{"id":"https://openalex.org/W4390901318","doi":"https://doi.org/10.1088/2631-8695/ad1f16","title":"Innovative mixed finite element method for bending analysis of functionally graded beams: modelling, validation, and applications","display_name":"Innovative mixed finite element method for bending analysis of functionally graded beams: modelling, validation, and applications","publication_year":2024,"publication_date":"2024-01-16","ids":{"openalex":"https://openalex.org/W4390901318","doi":"https://doi.org/10.1088/2631-8695/ad1f16"},"language":"en","primary_location":{"id":"doi:10.1088/2631-8695/ad1f16","doi":"https://doi.org/10.1088/2631-8695/ad1f16","is_oa":false,"landing_page_url":"https://doi.org/10.1088/2631-8695/ad1f16","pdf_url":null,"source":{"id":"https://openalex.org/S4210221144","display_name":"Engineering Research Express","issn_l":"2631-8695","issn":["2631-8695"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering Research Express","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5032001098","display_name":"Haroune Benmalek","orcid":"https://orcid.org/0000-0003-1963-7135","observed_orcids":["https://orcid.org/0000-0003-1963-7135"]},"institutions":[{"id":"https://openalex.org/I98962006","display_name":"University of Skikda","ror":"https://ror.org/02571vj15","country_code":"DZ","type":"education","lineage":["https://openalex.org/I98962006"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Haroune Benmalek","raw_affiliation_strings":["Civil Engineering Department, 20 August 1955 University of Skikda, Skikda, Skikda, Skikda, 21000, ALGERIA"],"raw_orcid":"https://orcid.org/0000-0003-1963-7135","affiliations":[{"raw_affiliation_string":"Civil Engineering Department, 20 August 1955 University of Skikda, Skikda, Skikda, Skikda, 21000, ALGERIA","institution_ids":["https://openalex.org/I98962006"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022494895","display_name":"Salah Bouziane","orcid":"https://orcid.org/0000-0002-0831-1167","observed_orcids":["https://orcid.org/0000-0002-0831-1167"]},"institutions":[{"id":"https://openalex.org/I98962006","display_name":"University of Skikda","ror":"https://ror.org/02571vj15","country_code":"DZ","type":"education","lineage":["https://openalex.org/I98962006"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Salah Bouziane","raw_affiliation_strings":["Civil Engineering Department, Universite 20 Aout 1955 Skikda Faculte de Technologie, Skikda, Skikda, Skikda, 21000, ALGERIA"],"raw_orcid":"https://orcid.org/0000-0002-0831-1167","affiliations":[{"raw_affiliation_string":"Civil Engineering Department, Universite 20 Aout 1955 Skikda Faculte de Technologie, Skikda, Skikda, Skikda, 21000, ALGERIA","institution_ids":["https://openalex.org/I98962006"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031750053","display_name":"Hamoudi Bouzerd","orcid":"https://orcid.org/0000-0002-8216-2980","observed_orcids":["https://orcid.org/0000-0002-8216-2980"]},"institutions":[{"id":"https://openalex.org/I98962006","display_name":"University of Skikda","ror":"https://ror.org/02571vj15","country_code":"DZ","type":"education","lineage":["https://openalex.org/I98962006"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Hamoudi Bouzerd","raw_affiliation_strings":["Civil Engineering Department, Universite 20 Aout 1955 Skikda Faculte de Technologie, Skikda, Skikda, Skikda, 21000, ALGERIA"],"raw_orcid":"https://orcid.org/0000-0002-8216-2980","affiliations":[{"raw_affiliation_string":"Civil Engineering Department, Universite 20 Aout 1955 Skikda Faculte de Technologie, Skikda, Skikda, Skikda, 21000, ALGERIA","institution_ids":["https://openalex.org/I98962006"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001674049","display_name":"Hisham Suleiman","orcid":"https://orcid.org/0000-0002-7815-4216","observed_orcids":["https://orcid.org/0000-0002-7815-4216"]},"institutions":[{"id":"https://openalex.org/I98962006","display_name":"University of Skikda","ror":"https://ror.org/02571vj15","country_code":"DZ","type":"education","lineage":["https://openalex.org/I98962006"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Hisham Suleiman","raw_affiliation_strings":["Civil Engineering Department, Universite 20 Aout 1955 Skikda Faculte de Technologie, Skikda, Skikda, Skikda, 21000, ALGERIA"],"raw_orcid":"https://orcid.org/0000-0002-7815-4216","affiliations":[{"raw_affiliation_string":"Civil Engineering Department, Universite 20 Aout 1955 Skikda Faculte de Technologie, Skikda, Skikda, Skikda, 21000, ALGERIA","institution_ids":["https://openalex.org/I98962006"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001674049"],"corresponding_institution_ids":["https://openalex.org/I98962006"],"apc_list":{"value":2285,"currency":"USD","value_usd":2285},"apc_paid":null,"fwci":0.527,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.46991594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":96},"biblio":{"volume":"6","issue":"1","first_page":"015055","last_page":"015055"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9976000189781189,"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/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9976000189781189,"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/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.0008999999845400453,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.0005000000237487257,"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/functionally-graded-beams","display_name":"functionally graded beams","score":0.8930000066757202},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"mixed finite element method","score":0.9419999718666077},{"id":"https://openalex.org/keywords/beam-bending","display_name":"beam bending","score":0.7549999952316284},{"id":"https://openalex.org/keywords/euler-bernoulli-beam","display_name":"Euler-Bernoulli beam","score":0.9570000171661377},{"id":"https://openalex.org/keywords/timoshenko-beam","display_name":"Timoshenko beam theory","score":1.0},{"id":"https://openalex.org/keywords/isoparametric-formulation","display_name":"isoparametric formulation","score":0.9200000166893005},{"id":"https://openalex.org/keywords/natural-coordinates","display_name":"natural coordinates","score":0.8569999933242798},{"id":"https://openalex.org/keywords/power-law-material-gradation","display_name":"power-law material gradation","score":0.8059999942779541},{"id":"https://openalex.org/keywords/cantilever-beam","display_name":"cantilever beam","score":0.9319999814033508},{"id":"https://openalex.org/keywords/simply-supported-beams","display_name":"simply supported beams","score":0.9409999847412109}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7671085000038147},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.6686609983444214},{"id":"https://openalex.org/C141354745","wikidata":"https://www.wikidata.org/wiki/Q17227","display_name":"Cantilever","level":2,"score":0.6143196821212769},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.5174142122268677},{"id":"https://openalex.org/C87210426","wikidata":"https://www.wikidata.org/wiki/Q1072476","display_name":"Bending","level":2,"score":0.500211238861084},{"id":"https://openalex.org/C31555180","wikidata":"https://www.wikidata.org/wiki/Q3523867","display_name":"Material properties","level":2,"score":0.49024635553359985},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.43247321248054504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3865741491317749},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.34556126594543457},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.28538423776626587},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.27337905764579773},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25756335258483887},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16851913928985596},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.13805747032165527},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12920963764190674},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1088/2631-8695/ad1f16","doi":"https://doi.org/10.1088/2631-8695/ad1f16","is_oa":false,"landing_page_url":"https://doi.org/10.1088/2631-8695/ad1f16","pdf_url":null,"source":{"id":"https://openalex.org/S4210221144","display_name":"Engineering Research Express","issn_l":"2631-8695","issn":["2631-8695"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering Research Express","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1974388759","https://openalex.org/W1979895214","https://openalex.org/W1989999879","https://openalex.org/W2049672963","https://openalex.org/W2108927873","https://openalex.org/W2112559156","https://openalex.org/W2135056187","https://openalex.org/W2142263219","https://openalex.org/W2146822595","https://openalex.org/W2164217077","https://openalex.org/W2195653852","https://openalex.org/W2210855187","https://openalex.org/W2291862047","https://openalex.org/W2519665915","https://openalex.org/W2600787158","https://openalex.org/W2760992518","https://openalex.org/W3095600205","https://openalex.org/W3154336161","https://openalex.org/W3158210086","https://openalex.org/W4249105824","https://openalex.org/W4319839713","https://openalex.org/W6849997332"],"related_works":["https://openalex.org/W3154336161","https://openalex.org/W4405974821","https://openalex.org/W3044352347","https://openalex.org/W2389638026","https://openalex.org/W4399933064","https://openalex.org/W4417401041","https://openalex.org/W4390488020","https://openalex.org/W2369480133","https://openalex.org/W7143376176","https://openalex.org/W2955988958"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"research,":[3],"we":[4,99],"consider":[5],"solutions":[6,154],"for":[7,27,172,193,207],"the":[8,13,68,75,114,138,162,167,195],"Euler-Bernoulli":[9],"theory":[10,14],"(CBT)":[11],"and":[12,60,97,106,143,152,164,209],"of":[15,53,78,166,197],"Timoshenko":[16],"(TBT).":[17],"It":[18],"presents":[19],"an":[20,44],"innovative":[21],"mixed":[22,69,168],"finite":[23,70,169],"element":[24,71,170],"method":[25,42,171],"tailored":[26],"analysing":[28],"beams":[29,109],"with":[30,110,133],"functionally":[31,79,130,174,198],"graded":[32,80,131,175,199],"properties,":[33],"focusing":[34],"on":[35],"their":[36],"behaviour":[37,77,196],"under":[38,177],"bending":[39,76,178],"loads.":[40],"The":[41,140],"employs":[43],"isoparametric":[45],"formulation":[46],"in":[47,57,156,183],"natural":[48],"coordinates,":[49],"enabling":[50],"precise":[51],"modelling":[52],"complex":[54],"geometries":[55],"common":[56],"structural":[58,184],"engineering":[59,208],"materials":[61,176,200,210],"science.":[62],"A":[63],"significant":[64],"contribution":[65],"is":[66,84],"extending":[67],"approach":[72],"to":[73,86,90,202],"assess":[74],"beams.":[81],"Hence,":[82],"it":[83],"vital":[85],"understand":[87],"material":[88,132],"responses":[89],"external":[91],"forces.":[92],"To":[93],"illustrate":[94],"its":[95,181],"effectiveness":[96],"versatility,":[98],"provide":[100],"two":[101],"numerical":[102,151,191],"examples":[103],"involving":[104],"cantilever":[105,126],"simply-supported":[107],"isotropic":[108,129],"property":[111,135],"variations":[112],"along":[113],"material\u2019s":[115],"thickness,":[116],"following":[117],"power-law":[118],"distributions.":[119],"Additionally,":[120],"a":[121,125,189],"third":[122],"example":[123],"features":[124],"made":[127],"from":[128],"quadratic":[134],"changes":[136],"through":[137,147],"thickness.":[139],"method\u2019s":[141],"robustness":[142],"credibility":[144],"are":[145],"established":[146],"rigorous":[148],"validation":[149,160],"against":[150],"analytical":[153],"found":[155],"existing":[157],"literature.":[158],"This":[159,186],"confirms":[161],"accuracy":[163],"reliability":[165],"assessing":[173],"conditions,":[179],"enhancing":[180],"utility":[182],"analysis.":[185],"research":[187],"introduces":[188],"potent":[190],"tool":[192],"investigating":[194],"subjected":[201],"bending,":[203],"providing":[204],"valuable":[205],"implications":[206],"science":[211],"applications.":[212]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2024-01-17T00:00:00"}
