Topological Derivative in Shape Optimization

Name: Work Video:
Duration: 3 min 30 s
Description: In this paper the topological derivative for an arbitrary shape functional is defined. Examples are provided for elliptic equations and the elasticity system in the plane. The topological derivative can be used for solving shape optimization problems in structural mechanics.
{'id': 'https://openalex.org/W3142828186', 'doi': 'https://doi.org/10.1007/springerreference_72760', 'title': 'Topological Derivative in Shape Optimization', 'display_name': 'Topological Derivative in Shape Optimization', 'publication_year': 2012, 'publication_date': '2012-01-20', 'ids': {'openalex': 'https://openalex.org/W3142828186', 'doi': 'https://doi.org/10.1007/springerreference_72760', 'mag': '3142828186'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/springerreference_72760', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4363604060', 'display_name': 'SpringerReference', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'reference-entry', 'type_crossref': 'reference-entry', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': 'https://inria.hal.science/inria-00073518/file/RR-3170.pdf', 'any_repository_has_fulltext': True}, 'authorships': [], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 112, 'citation_normalized_percentile': {'value': 0.974026, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 98, 'max': 99}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11115', 'display_name': 'Topology Optimization in Engineering', 'score': 0.9989, 'subfield': {'id': 'https://openalex.org/subfields/2205', 'display_name': 'Civil and Structural Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T11115', 'display_name': 'Topology Optimization in Engineering', 'score': 0.9989, 'subfield': {'id': 'https://openalex.org/subfields/2205', 'display_name': 'Civil and Structural Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11245', 'display_name': 'Advanced Numerical Analysis Techniques', 'score': 0.9956, 'subfield': {'id': 'https://openalex.org/subfields/2206', 'display_name': 'Computational Mechanics'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10221', 'display_name': 'Composite Structure Analysis and Optimization', 'score': 0.9785, 'subfield': {'id': 'https://openalex.org/subfields/2211', 'display_name': 'Mechanics of Materials'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/derivative', 'display_name': 'Derivative (finance)', 'score': 0.57574457}], 'concepts': [{'id': 'https://openalex.org/C111771559', 'wikidata': 'https://www.wikidata.org/wiki/Q66295', 'display_name': 'Derivative (finance)', 'level': 2, 'score': 0.57574457}, {'id': 'https://openalex.org/C184720557', 'wikidata': 'https://www.wikidata.org/wiki/Q7825049', 'display_name': 'Topology (electrical circuits)', 'level': 2, 'score': 0.5661762}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.4665584}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.34175006}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.33131766}, {'id': 'https://openalex.org/C162324750', 'wikidata': 'https://www.wikidata.org/wiki/Q8134', 'display_name': 'Economics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C106159729', 'wikidata': 'https://www.wikidata.org/wiki/Q2294553', 'display_name': 'Financial economics', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 5, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/springerreference_72760', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4363604060', 'display_name': 'SpringerReference', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://inria.hal.science/inria-00073518/file/RR-3170.pdf', 'pdf_url': 'https://inria.hal.science/inria-00073518/file/RR-3170.pdf', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.inria.fr/inria-00073518', 'pdf_url': 'https://hal.inria.fr/inria-00073518/document', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://inria.hal.science/inria-00073518', 'pdf_url': 'https://inria.hal.science/inria-00073518/document', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.inria.fr/inria-00073518/file/RR-3170.pdf', 'pdf_url': 'https://hal.inria.fr/inria-00073518/file/RR-3170.pdf', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://inria.hal.science/inria-00073518/file/RR-3170.pdf', 'pdf_url': 'https://inria.hal.science/inria-00073518/file/RR-3170.pdf', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 3, 'referenced_works': ['https://openalex.org/W1496364532', 'https://openalex.org/W1502992081', 'https://openalex.org/W2024753911'], 'related_works': ['https://openalex.org/W4245490552', 'https://openalex.org/W4225152035', 'https://openalex.org/W3002753104', 'https://openalex.org/W2911598644', 'https://openalex.org/W2142036596', 'https://openalex.org/W2077600819', 'https://openalex.org/W2061531152', 'https://openalex.org/W2007980826', 'https://openalex.org/W1979597421', 'https://openalex.org/W1587224694'], 'abstract_inverted_index': {'In': [0], 'this': [1], 'paper': [2], 'the': [3, 20, 24], 'topological': [4, 27], 'derivative': [5, 28], 'for': [6, 16, 32], 'an': [7], 'arbitrary': [8], 'shape': [9, 34], 'functional': [10], 'is': [11], 'defined.': [12], 'Examples': [13], 'are': [14], 'provided': [15], 'elliptic': [17], 'equations': [18], 'and': [19], 'elasticity': [21], 'system': [22], 'in': [23, 37], 'plane.': [25], 'The': [26], 'can': [29], 'be': [30], 'used': [31], 'solving': [33], 'optimization': [35], 'problems': [36], 'structural': [38], 'mechanics.': [39]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W3142828186', 'counts_by_year': [{'year': 2022, 'cited_by_count': 3}, {'year': 2020, 'cited_by_count': 2}, {'year': 2018, 'cited_by_count': 5}, {'year': 2017, 'cited_by_count': 5}, {'year': 2016, 'cited_by_count': 6}, {'year': 2015, 'cited_by_count': 9}, {'year': 2014, 'cited_by_count': 12}, {'year': 2013, 'cited_by_count': 10}, {'year': 2012, 'cited_by_count': 7}], 'updated_date': '2024-12-30T22:52:51.264845', 'created_date': '2021-04-13'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
