{"id":"https://openalex.org/W1994930212","doi":"https://doi.org/10.1137/100817619","title":"Elliptic-Spline Solutions for Large Localizations in a Circular Blatz\u2013Ko Cylinder Due to Geometric Softening","display_name":"Elliptic-Spline Solutions for Large Localizations in a Circular Blatz\u2013Ko Cylinder Due to Geometric Softening","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1994930212","doi":"https://doi.org/10.1137/100817619","mag":"1994930212"},"language":"en","primary_location":{"id":"doi:10.1137/100817619","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100817619","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","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/A5043975778","display_name":"Hui\u2013Hui Dai","orcid":"https://orcid.org/0000-0003-3807-4585"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hui-Hui Dai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101835943","display_name":"Xiaochun Peng","orcid":"https://orcid.org/0000-0003-0056-5960"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaochun Peng","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043975778"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4391,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.59001213,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"72","issue":"1","first_page":"181","last_page":"200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9991000294685364,"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/T10514","display_name":"Numerical methods in engineering","score":0.9980999827384949,"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/mathematics","display_name":"Mathematics","score":0.6128807067871094},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6062407493591309},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4927704632282257},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.47698265314102173},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.4463024139404297},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.4122939705848694},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19668015837669373},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15533694624900818}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6128807067871094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6062407493591309},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4927704632282257},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.47698265314102173},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.4463024139404297},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.4122939705848694},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19668015837669373},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15533694624900818},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100817619","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100817619","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6800000071525574,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W31927281","https://openalex.org/W1487455380","https://openalex.org/W1966119870","https://openalex.org/W1968398117","https://openalex.org/W1968967906","https://openalex.org/W1973124216","https://openalex.org/W1988403756","https://openalex.org/W1992627230","https://openalex.org/W1996003856","https://openalex.org/W2001102895","https://openalex.org/W2005304063","https://openalex.org/W2005506380","https://openalex.org/W2025341470","https://openalex.org/W2040101617","https://openalex.org/W2054992112","https://openalex.org/W2061411896","https://openalex.org/W2064216797","https://openalex.org/W2074127247","https://openalex.org/W2081452007","https://openalex.org/W2088542348","https://openalex.org/W2116379499","https://openalex.org/W2118273608","https://openalex.org/W2234965686","https://openalex.org/W2309987763","https://openalex.org/W4244028180","https://openalex.org/W4244138646"],"related_works":["https://openalex.org/W2017296099","https://openalex.org/W2910133962","https://openalex.org/W2401850100","https://openalex.org/W3117324600","https://openalex.org/W2141704600","https://openalex.org/W4226067901","https://openalex.org/W4313705710","https://openalex.org/W3157737782","https://openalex.org/W3043663456","https://openalex.org/W3015266405"],"abstract_inverted_index":{"It":[0],"has":[1],"been":[2],"known":[3],"that":[4],"geometric":[5,73,228],"softening":[6],"can":[7,111,120],"induce":[8],"strain":[9,177,212],"localizations":[10,61,213],"in":[11,62,91,107,145,209],"solids.":[12],"However,":[13],"it":[14],"is":[15,33,95,224,231],"very":[16],"difficult":[17],"to":[18,50,54,72,160],"analytically":[19],"capture":[20,193],"the":[21,31,45,81,88,126,138,142,162,166,175,190,195,198,202,221,235],"localized":[22],"deformation":[23,32,139],"states":[24,140],"within":[25],"a":[26,40,48,52,63,68,92,100,108,122,131,146,150,169,180,184],"three-dimensional":[27],"framework,":[28],"especially":[29],"when":[30,211],"large.":[34],"In":[35,215],"this":[36,133,154],"paper,":[37],"we":[38,158],"introduce":[39],"novel":[41],"approach,":[42],"which":[43,205],"resembles":[44],"use":[46],"of":[47,67,83,102,116,125,135,156,168,171,197],"spline":[49,170],"approximate":[51],"curve,":[53],"construct":[55],"analytical":[56,163,191,236],"(asymptotic)":[57],"solutions":[58,164],"for":[59,87,141,174],"large":[60,123,147,176],"circular":[64],"cylinder":[65],"composed":[66],"Blatz\u2013Ko":[69],"material":[70],"due":[71],"softening.":[74],"The":[75,114,226],"asymptotic":[76],"normal":[77],"form":[78,82,167],"equation":[79],"(in":[80,165],"an":[84],"ODE)":[85],"valid":[86,106],"axial":[89,127,143],"stretch":[90,144],"small":[93,109,118],"neighborhood":[94],"first":[96],"derived":[97],"and":[98,129,183,189,201],"then":[99],"set":[101,134,155],"these":[103,117],"equations,":[104],"each":[105],"neighborhood,":[110],"be":[112],"obtained.":[113,225],"union":[115],"neighborhoods":[119],"cover":[121],"range":[124],"stretch,":[128],"as":[130],"result":[132],"equations":[136],"governs":[137],"interval.":[148],"Through":[149],"phase-plane":[151],"analysis":[152],"on":[153,220],"ODEs":[157],"manage":[159],"obtain":[161],"elliptic":[172],"integrals)":[173],"localizations.":[178],"Both":[179],"force-controlled":[181],"problem":[182,186],"displacement-controlled":[185],"are":[187,206],"solved":[188],"results":[192],"well":[194],"nonuniqueness":[196],"stress-displacement":[199],"relation":[200],"snap-through":[203],"phenomenon,":[204],"often":[207],"observed":[208],"experiments":[210],"happen.":[214],"addition,":[216],"some":[217],"insightful":[218],"information":[219],"bifurcation":[222],"points":[223],"important":[227],"size":[229],"effect":[230],"also":[232],"discussed":[233],"through":[234],"solutions.":[237]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
