Introduction to Shape Optimization: Shape Sensitivity Analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1992
|
| Schriftenreihe: | Springer Series in Computational Mathematics
16 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem |
| Beschreibung: | 1 Online-Ressource (IV, 250 p) |
| ISBN: | 9783642581069 9783642634710 |
| ISSN: | 0179-3632 |
| DOI: | 10.1007/978-3-642-58106-9 |
Internformat
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| 500 | |a This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem | ||
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Datensatz im Suchindex
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| author | Sokołowski, Jan 1949- |
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| building | Verbundindex |
| bvnumber | BV042422710 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863766928 (DE-599)BVBBV042422710 |
| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-58106-9 |
| format | Electronic eBook |
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| id | DE-604.BV042422710 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642581069 9783642634710 |
| issn | 0179-3632 |
| language | English |
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| spelling | Sokołowski, Jan 1949- Verfasser (DE-588)172379571 aut Introduction to Shape Optimization Shape Sensitivity Analysis by Jan Sokolowski, Jean-Paul Zolesio Berlin, Heidelberg Springer Berlin Heidelberg 1992 1 Online-Ressource (IV, 250 p) txt rdacontent c rdamedia cr rdacarrier Springer Series in Computational Mathematics 16 0179-3632 This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem Mathematics Systems theory Numerical analysis Mathematical optimization Engineering mathematics Numerical Analysis Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Appl.Mathematics/Computational Methods of Engineering Mathematik Freies Randwertproblem (DE-588)4155303-2 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Formgebung (DE-588)4113598-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Gestaltoptimierung (DE-588)4329076-0 gnd rswk-swf Shape-Theorie (DE-588)4193842-2 gnd rswk-swf Strukturoptimierung (DE-588)4183811-7 gnd rswk-swf Strukturoptimierung (DE-588)4183811-7 s Partielle Differentialgleichung (DE-588)4044779-0 s Freies Randwertproblem (DE-588)4155303-2 s 1\p DE-604 Formgebung (DE-588)4113598-2 s 2\p DE-604 Shape-Theorie (DE-588)4193842-2 s Optimierung (DE-588)4043664-0 s 3\p DE-604 Gestaltoptimierung (DE-588)4329076-0 s 4\p DE-604 Zolesio, Jean-Paul Sonstige oth https://doi.org/10.1007/978-3-642-58106-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sokołowski, Jan 1949- Introduction to Shape Optimization Shape Sensitivity Analysis Mathematics Systems theory Numerical analysis Mathematical optimization Engineering mathematics Numerical Analysis Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Appl.Mathematics/Computational Methods of Engineering Mathematik Freies Randwertproblem (DE-588)4155303-2 gnd Optimierung (DE-588)4043664-0 gnd Formgebung (DE-588)4113598-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Gestaltoptimierung (DE-588)4329076-0 gnd Shape-Theorie (DE-588)4193842-2 gnd Strukturoptimierung (DE-588)4183811-7 gnd |
| subject_GND | (DE-588)4155303-2 (DE-588)4043664-0 (DE-588)4113598-2 (DE-588)4044779-0 (DE-588)4329076-0 (DE-588)4193842-2 (DE-588)4183811-7 |
| title | Introduction to Shape Optimization Shape Sensitivity Analysis |
| title_auth | Introduction to Shape Optimization Shape Sensitivity Analysis |
| title_exact_search | Introduction to Shape Optimization Shape Sensitivity Analysis |
| title_full | Introduction to Shape Optimization Shape Sensitivity Analysis by Jan Sokolowski, Jean-Paul Zolesio |
| title_fullStr | Introduction to Shape Optimization Shape Sensitivity Analysis by Jan Sokolowski, Jean-Paul Zolesio |
| title_full_unstemmed | Introduction to Shape Optimization Shape Sensitivity Analysis by Jan Sokolowski, Jean-Paul Zolesio |
| title_short | Introduction to Shape Optimization |
| title_sort | introduction to shape optimization shape sensitivity analysis |
| title_sub | Shape Sensitivity Analysis |
| topic | Mathematics Systems theory Numerical analysis Mathematical optimization Engineering mathematics Numerical Analysis Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Appl.Mathematics/Computational Methods of Engineering Mathematik Freies Randwertproblem (DE-588)4155303-2 gnd Optimierung (DE-588)4043664-0 gnd Formgebung (DE-588)4113598-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Gestaltoptimierung (DE-588)4329076-0 gnd Shape-Theorie (DE-588)4193842-2 gnd Strukturoptimierung (DE-588)4183811-7 gnd |
| topic_facet | Mathematics Systems theory Numerical analysis Mathematical optimization Engineering mathematics Numerical Analysis Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Appl.Mathematics/Computational Methods of Engineering Mathematik Freies Randwertproblem Optimierung Formgebung Partielle Differentialgleichung Gestaltoptimierung Shape-Theorie Strukturoptimierung |
| url | https://doi.org/10.1007/978-3-642-58106-9 |
| work_keys_str_mv | AT sokołowskijan introductiontoshapeoptimizationshapesensitivityanalysis AT zolesiojeanpaul introductiontoshapeoptimizationshapesensitivityanalysis |