{"id":"https://openalex.org/W7124301669","doi":"https://doi.org/10.34910/mce.135.2","title":"Rectangular flat finite element for modeling the process of crack formation","display_name":"Rectangular flat finite element for modeling the process of crack formation","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W7124301669","doi":"https://doi.org/10.34910/mce.135.2"},"language":"en","primary_location":{"id":"doi:10.34910/mce.135.2","doi":"https://doi.org/10.34910/mce.135.2","is_oa":true,"landing_page_url":"https://doi.org/10.34910/mce.135.2","pdf_url":null,"source":{"id":"https://openalex.org/S7407052753","display_name":"Magazine of Civil Engineering","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I212220629","host_organization_name":"Peter the Great St. Petersburg Polytechnic University","host_organization_lineage":["https://openalex.org/I212220629"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.34910/mce.135.2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079233557","display_name":"Yury Tyukalov","orcid":"https://orcid.org/0000-0001-6184-2365","observed_orcids":["https://orcid.org/0000-0001-6184-2365"]},"institutions":[{"id":"https://openalex.org/I4210103655","display_name":"Vyatka State University","ror":"https://ror.org/01anxqg21","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210103655"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Tyukalov, Yury","raw_affiliation_strings":["Vyatka State University"],"raw_orcid":"https://orcid.org/0000-0001-6184-2365","affiliations":[{"raw_affiliation_string":"Vyatka State University","institution_ids":["https://openalex.org/I4210103655"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079233557"],"corresponding_institution_ids":["https://openalex.org/I4210103655"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10479","display_name":"Structural Behavior of Reinforced Concrete","score":0.5332000255584717,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/T10479","display_name":"Structural Behavior of Reinforced Concrete","score":0.5332000255584717,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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":0.38040000200271606,"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/T11352","display_name":"Masonry and Concrete Structural Analysis","score":0.0406000018119812,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reinforced-concrete-structures","display_name":"reinforced concrete structures","score":0.7450000047683716},{"id":"https://openalex.org/keywords/masonry-structures","display_name":"masonry structures","score":0.7960000038146973},{"id":"https://openalex.org/keywords/fiber-reinforced-concrete","display_name":"fiber-reinforced concrete","score":0.9449999928474426},{"id":"https://openalex.org/keywords/lagrange-multiplier-method","display_name":"Lagrange multipliers","score":0.9359999895095825},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"stiffness matrix","score":0.7599999904632568},{"id":"https://openalex.org/keywords/crack-width","display_name":"crack width","score":0.6830000281333923}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7824000120162964},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.5852000117301941},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.5446000099182129},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.49149999022483826},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.49050000309944153},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.4747999906539917},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.4528000056743622},{"id":"https://openalex.org/C112950240","wikidata":"https://www.wikidata.org/wiki/Q76005","display_name":"Ultimate tensile strength","level":2,"score":0.42890000343322754},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.4262000024318695},{"id":"https://openalex.org/C51830879","wikidata":"https://www.wikidata.org/wiki/Q17008045","display_name":"Crack tip opening displacement","level":4,"score":0.4226999878883362},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4180999994277954},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3711000084877014},{"id":"https://openalex.org/C59085676","wikidata":"https://www.wikidata.org/wiki/Q957852","display_name":"Fracture mechanics","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C21036866","wikidata":"https://www.wikidata.org/wiki/Q181767","display_name":"Stress (linguistics)","level":2,"score":0.3700999915599823},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3635999858379364},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.35679998993873596},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.3564000129699707},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.35359999537467957},{"id":"https://openalex.org/C87210426","wikidata":"https://www.wikidata.org/wiki/Q1072476","display_name":"Bending","level":2,"score":0.34599998593330383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34380000829696655},{"id":"https://openalex.org/C128172907","wikidata":"https://www.wikidata.org/wiki/Q4887116","display_name":"Bending stiffness","level":3,"score":0.3336000144481659},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C190699663","wikidata":"https://www.wikidata.org/wiki/Q2435044","display_name":"Timoshenko beam theory","level":3,"score":0.3174000084400177},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27390000224113464},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.27160000801086426},{"id":"https://openalex.org/C118519418","wikidata":"https://www.wikidata.org/wiki/Q7310313","display_name":"Reinforced solid","level":3,"score":0.26989999413490295},{"id":"https://openalex.org/C93949632","wikidata":"https://www.wikidata.org/wiki/Q5450392","display_name":"Finite element limit analysis","level":4,"score":0.262800008058548},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C67203356","wikidata":"https://www.wikidata.org/wiki/Q1321905","display_name":"Reinforcement","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C2780749890","wikidata":"https://www.wikidata.org/wiki/Q108822283","display_name":"Fissure","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.34910/mce.135.2","doi":"https://doi.org/10.34910/mce.135.2","is_oa":true,"landing_page_url":"https://doi.org/10.34910/mce.135.2","pdf_url":null,"source":{"id":"https://openalex.org/S7407052753","display_name":"Magazine of Civil Engineering","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I212220629","host_organization_name":"Peter the Great St. Petersburg Polytechnic University","host_organization_lineage":["https://openalex.org/I212220629"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.34910/mce.135.2","doi":"https://doi.org/10.34910/mce.135.2","is_oa":true,"landing_page_url":"https://doi.org/10.34910/mce.135.2","pdf_url":null,"source":{"id":"https://openalex.org/S7407052753","display_name":"Magazine of Civil Engineering","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I212220629","host_organization_name":"Peter the Great St. Petersburg Polytechnic University","host_organization_lineage":["https://openalex.org/I212220629"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2045699157","https://openalex.org/W2743317766","https://openalex.org/W12550573","https://openalex.org/W2008864452","https://openalex.org/W3177316805","https://openalex.org/W2128505888","https://openalex.org/W1985891882","https://openalex.org/W2064546485","https://openalex.org/W4232398126","https://openalex.org/W2526198222"],"abstract_inverted_index":{"A":[0],"rectangular":[1,150],"flat":[2],"finite":[3,23,60,90,120,179],"element":[4,24,61],"is":[5],"proposed":[6,22],"that":[7,195],"allows":[8],"modeling":[9],"the":[10,17,66,71,78,85,89,92,108,117,132,137,142,164,168,172,184,187,191,208,226],"process":[11],"of":[12,32,73,81,88,94,119,124,136,167,183],"crack":[13,114,188,223],"formation":[14,115],"without":[15],"changing":[16],"initial":[18,57],"elements\u2019":[19],"grid.":[20],"The":[21,59,144,159,181,201,222],"can":[25,53],"be":[26,54],"used":[27],"to":[28,76,100],"calculate":[29,46,84],"structures":[30,47],"made":[31],"reinforced":[33],"concrete,":[34,37],"masonry,":[35],"fiber":[36],"and":[38,70,214],"other":[39],"materials":[40],"with":[41,48,154,198],"low":[42,156],"tensile":[43,157,165],"strength.":[44,158],"To":[45,83],"existing":[49],"cracks,":[50],"their":[51],"position":[52],"specified":[55],"as":[56],"data.":[58],"was":[62,98,161,174],"formed":[63],"based":[64],"on":[65],"stress":[67],"fields":[68],"approximations":[69],"principle":[72,93],"possible":[74,133],"displacements":[75,203],"obtain":[77],"equilibrium":[79,103],"equations":[80,104],"nodes.":[82],"stiffness":[86],"matrix":[87],"element,":[91,121],"minimum":[95],"additional":[96,122],"energy":[97],"used,":[99],"which":[101],"algebraic":[102],"were":[105,126,146],"added":[106],"using":[107,177],"Lagrange":[109],"multiplier":[110],"method.":[111],"After":[112],"a":[113,149,155],"in":[116,163,211],"centre":[118],"degrees":[123],"freedom":[125],"introduced":[127],"into":[128],"its":[129],"nodes,":[130],"determining":[131],"mutual":[134],"displacement":[135],"element\u2019s":[138],"parts":[139],"separated":[140],"by":[141,205,217,230],"crack.":[143],"calculations":[145],"performed":[147],"for":[148,190,225],"elastic":[151],"bending":[152],"beam":[153,173],"reinforcement":[160,215],"located":[162],"zone":[166],"beam.":[169],"For":[170],"comparison,":[171],"also":[175],"calculated":[176],"standard":[178],"elements.":[180],"comparison":[182],"results,":[185],"including":[186],"width,":[189],"two":[192,227],"solutions":[193,228],"showed":[194],"they":[196],"coincided":[197],"high":[199],"accuracy.":[200],"maximum":[202,209],"differ":[204,216],"1.5":[206],"%,":[207],"stresses":[210],"compressed":[212],"concrete":[213],"less":[218],"than":[219,233],"1":[220],"%.":[221,235],"width":[224],"differs":[229],"no":[231],"more":[232],"5\u20137":[234]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-01-16T00:00:00"}