{"id":"https://openalex.org/W4311784639","doi":"https://doi.org/10.1007/s00366-022-01763-x","title":"Weak form of bond-associated peridynamic differential operator for solving differential equations","display_name":"Weak form of bond-associated peridynamic differential operator for solving differential equations","publication_year":2022,"publication_date":"2022-12-07","ids":{"openalex":"https://openalex.org/W4311784639","doi":"https://doi.org/10.1007/s00366-022-01763-x"},"language":"en","primary_location":{"id":"doi:10.1007/s00366-022-01763-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00366-022-01763-x","pdf_url":null,"source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering with Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100337926","display_name":"Zhiyuan Li","orcid":"https://orcid.org/0000-0001-8695-6668"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]},{"id":"https://openalex.org/I51441396","display_name":"Bauhaus-Universit\u00e4t Weimar","ror":"https://ror.org/033bb5z47","country_code":"DE","type":"education","lineage":["https://openalex.org/I51441396"]}],"countries":["CN","DE"],"is_corresponding":true,"raw_author_name":"Zhiyuan Li","raw_affiliation_strings":["College of Mechanics and Materials, Hohai University, Nanjing, 211100, China","Institute of Structural Mechanics, Bauhaus-University Weimar, 99423, Weimar, Germany"],"affiliations":[{"raw_affiliation_string":"College of Mechanics and Materials, Hohai University, Nanjing, 211100, China","institution_ids":["https://openalex.org/I163340411"]},{"raw_affiliation_string":"Institute of Structural Mechanics, Bauhaus-University Weimar, 99423, Weimar, Germany","institution_ids":["https://openalex.org/I51441396"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073816567","display_name":"Dan Huang","orcid":"https://orcid.org/0000-0002-5252-5832"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dan Huang","raw_affiliation_strings":["College of Mechanics and Materials, Hohai University, Nanjing, 211100, China"],"affiliations":[{"raw_affiliation_string":"College of Mechanics and Materials, Hohai University, Nanjing, 211100, China","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063981203","display_name":"Huilong Ren","orcid":"https://orcid.org/0000-0002-9997-8193"},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Huilong Ren","raw_affiliation_strings":["Institute of Photonics, Department of Mathematics and Physics, Leibniz University, Hannover, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Photonics, Department of Mathematics and Physics, Leibniz University, Hannover, Germany","institution_ids":["https://openalex.org/I114112103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065190539","display_name":"Timon Rabczuk","orcid":"https://orcid.org/0000-0002-7150-296X"},"institutions":[{"id":"https://openalex.org/I51441396","display_name":"Bauhaus-Universit\u00e4t Weimar","ror":"https://ror.org/033bb5z47","country_code":"DE","type":"education","lineage":["https://openalex.org/I51441396"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Timon Rabczuk","raw_affiliation_strings":["Institute of Structural Mechanics, Bauhaus-University Weimar, 99423, Weimar, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Structural Mechanics, Bauhaus-University Weimar, 99423, Weimar, Germany","institution_ids":["https://openalex.org/I51441396"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100337926"],"corresponding_institution_ids":["https://openalex.org/I163340411","https://openalex.org/I51441396"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.8845,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.91113578,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"39","issue":"5","first_page":"3491","last_page":"3507"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6057771444320679},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.577624499797821},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5180766582489014},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5041011571884155},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.49199315905570984},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.48920321464538574},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.46571850776672363},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4647969603538513},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.44589143991470337},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38064607977867126},{"id":"https://openalex.org/keywords/stiffness","display_name":"Stiffness","score":0.3039226531982422},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18762189149856567},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1119638979434967}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6057771444320679},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.577624499797821},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5180766582489014},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5041011571884155},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.49199315905570984},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.48920321464538574},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.46571850776672363},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4647969603538513},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.44589143991470337},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38064607977867126},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.3039226531982422},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18762189149856567},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1119638979434967},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00366-022-01763-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00366-022-01763-x","pdf_url":null,"source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering with Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3867870744","display_name":null,"funder_award_id":"51679077","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4647156973","display_name":null,"funder_award_id":"202006710119","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"},{"id":"https://openalex.org/G5379507034","display_name":null,"funder_award_id":"12072104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W23630133","https://openalex.org/W1549748890","https://openalex.org/W1555206904","https://openalex.org/W1976897077","https://openalex.org/W2000425991","https://openalex.org/W2003919582","https://openalex.org/W2005215948","https://openalex.org/W2012828992","https://openalex.org/W2018288761","https://openalex.org/W2028811441","https://openalex.org/W2036767781","https://openalex.org/W2063689517","https://openalex.org/W2066824552","https://openalex.org/W2097854981","https://openalex.org/W2142136198","https://openalex.org/W2221457781","https://openalex.org/W2292106027","https://openalex.org/W2323434218","https://openalex.org/W2325830745","https://openalex.org/W2368610919","https://openalex.org/W2586421493","https://openalex.org/W2607582768","https://openalex.org/W2608663096","https://openalex.org/W2620365740","https://openalex.org/W2759424069","https://openalex.org/W2773518436","https://openalex.org/W2795839021","https://openalex.org/W2802868696","https://openalex.org/W2807612291","https://openalex.org/W2808071316","https://openalex.org/W2890979227","https://openalex.org/W2895912046","https://openalex.org/W2905146763","https://openalex.org/W2909056172","https://openalex.org/W2910769511","https://openalex.org/W2948661972","https://openalex.org/W2966391176","https://openalex.org/W3027895456","https://openalex.org/W3031879091","https://openalex.org/W3108679984","https://openalex.org/W3117429244","https://openalex.org/W3126126937","https://openalex.org/W3128521465","https://openalex.org/W3197449622","https://openalex.org/W3197722622","https://openalex.org/W4210441268","https://openalex.org/W4210948763","https://openalex.org/W4229456720","https://openalex.org/W4280523769","https://openalex.org/W4281558948"],"related_works":["https://openalex.org/W2165749285","https://openalex.org/W4364386808","https://openalex.org/W2001036795","https://openalex.org/W2154748900","https://openalex.org/W2474979212","https://openalex.org/W3093811938","https://openalex.org/W4390092784","https://openalex.org/W1601247381","https://openalex.org/W127450631","https://openalex.org/W2062626603"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-21T08:13:44.787528","created_date":"2025-10-10T00:00:00"}