scalanzation
........................146
4.4.3
On interactive methods for multiobjective optimization
. 147
4.4.4
Genetic algorithms for multiobjective optimization
problems
..........................148
Problems
.....................................150
5
On Automatic Differentiation of Computer Programs
153
5.1
Introduction to automatic differentiation of programs
......... 153
5.1.1
Evaluation of the gradient using the forward and
reverse methods
...................... 156
5.2
Implementation of automatic differentiation
.............. 160
5.3
Application to sizing and shape optimization
.............. 165
Problems
..................................... 167
6
Fictitious Domain Methods in Shape Optimization
169
6.1
Fictitious domain formulations based on boundary and distributed
Lagrange multipliers
...........................170
6.2
Fictitious domain formulations of state problems in shape optimization
181
Problems
.....................................197
Contents
vii
Part
Ш
Applications
199
7
Applications in Elasticity
201
7.1
Mul
ticriteria optimization of a beam
.................. 201
7.1.1
Setting of the problem
................... 201
7.1.2
Approximation and numerical realization of (Tw)
..... 204
7.2
Shape optimization of elasto-plastic bodies in contact
......... 211
7.2.1
Setting of the problem
................... 211
7.2.2
Approximation and numerical realization of (F)
..... 213
Problems
..................................... 219
8
Fluid Mechanical and Multidisciplinary Applications
223
8.1
Shape optimization of a dividing tube
.................. 223
8.1.1
Introduction
........................ 223
8.1.2
Setting of the problem
................... 224
8.1.3
Approximation and numerical realization of
(Рє)
..... 227
8.1.4
Numerical example
.................... 230
8.2
Multidisciplinary optimization of an airfoil profile using genetic
algonthms
................................ 230
8.2.1
Setting of the problem
................... 232
8.2.2
Approximation and numerical realization
......... 236
8.2.3
Numerical example
.................... 239
Problems
..................................... 243
Appendix A Weak Formulations and Approximations of Elliptic
Equations and Inequalities
245
Appendix
В
On Parametrizations of Shapes and Mesh Generation
257
B.I
Parametrizaţi
on of shapes
........................257
B.2 Mesh generation in shape optimization
.................260
Bibliography
263
Index
271
The efficiency and reliability of manufactured products depend on, among other things,
geometrical aspects; it is therefore not surprising that optimal shape design problems have
attracted the interest of applied mathematicians and engineers. This self-contained, elemen¬
tary introduction to the mathematical and computational aspects of sizing and shape
optimization enables readers to gain a firm understanding of the theoretical and
practica
aspects so they may confidently enter this field.
In contrast to existing texts on structural optimization, Introduction to Shape Optimization:
Theory, Approximation, and Computation treats sizing and shape optimization in a compre¬
hensive way, covering everything from mathematical theory (existence analysis, discretizations,
and convergence analysis for discretized problems) through computationa aspects (sensi¬
tivity analysis, numerical minimization methods) to
industria!
applications. Some of the
applications included are contact stress minimization for elastoplastic bodies, multidiscipli-
nary optimization of an airfoil, and shape optimization of a dividing tube. By presenting
sizing and shape optimization in an abstract way, the authors are able to use a unified
approach in the mathematical analysis for a large class of optimization problems in various
fields of physics.
Introduction to Shape Optimization: Theory, Approximation, and Computation is written
primarily for students of applied mathematics, scientific computing, and mechanics. Most
of the material is directed toward graduate students, although a portion of it is suitable for
senior undergraduate students. Readers are assumed to have some knowledge of partial
differential equations and their
numerica!
solution, as well as a modern programming
anguage such as
C++
or Fortran
90.
J. Haslinger is a Professor in the Department of Physics of Metals at Charles University in
Prague. He is the author or coauthor of five monographs and over
110
publications in
scientific journals. His research interests include the approximation of elliptic equations and
inequalities, contact mechanics, nonsmooth analysis, approximation of differential inclu¬
sions, and shape and material optimization.
R. A. E. Mikinen is a Professor in the Department of Mathematical Information
Technology at the University of
Jyväskylä ¡n
Finland. He has also acted as a mode ing
specialist at
Numeróla Oy
(Inc.).
Professor Mäkinen
is the author or co-author of over
50
publications in scientific journals and conference proceedings. His research interests include
structural optimization, especially shape optimization; numerical solution of partial differen¬
tial equations; and numerical software.
|
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| spelling | Haslinger, Jaroslav Verfasser (DE-588)113331002 aut Introduction to shape optimization theory, approximation, and computation J. Haslinger ; R. A. E. Mäkinen Philadelphia, Pa. Soc. for Industrial and Applied Mathematics 2003 XVIII, 273 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advances in design and control Mathematik Structural optimization Mathematics Formgebung (DE-588)4113598-2 gnd rswk-swf Strukturoptimierung (DE-588)4183811-7 gnd rswk-swf Formgebung (DE-588)4113598-2 s Strukturoptimierung (DE-588)4183811-7 s DE-604 Mäkinen, Raino A. E. Verfasser aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010185700&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010185700&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Haslinger, Jaroslav Mäkinen, Raino A. E. Introduction to shape optimization theory, approximation, and computation Mathematik Structural optimization Mathematics Formgebung (DE-588)4113598-2 gnd Strukturoptimierung (DE-588)4183811-7 gnd |
| subject_GND | (DE-588)4113598-2 (DE-588)4183811-7 |
| title | Introduction to shape optimization theory, approximation, and computation |
| title_auth | Introduction to shape optimization theory, approximation, and computation |
| title_exact_search | Introduction to shape optimization theory, approximation, and computation |
| title_full | Introduction to shape optimization theory, approximation, and computation J. Haslinger ; R. A. E. Mäkinen |
| title_fullStr | Introduction to shape optimization theory, approximation, and computation J. Haslinger ; R. A. E. Mäkinen |
| title_full_unstemmed | Introduction to shape optimization theory, approximation, and computation J. Haslinger ; R. A. E. Mäkinen |
| title_short | Introduction to shape optimization |
| title_sort | introduction to shape optimization theory approximation and computation |
| title_sub | theory, approximation, and computation |
| topic | Mathematik Structural optimization Mathematics Formgebung (DE-588)4113598-2 gnd Strukturoptimierung (DE-588)4183811-7 gnd |
| topic_facet | Mathematik Structural optimization Mathematics Formgebung Strukturoptimierung |
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