Topological derivatives in shape optimization:
<p>The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
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| Schriftenreihe: | Interaction of mechanics and mathematics
|
| Schlagworte: | |
| Online-Zugang: | BTU01 FHA01 FHI01 FHN01 FHR01 FKE01 FWS01 UBY01 Volltext Inhaltsverzeichnis Abstract |
| Zusammenfassung: | <p>The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, sensitivity analysis in fracture mechanics and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested in the mathematical aspects of topological asymptotic analysis as well as in applications of topological derivatives in computational mechanics.</p> |
| Beschreibung: | <p>Domain Derivation in Continuum Mechanics -- Material and Shape Derivatives for Boundary Value Problems -- Singular Perturbations of Energy Functionals -- Configurational Perturbations of Energy Functionals -- Topological Derivative Evaluation with Adjoint States -- Topological Derivative for Steady-State Orthotropic Heat Diffusion Problems -- Topological Derivative for Three-Dimensional Linear Elasticity Problems -- Compound Asymptotic Expansions for Spectral Problems -- Topological Asymptotic Analysis for Semilinear Elliptic Boundary Value Problems -- Topological Derivatives for Unilateral Problems.</p> |
| Beschreibung: | 1 Online-Ressource (XII, 324 p. 68 illus) |
| ISBN: | 9783642352454 |
| DOI: | 10.1007/978-3-642-35245-4 |
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| adam_text | TOPOLOGICAL DERIVATIVES IN SHAPE OPTIMIZATION
/ NOVOTNY, ANTONIO ANDRE
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
DOMAIN DERIVATION IN CONTINUUM MECHANICS
MATERIAL AND SHAPE DERIVATIVES FOR BOUNDARY VALUE PROBLEMS
SINGULAR PERTURBATIONS OF ENERGY FUNCTIONALS
CONFIGURATIONAL PERTURBATIONS OF ENERGY FUNCTIONALS
TOPOLOGICAL DERIVATIVE EVALUATION WITH ADJOINT STATES
TOPOLOGICAL DERIVATIVE FOR STEADY-STATE ORTHOTROPIC HEAT DIFFUSION
PROBLEMS
TOPOLOGICAL DERIVATIVE FOR THREE-DIMENSIONAL LINEAR ELASTICITY PROBLEMS
COMPOUND ASYMPTOTIC EXPANSIONS FOR SPECTRAL PROBLEMS
TOPOLOGICAL ASYMPTOTIC ANALYSIS FOR SEMILINEAR ELLIPTIC BOUNDARY VALUE
PROBLEMS
TOPOLOGICAL DERIVATIVES FOR UNILATERAL PROBLEMS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
TOPOLOGICAL DERIVATIVES IN SHAPE OPTIMIZATION
/ NOVOTNY, ANTONIO ANDRE
: 2013
ABSTRACT / INHALTSTEXT
THE TOPOLOGICAL DERIVATIVE IS DEFINED AS THE FIRST TERM (CORRECTION) OF
THE ASYMPTOTIC EXPANSION OF A GIVEN SHAPE FUNCTIONAL WITH RESPECT TO A
SMALL PARAMETER THAT MEASURES THE SIZE OF SINGULAR DOMAIN PERTURBATIONS,
SUCH AS HOLES, INCLUSIONS, DEFECTS, SOURCE-TERMS AND CRACKS. OVER THE
LAST DECADE, TOPOLOGICAL ASYMPTOTIC ANALYSIS HAS BECOME A BROAD, RICH
AND FASCINATING RESEARCH AREA FROM BOTH THEORETICAL AND NUMERICAL
STANDPOINTS. IT HAS APPLICATIONS IN MANY DIFFERENT FIELDS SUCH AS SHAPE
AND TOPOLOGY OPTIMIZATION, INVERSE PROBLEMS, IMAGING PROCESSING AND
MECHANICAL MODELING INCLUDING SYNTHESIS AND/OR OPTIMAL DESIGN OF
MICROSTRUCTURES, SENSITIVITY ANALYSIS IN FRACTURE MECHANICS AND DAMAGE
EVOLUTION MODELING. SINCE THERE IS NO MONOGRAPH ON THE SUBJECT AT
PRESENT, THE AUTHORS PROVIDE HERE THE FIRST ACCOUNT OF THE THEORY WHICH
COMBINES CLASSICAL SENSITIVITY ANALYSIS IN SHAPE OPTIMIZATION WITH
ASYMPTOTIC ANALYSIS BY MEANS OF COMPOUND ASYMPTOTIC EXPANSIONS FOR
ELLIPTIC BOUNDARY VALUE PROBLEMS. THIS BOOK IS INTENDED FOR RESEARCHERS
AND GRADUATE STUDENTS IN APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS
INTERESTED IN ANY ASPECT OF TOPOLOGICAL ASYMPTOTIC ANALYSIS. IN
PARTICULAR, IT CAN BE ADOPTED AS A TEXTBOOK IN ADVANCED COURSES ON THE
SUBJECT AND SHALL BE USEFUL FOR READERS INTERESTED IN THE MATHEMATICAL
ASPECTS OF TOPOLOGICAL ASYMPTOTIC ANALYSIS AS WELL AS IN APPLICATIONS OF
TOPOLOGICAL DERIVATIVES IN COMPUTATIONAL MECHANICS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Novotny, Antonio André |
| author_facet | Novotny, Antonio André |
| author_role | aut |
| author_sort | Novotny, Antonio André |
| author_variant | a a n aa aan |
| building | Verbundindex |
| bvnumber | BV040963578 |
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| collection | ZDB-2-ENG |
| ctrlnum | (OCoLC)827054288 (DE-599)BVBBV040963578 |
| dewey-full | 620.1 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.1 |
| dewey-search | 620.1 |
| dewey-sort | 3620.1 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-35245-4 |
| format | Electronic eBook |
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| record_format | marc |
| series2 | Interaction of mechanics and mathematics |
| spellingShingle | Novotny, Antonio André Topological derivatives in shape optimization Informatik Ingenieurwissenschaften Engineering Computer science Mechanics, applied Gestaltoptimierung (DE-588)4329076-0 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd Topologieoptimierung (DE-588)7662388-9 gnd Singuläre Störung (DE-588)4055100-3 gnd |
| subject_GND | (DE-588)4329076-0 (DE-588)4112609-9 (DE-588)4193399-0 (DE-588)7662388-9 (DE-588)4055100-3 |
| title | Topological derivatives in shape optimization |
| title_auth | Topological derivatives in shape optimization |
| title_exact_search | Topological derivatives in shape optimization |
| title_full | Topological derivatives in shape optimization Antonio André Novotny and Jan Sokołowski |
| title_fullStr | Topological derivatives in shape optimization Antonio André Novotny and Jan Sokołowski |
| title_full_unstemmed | Topological derivatives in shape optimization Antonio André Novotny and Jan Sokołowski |
| title_short | Topological derivatives in shape optimization |
| title_sort | topological derivatives in shape optimization |
| topic | Informatik Ingenieurwissenschaften Engineering Computer science Mechanics, applied Gestaltoptimierung (DE-588)4329076-0 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd Topologieoptimierung (DE-588)7662388-9 gnd Singuläre Störung (DE-588)4055100-3 gnd |
| topic_facet | Informatik Ingenieurwissenschaften Engineering Computer science Mechanics, applied Gestaltoptimierung Asymptotische Entwicklung Elliptisches Randwertproblem Topologieoptimierung Singuläre Störung |
| url | https://doi.org/10.1007/978-3-642-35245-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025941906&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025941906&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT novotnyantonioandre topologicalderivativesinshapeoptimization AT sokołowskijan topologicalderivativesinshapeoptimization |