{"id":"https://openalex.org/W4399860179","doi":"https://doi.org/10.3390/sym16060767","title":"Four-Point Bending of Basic Rails: Theory and Experimental Verification","display_name":"Four-Point Bending of Basic Rails: Theory and Experimental Verification","publication_year":2024,"publication_date":"2024-06-19","ids":{"openalex":"https://openalex.org/W4399860179","doi":"https://doi.org/10.3390/sym16060767"},"language":"en","primary_location":{"id":"doi:10.3390/sym16060767","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16060767","pdf_url":"https://www.mdpi.com/2073-8994/16/6/767/pdf?version=1718778194","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/6/767/pdf?version=1718778194","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059254299","display_name":"Zhikui Dong","orcid":"https://orcid.org/0000-0001-7517-904X"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhikui Dong","raw_affiliation_strings":["School of Mechanical Engineering, Yanshan University, Hebei Street 438, Qinhuangdao 066004, China"],"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Yanshan University, Hebei Street 438, Qinhuangdao 066004, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076664381","display_name":"Chunjiang Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunjiang Liu","raw_affiliation_strings":["School of Mechanical Engineering, Yanshan University, Hebei Street 438, Qinhuangdao 066004, China"],"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Yanshan University, Hebei Street 438, Qinhuangdao 066004, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104333848","display_name":"Long Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Long Ma","raw_affiliation_strings":["School of Mechanical Engineering, Yanshan University, Hebei Street 438, Qinhuangdao 066004, China"],"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Yanshan University, Hebei Street 438, Qinhuangdao 066004, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101701778","display_name":"Jiahao Yang","orcid":"https://orcid.org/0009-0006-1008-9442"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiahao Yang","raw_affiliation_strings":["School of Mechanical Engineering, Yanshan University, Hebei Street 438, Qinhuangdao 066004, China"],"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Yanshan University, Hebei Street 438, Qinhuangdao 066004, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055309828","display_name":"Yunhong Jiang","orcid":"https://orcid.org/0000-0003-3292-8164"},"institutions":[{"id":"https://openalex.org/I32394136","display_name":"Northumbria University","ror":"https://ror.org/049e6bc10","country_code":"GB","type":"education","lineage":["https://openalex.org/I32394136"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Yunhong Jiang","raw_affiliation_strings":["Department of Applied Sciences, Northumbria University, Newcastle upon Tyne NE1 8ST, UK"],"affiliations":[{"raw_affiliation_string":"Department of Applied Sciences, Northumbria University, Newcastle upon Tyne NE1 8ST, UK","institution_ids":["https://openalex.org/I32394136"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5055309828","https://openalex.org/A5059254299"],"corresponding_institution_ids":["https://openalex.org/I32394136","https://openalex.org/I39333907"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08664714,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"6","first_page":"767","last_page":"767"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10700","display_name":"Metal Forming Simulation Techniques","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10700","display_name":"Metal Forming Simulation Techniques","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10386","display_name":"Microstructure and Mechanical Properties of Steels","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T12427","display_name":"Metal Alloys Wear and Properties","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/deflection","display_name":"Deflection (physics)","score":0.6736794710159302},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.65484619140625},{"id":"https://openalex.org/keywords/bending","display_name":"Bending","score":0.6478565335273743},{"id":"https://openalex.org/keywords/pure-bending","display_name":"Pure bending","score":0.592962384223938},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.5471788644790649},{"id":"https://openalex.org/keywords/plastic-bending","display_name":"Plastic bending","score":0.5405195951461792},{"id":"https://openalex.org/keywords/bending-moment","display_name":"Bending moment","score":0.5383459329605103},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.517326831817627},{"id":"https://openalex.org/keywords/bending-stiffness","display_name":"Bending stiffness","score":0.4115602374076843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38320526480674744},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.22435671091079712},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17784124612808228},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16076692938804626},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14273056387901306},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.0886889398097992}],"concepts":[{"id":"https://openalex.org/C2781355719","wikidata":"https://www.wikidata.org/wiki/Q2080698","display_name":"Deflection (physics)","level":2,"score":0.6736794710159302},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.65484619140625},{"id":"https://openalex.org/C87210426","wikidata":"https://www.wikidata.org/wiki/Q1072476","display_name":"Bending","level":2,"score":0.6478565335273743},{"id":"https://openalex.org/C5475335","wikidata":"https://www.wikidata.org/wiki/Q7261145","display_name":"Pure bending","level":3,"score":0.592962384223938},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.5471788644790649},{"id":"https://openalex.org/C135986590","wikidata":"https://www.wikidata.org/wiki/Q7202074","display_name":"Plastic bending","level":4,"score":0.5405195951461792},{"id":"https://openalex.org/C70673446","wikidata":"https://www.wikidata.org/wiki/Q857244","display_name":"Bending moment","level":2,"score":0.5383459329605103},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.517326831817627},{"id":"https://openalex.org/C128172907","wikidata":"https://www.wikidata.org/wiki/Q4887116","display_name":"Bending stiffness","level":3,"score":0.4115602374076843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38320526480674744},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.22435671091079712},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17784124612808228},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16076692938804626},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14273056387901306},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0886889398097992}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16060767","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16060767","pdf_url":"https://www.mdpi.com/2073-8994/16/6/767/pdf?version=1718778194","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:dc80a87b684b4f56964d9eed7b93788d","is_oa":true,"landing_page_url":"https://doaj.org/article/dc80a87b684b4f56964d9eed7b93788d","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 6, p 767 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16060767","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16060767","pdf_url":"https://www.mdpi.com/2073-8994/16/6/767/pdf?version=1718778194","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6068669304","display_name":null,"funder_award_id":"52075473","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"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4399860179.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W2011194465","https://openalex.org/W2011224160","https://openalex.org/W2046003704","https://openalex.org/W2064454945","https://openalex.org/W2072137278","https://openalex.org/W2091316227","https://openalex.org/W2110285139","https://openalex.org/W2787478845","https://openalex.org/W2832966597","https://openalex.org/W2888784291","https://openalex.org/W4281694539","https://openalex.org/W4379801002","https://openalex.org/W4387603167","https://openalex.org/W4387978821"],"related_works":["https://openalex.org/W2393811428","https://openalex.org/W2128208310","https://openalex.org/W3170401868","https://openalex.org/W2316322702","https://openalex.org/W1489784569","https://openalex.org/W4313317910","https://openalex.org/W3146319868","https://openalex.org/W2480156399","https://openalex.org/W2382120218","https://openalex.org/W2377276221"],"abstract_inverted_index":{"Mathematical":[0],"models":[1],"of":[2,59,164,205,224],"prediction":[3,121,168,209],"provide":[4],"theoretical":[5,192,219],"support":[6,220],"for":[7,15,50,90,221],"basic":[8,16,225],"rail":[9,226],"automation.":[10],"The":[11,185,211],"three-point":[12],"bending":[13,33,72,87,120,131,167,177,208],"method":[14],"rails":[17],"is":[18,29,47,62],"characterized":[19],"by":[20],"its":[21,57],"simplicity":[22],"and":[23,56,77,103,147,162,200],"flexibility,":[24],"and,":[25],"as":[26],"such,":[27],"it":[28,46],"widely":[30],"used":[31],"in":[32,170,215],"processes.":[34],"However,":[35],"due":[36],"to":[37,84,128,144,154],"the":[38,71,95,112,118,130,160,165,191,203,206,222],"significant":[39],"curvature":[40],"changes":[41],"that":[42],"occur":[43],"after":[44],"bending,":[45,55,69],"not":[48],"suitable":[49],"scenarios":[51],"requiring":[52],"large":[53,171],"arc":[54,172],"range":[58],"achievable":[60],"deflections":[61],"limited.":[63],"This":[64],"study":[65,217],"focuses":[66],"on":[67,111],"four-point":[68,166,176,207],"dividing":[70],"process":[73,132],"into":[74],"three":[75],"stages":[76],"using":[78,136],"a":[79,107,175],"power-law":[80],"material":[81],"hardening":[82],"model":[83,169,193,213],"establish":[85],"different":[86],"moment":[88],"expressions":[89],"each":[91],"stage.":[92],"We":[93],"derived":[94],"relationships":[96],"between":[97],"curvature,":[98],"elastic":[99],"zone":[100],"ratio,":[101],"load,":[102],"deflection,":[104],"ultimately":[105],"creating":[106],"load\u2013deflection":[108],"model.":[109,122,210],"Based":[110],"simple":[113],"springback":[114],"law,":[115],"we":[116],"developed":[117,214],"final":[119],"Finite":[123],"element":[124],"simulations":[125,158],"were":[126,188],"conducted":[127],"simulate":[129],"under":[133,182],"various":[134],"conditions,":[135],"top":[137],"punch":[138],"distances":[139,149],"ranging":[140,150],"from":[141,151],"200":[142],"mm":[143,146,153,199],"400":[145],"die":[148],"600":[152],"1000":[155],"mm.":[156],"These":[157],"validated":[159],"advantages":[161],"accuracy":[163,204],"bending.":[173,227],"Additionally,":[174],"experimental":[178,186],"setup":[179],"was":[180],"established":[181],"specified":[183],"conditions.":[184],"results":[187],"compared":[189],"with":[190],"calculations,":[194],"showing":[195],"errors":[196],"within":[197],"0.2":[198],"thus":[201],"verifying":[202],"mathematical":[212],"this":[216],"provides":[218],"automation":[223]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
