{"id":"https://openalex.org/W4388364669","doi":"https://doi.org/10.13052/ejcm2642-2085.3244","title":"A Novel Differential Quadrature Galerkin Method for Dynamic and Stability Behaviour of Bi-directional Functionally Graded Porous Micro Beams","display_name":"A Novel Differential Quadrature Galerkin Method for Dynamic and Stability Behaviour of Bi-directional Functionally Graded Porous Micro Beams","publication_year":2023,"publication_date":"2023-11-04","ids":{"openalex":"https://openalex.org/W4388364669","doi":"https://doi.org/10.13052/ejcm2642-2085.3244"},"language":"en","primary_location":{"id":"doi:10.13052/ejcm2642-2085.3244","doi":"https://doi.org/10.13052/ejcm2642-2085.3244","is_oa":true,"landing_page_url":"https://doi.org/10.13052/ejcm2642-2085.3244","pdf_url":"https://journals.riverpublishers.com/index.php/EJCM/article/download/23191/18917","source":{"id":"https://openalex.org/S2911508756","display_name":"European Journal of Computational Mechanics","issn_l":"1779-7179","issn":["1779-7179","1958-5829","2642-2050","2642-2085"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Computational Mechanics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://journals.riverpublishers.com/index.php/EJCM/article/download/23191/18917","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028482847","display_name":"Ahmed Saimi","orcid":"https://orcid.org/0000-0002-3722-2526","observed_orcids":["https://orcid.org/0000-0002-3722-2526"]},"institutions":[{"id":"https://openalex.org/I233209018","display_name":"University of Abou Bekr Belka\u00efd","ror":"https://ror.org/00jsjm362","country_code":"DZ","type":"education","lineage":["https://openalex.org/I233209018"]},{"id":"https://openalex.org/I4210100912","display_name":"Institut de Sciences des Mat\u00e9riaux de Mulhouse","ror":"https://ror.org/012wxdw12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2800745255","https://openalex.org/I4210100912","https://openalex.org/I4210128300"]}],"countries":["DZ","FR"],"is_corresponding":false,"raw_author_name":"Ahmed Saimi","raw_affiliation_strings":["IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria"],"raw_orcid":"https://orcid.org/0000-0002-3722-2526","affiliations":[{"raw_affiliation_string":"IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria","institution_ids":["https://openalex.org/I233209018","https://openalex.org/I4210100912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063184233","display_name":"Ismail Bensaid","orcid":"https://orcid.org/0000-0003-4316-0648","observed_orcids":["https://orcid.org/0000-0003-4316-0648"]},"institutions":[{"id":"https://openalex.org/I233209018","display_name":"University of Abou Bekr Belka\u00efd","ror":"https://ror.org/00jsjm362","country_code":"DZ","type":"education","lineage":["https://openalex.org/I233209018"]},{"id":"https://openalex.org/I4210100912","display_name":"Institut de Sciences des Mat\u00e9riaux de Mulhouse","ror":"https://ror.org/012wxdw12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2800745255","https://openalex.org/I4210100912","https://openalex.org/I4210128300"]}],"countries":["DZ","FR"],"is_corresponding":false,"raw_author_name":"Ismail Bensaid","raw_affiliation_strings":["IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria"],"raw_orcid":"https://orcid.org/0000-0003-4316-0648","affiliations":[{"raw_affiliation_string":"IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria","institution_ids":["https://openalex.org/I233209018","https://openalex.org/I4210100912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093196973","display_name":"Besma Khouani","orcid":"https://orcid.org/0009-0008-3096-2995","observed_orcids":["https://orcid.org/0009-0008-3096-2995"]},"institutions":[{"id":"https://openalex.org/I233209018","display_name":"University of Abou Bekr Belka\u00efd","ror":"https://ror.org/00jsjm362","country_code":"DZ","type":"education","lineage":["https://openalex.org/I233209018"]},{"id":"https://openalex.org/I4210100912","display_name":"Institut de Sciences des Mat\u00e9riaux de Mulhouse","ror":"https://ror.org/012wxdw12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2800745255","https://openalex.org/I4210100912","https://openalex.org/I4210128300"]}],"countries":["DZ","FR"],"is_corresponding":false,"raw_author_name":"Besma Khouani","raw_affiliation_strings":["IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria","institution_ids":["https://openalex.org/I233209018","https://openalex.org/I4210100912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102575824","display_name":"Med Yassin Mazari","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I233209018","display_name":"University of Abou Bekr Belka\u00efd","ror":"https://ror.org/00jsjm362","country_code":"DZ","type":"education","lineage":["https://openalex.org/I233209018"]},{"id":"https://openalex.org/I4210100912","display_name":"Institut de Sciences des Mat\u00e9riaux de Mulhouse","ror":"https://ror.org/012wxdw12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2800745255","https://openalex.org/I4210100912","https://openalex.org/I4210128300"]}],"countries":["DZ","FR"],"is_corresponding":false,"raw_author_name":"Med Yassin Mazari","raw_affiliation_strings":["IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria","institution_ids":["https://openalex.org/I233209018","https://openalex.org/I4210100912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063849951","display_name":"Ihab Eddine Houalef","orcid":"https://orcid.org/0000-0001-9130-9422","observed_orcids":["https://orcid.org/0000-0001-9130-9422"]},"institutions":[{"id":"https://openalex.org/I233209018","display_name":"University of Abou Bekr Belka\u00efd","ror":"https://ror.org/00jsjm362","country_code":"DZ","type":"education","lineage":["https://openalex.org/I233209018"]},{"id":"https://openalex.org/I4210100912","display_name":"Institut de Sciences des Mat\u00e9riaux de Mulhouse","ror":"https://ror.org/012wxdw12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2800745255","https://openalex.org/I4210100912","https://openalex.org/I4210128300"]}],"countries":["DZ","FR"],"is_corresponding":false,"raw_author_name":"Ihab Eddine Houalef","raw_affiliation_strings":["IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria","institution_ids":["https://openalex.org/I233209018","https://openalex.org/I4210100912"]}]},{"author_position":"last","author":{"id":null,"display_name":"Abdelmadjid Cheikh","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I233209018","display_name":"University of Abou Bekr Belka\u00efd","ror":"https://ror.org/00jsjm362","country_code":"DZ","type":"education","lineage":["https://openalex.org/I233209018"]},{"id":"https://openalex.org/I4210100912","display_name":"Institut de Sciences des Mat\u00e9riaux de Mulhouse","ror":"https://ror.org/012wxdw12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2800745255","https://openalex.org/I4210100912","https://openalex.org/I4210128300"]}],"countries":["DZ","FR"],"is_corresponding":false,"raw_author_name":"Abdelmadjid Cheikh","raw_affiliation_strings":["IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University Abou Bekr Belkaid, Tlemcen, Algeria","institution_ids":["https://openalex.org/I233209018","https://openalex.org/I4210100912"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4979,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.46440452,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"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/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9800000190734863,"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/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9800000190734863,"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/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.016300000250339508,"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/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.0005000000237487257,"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/free-vibration","display_name":"free vibration","score":0.8769999742507935},{"id":"https://openalex.org/keywords/buckling","display_name":"buckling","score":0.9890000224113464},{"id":"https://openalex.org/keywords/modified-couple-stress-theory","display_name":"modified couple stress theory","score":0.8560000061988831},{"id":"https://openalex.org/keywords/gauss-lobatto-quadrature","display_name":"Gauss-Lobatto quadrature","score":0.8769999742507935},{"id":"https://openalex.org/keywords/material-length-scale-parameter","display_name":"material length scale parameter","score":0.8220000267028809},{"id":"https://openalex.org/keywords/natural-frequencies","display_name":"natural frequencies","score":0.8149999976158142},{"id":"https://openalex.org/keywords/critical-buckling-load","display_name":"critical buckling load","score":0.9950000047683716},{"id":"https://openalex.org/keywords/boundary-conditions","display_name":"boundary conditions","score":0.8550000190734863},{"id":"https://openalex.org/keywords/gradient-index","display_name":"gradient index","score":0.722000002861023},{"id":"https://openalex.org/keywords/aspect-ratio","display_name":"aspect ratio","score":0.6480000019073486}],"concepts":[{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.8050422668457031},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.7891192436218262},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.7210748195648193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5432648658752441},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5170172452926636},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4856630563735962},{"id":"https://openalex.org/C85476182","wikidata":"https://www.wikidata.org/wiki/Q693104","display_name":"Buckling","level":2,"score":0.4240816831588745},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.39161109924316406},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.16833508014678955},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.16560956835746765},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1547982394695282},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.13052/ejcm2642-2085.3244","doi":"https://doi.org/10.13052/ejcm2642-2085.3244","is_oa":true,"landing_page_url":"https://doi.org/10.13052/ejcm2642-2085.3244","pdf_url":"https://journals.riverpublishers.com/index.php/EJCM/article/download/23191/18917","source":{"id":"https://openalex.org/S2911508756","display_name":"European Journal of Computational Mechanics","issn_l":"1779-7179","issn":["1779-7179","1958-5829","2642-2050","2642-2085"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Computational Mechanics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.13052/ejcm2642-2085.3244","doi":"https://doi.org/10.13052/ejcm2642-2085.3244","is_oa":true,"landing_page_url":"https://doi.org/10.13052/ejcm2642-2085.3244","pdf_url":"https://journals.riverpublishers.com/index.php/EJCM/article/download/23191/18917","source":{"id":"https://openalex.org/S2911508756","display_name":"European Journal of Computational Mechanics","issn_l":"1779-7179","issn":["1779-7179","1958-5829","2642-2050","2642-2085"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Computational Mechanics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4388364669.pdf","grobid_xml":"https://content.openalex.org/works/W4388364669.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1149333185","https://openalex.org/W1465633523","https://openalex.org/W1966330485","https://openalex.org/W1998494366","https://openalex.org/W1999544762","https://openalex.org/W2009574936","https://openalex.org/W2026252716","https://openalex.org/W2044675897","https://openalex.org/W2051912022","https://openalex.org/W2073005612","https://openalex.org/W2082902836","https://openalex.org/W2155897712","https://openalex.org/W2163866421","https://openalex.org/W2166864868","https://openalex.org/W2378515186","https://openalex.org/W2418721418","https://openalex.org/W2510224654","https://openalex.org/W2518388871","https://openalex.org/W2553986288","https://openalex.org/W2594154074","https://openalex.org/W2606523051","https://openalex.org/W2614400221","https://openalex.org/W2643984835","https://openalex.org/W2729277711","https://openalex.org/W2808079821","https://openalex.org/W2809372571","https://openalex.org/W2898206631","https://openalex.org/W2953247028","https://openalex.org/W2991627123","https://openalex.org/W2999551422","https://openalex.org/W3020966181","https://openalex.org/W3119841077","https://openalex.org/W3121866536","https://openalex.org/W3138594561","https://openalex.org/W3157448231","https://openalex.org/W3161586116","https://openalex.org/W3162378875","https://openalex.org/W3208133577","https://openalex.org/W3216329107","https://openalex.org/W4205350717","https://openalex.org/W4285807101","https://openalex.org/W4292099799","https://openalex.org/W4319659425","https://openalex.org/W4368371420"],"related_works":["https://openalex.org/W4365141017","https://openalex.org/W4206669638","https://openalex.org/W3091839661","https://openalex.org/W4224271536","https://openalex.org/W4413271037","https://openalex.org/W2594154074","https://openalex.org/W2736964063","https://openalex.org/W2614400221","https://openalex.org/W3209420360","https://openalex.org/W4386233899"],"abstract_inverted_index":{"The":[0,61,70,92,120,130,168],"free":[1],"vibration":[2],"and":[3,28,45,72,88,144,165],"buckling":[4,147],"behaviours":[5],"of":[6,39,102,116,132,149,159,178,192,198,209],"2D-FG":[7,150],"porous":[8,151,210],"microbeams":[9,152],"are":[10,64,75,94,123,153,170],"explored":[11],"in":[12,59,96,195],"this":[13],"paper":[14],"utilizing":[15],"the":[16,23,40,46,67,78,84,103,113,117,126,133,140,157,160,176,179,190,196,206],"Quasi-3D":[17],"beam":[18],"deformation":[19],"theory":[20,27],"based":[21],"on":[22,112,139],"modified":[24],"couple":[25],"stress":[26],"a":[29,37,97,186],"Differential":[30,41,104],"Quadrature":[31,42,105],"Galerkin":[32,48,118],"Method":[33,43,106],"(DQGM)":[34],"systematically,":[35],"as":[36],"combination":[38],"(DQM)":[44],"semi-analytical":[47],"method,":[49],"which":[50],"has":[51],"used":[52],"to":[53,100,174,205],"reduce":[54],"computational":[55],"cost":[56],"for":[57,189],"problems":[58],"dynamics.":[60],"governing":[62],"equations":[63],"obtained":[65],"using":[66,77],"Lagrange\u2019s":[68],"principle.":[69],"mass":[71],"stiffness":[73],"matrices":[74,81,93],"calculated":[76],"weighting":[79],"coefficient":[80],"given":[82],"by":[83,107,125],"differential":[85],"quadrature":[86,90],"(DQ)":[87],"Gauss-Lobatto":[89,127],"rules.":[91],"expressed":[95],"similar":[98],"form":[99],"that":[101],"introducing":[108],"an":[109],"interpolation":[110],"basis":[111,188],"element":[114],"boundary":[115,161],"method.":[119,129],"sampling":[121],"points":[122],"determined":[124],"node":[128],"influence":[131],"thickness-to-material":[134],"length":[135],"scale":[136],"parameter":[137],"(MLSP)":[138],"nondimensional":[141,145],"natural":[142],"frequencies":[143],"critical":[146],"loads":[148],"investigated,":[154],"along":[155],"with":[156,172],"effects":[158],"condition,":[162],"aspect":[163],"ratio":[164],"gradient":[166],"index.":[167],"results":[169,201],"validated":[171],"literature":[173],"establish":[175],"accuracy":[177],"procedure":[180],"described.":[181],"This":[182],"work":[183],"will":[184],"provide":[185],"numerical":[187],"design":[191,208],"FG":[193,211],"microstructures":[194],"field":[197],"micromechanics.":[199],"These":[200],"can":[202],"be":[203],"applied":[204],"engineering":[207],"microstructures.":[212]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2023-11-05T00:00:00"}
