{"id":"https://openalex.org/W3008252847","doi":"https://doi.org/10.3390/sym12020321","title":"Energy of Accelerations Used to Obtain the Motion Equations of a Three- Dimensional Finite Element","display_name":"Energy of Accelerations Used to Obtain the Motion Equations of a Three- Dimensional Finite Element","publication_year":2020,"publication_date":"2020-02-23","ids":{"openalex":"https://openalex.org/W3008252847","doi":"https://doi.org/10.3390/sym12020321","mag":"3008252847"},"language":"en","primary_location":{"id":"doi:10.3390/sym12020321","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12020321","pdf_url":"https://www.mdpi.com/2073-8994/12/2/321/pdf?version=1582464234","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/2073-8994/12/2/321/pdf?version=1582464234","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057324856","display_name":"Sorin Vlase","orcid":"https://orcid.org/0000-0001-8679-2579"},"institutions":[{"id":"https://openalex.org/I3123573182","display_name":"Transylvania University of Bra\u0219ov","ror":"https://ror.org/01cg9ws23","country_code":"RO","type":"education","lineage":["https://openalex.org/I3123573182"]},{"id":"https://openalex.org/I33800924","display_name":"Academia Oamenilor de \u0218tiin\u021b\u0103 din Rom\u00e2nia","ror":"https://ror.org/04ybnj478","country_code":"RO","type":"facility","lineage":["https://openalex.org/I33800924"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Sorin Vlase","raw_affiliation_strings":["Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transilvania University of Bra\u0219ov, B-dul Eroilor 29, 500036 Bra\u0219ov, Romania","Technical Sciences Academy of Romania; B-dul Dacia 26, 030167 Bucharest, Romania"],"raw_orcid":"https://orcid.org/0000-0001-8679-2579","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transilvania University of Bra\u0219ov, B-dul Eroilor 29, 500036 Bra\u0219ov, Romania","institution_ids":["https://openalex.org/I3123573182"]},{"raw_affiliation_string":"Technical Sciences Academy of Romania; B-dul Dacia 26, 030167 Bucharest, Romania","institution_ids":["https://openalex.org/I33800924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065680375","display_name":"Iuliu Negrean","orcid":"https://orcid.org/0000-0003-0018-5183"},"institutions":[{"id":"https://openalex.org/I158333966","display_name":"Technical University of Cluj-Napoca","ror":"https://ror.org/03r8nwp71","country_code":"RO","type":"education","lineage":["https://openalex.org/I158333966"]},{"id":"https://openalex.org/I33800924","display_name":"Academia Oamenilor de \u0218tiin\u021b\u0103 din Rom\u00e2nia","ror":"https://ror.org/04ybnj478","country_code":"RO","type":"facility","lineage":["https://openalex.org/I33800924"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Iuliu Negrean","raw_affiliation_strings":["Department of Mechanical Systems Engineering, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania","Technical Sciences Academy of Romania; B-dul Dacia 26, 030167 Bucharest, Romania","B-dul Dacia 26, 030167 Bucharest, Romania"],"raw_orcid":"https://orcid.org/0000-0003-0018-5183","affiliations":[{"raw_affiliation_string":"Department of Mechanical Systems Engineering, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I158333966"]},{"raw_affiliation_string":"Technical Sciences Academy of Romania; B-dul Dacia 26, 030167 Bucharest, Romania","institution_ids":["https://openalex.org/I33800924"]},{"raw_affiliation_string":"B-dul Dacia 26, 030167 Bucharest, Romania","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015681053","display_name":"Mar\u00edn Mar\u00edn","orcid":"https://orcid.org/0000-0003-1552-3763"},"institutions":[{"id":"https://openalex.org/I3123573182","display_name":"Transylvania University of Bra\u0219ov","ror":"https://ror.org/01cg9ws23","country_code":"RO","type":"education","lineage":["https://openalex.org/I3123573182"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Marin Marin","raw_affiliation_strings":["Department of Mathematics and Computer Science, Transilvania University of Bra\u0219ov, B-dul Eroilor 29, 500036 Bra\u0219ov, Romania"],"raw_orcid":"https://orcid.org/0000-0003-1552-3763","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Transilvania University of Bra\u0219ov, B-dul Eroilor 29, 500036 Bra\u0219ov, Romania","institution_ids":["https://openalex.org/I3123573182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103172224","display_name":"Maria Lumini\u0163a Scutaru","orcid":"https://orcid.org/0000-0001-8554-2973"},"institutions":[{"id":"https://openalex.org/I3123573182","display_name":"Transylvania University of Bra\u0219ov","ror":"https://ror.org/01cg9ws23","country_code":"RO","type":"education","lineage":["https://openalex.org/I3123573182"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Maria Lumini\u021ba Scutaru","raw_affiliation_strings":["Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transilvania University of Bra\u0219ov, B-dul Eroilor 29, 500036 Bra\u0219ov, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transilvania University of Bra\u0219ov, B-dul Eroilor 29, 500036 Bra\u0219ov, Romania","institution_ids":["https://openalex.org/I3123573182"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5103172224"],"corresponding_institution_ids":["https://openalex.org/I3123573182"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.2735,"has_fulltext":true,"cited_by_count":72,"citation_normalized_percentile":{"value":0.91995556,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"12","issue":"2","first_page":"321","last_page":"321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T13752","display_name":"Mechanics and Biomechanics Studies","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/finite-element-method","display_name":"Finite element method","score":0.7484664916992188},{"id":"https://openalex.org/keywords/equations-of-motion","display_name":"Equations of motion","score":0.5866782665252686},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5809425711631775},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.5411031246185303},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5145946741104126},{"id":"https://openalex.org/keywords/rigid-body","display_name":"Rigid body","score":0.4778425395488739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46347862482070923},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.4472818076610565},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43620967864990234},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38875967264175415},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3608155846595764},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.31833159923553467},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29141923785209656},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21351870894432068},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.16503095626831055},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11440879106521606}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7484664916992188},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.5866782665252686},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5809425711631775},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.5411031246185303},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5145946741104126},{"id":"https://openalex.org/C145980571","wikidata":"https://www.wikidata.org/wiki/Q192788","display_name":"Rigid body","level":2,"score":0.4778425395488739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46347862482070923},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.4472818076610565},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43620967864990234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38875967264175415},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3608155846595764},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.31833159923553467},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29141923785209656},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21351870894432068},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.16503095626831055},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11440879106521606}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12020321","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12020321","pdf_url":"https://www.mdpi.com/2073-8994/12/2/321/pdf?version=1582464234","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:0234e6da37b544f786778ee9e62d6d31","is_oa":true,"landing_page_url":"https://doaj.org/article/0234e6da37b544f786778ee9e62d6d31","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 2, p 321 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/2/321/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12020321","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12020321","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12020321","pdf_url":"https://www.mdpi.com/2073-8994/12/2/321/pdf?version=1582464234","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3008252847.pdf","grobid_xml":"https://content.openalex.org/works/W3008252847.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1973876419","https://openalex.org/W1981092967","https://openalex.org/W1995793617","https://openalex.org/W2019405070","https://openalex.org/W2031334631","https://openalex.org/W2046008233","https://openalex.org/W2047088299","https://openalex.org/W2055571167","https://openalex.org/W2061085351","https://openalex.org/W2081530616","https://openalex.org/W2084523801","https://openalex.org/W2092203520","https://openalex.org/W2094593572","https://openalex.org/W2307225133","https://openalex.org/W2328053688","https://openalex.org/W2339768787","https://openalex.org/W2410622230","https://openalex.org/W2568701359","https://openalex.org/W2617080776","https://openalex.org/W2890089004","https://openalex.org/W2890727183","https://openalex.org/W2898062634","https://openalex.org/W2922165091","https://openalex.org/W2971190938","https://openalex.org/W2973688454","https://openalex.org/W2997250811","https://openalex.org/W4285719527","https://openalex.org/W6636020184","https://openalex.org/W6714249727"],"related_works":["https://openalex.org/W1567939749","https://openalex.org/W1977906733","https://openalex.org/W2033950943","https://openalex.org/W2010821947","https://openalex.org/W1573186872","https://openalex.org/W2071722255","https://openalex.org/W2021654023","https://openalex.org/W2165887158","https://openalex.org/W2352023866","https://openalex.org/W4234008889"],"abstract_inverted_index":{"When":[0],"analyzing":[1],"the":[2,14,32,51,75,78,93,104,114,135,142,157],"dynamic":[3],"behavior":[4],"of":[5,34,47,60,77,106,116,130,153,159],"multi-body":[6,107],"elastic":[7,110,126],"systems,":[8],"a":[9,28,37,57,64,150],"commonly":[10],"used":[11,90,146],"method":[12,17,46,97,137,144],"is":[13,30,66,85,138,145],"finite":[15,39,83],"element":[16,84],"conjunctively":[18],"with":[19,109],"Lagrange\u2019s":[20],"equations.":[21,95],"The":[22,41,128],"central":[23],"problem":[24],"when":[25,133],"approaching":[26],"such":[27],"system":[29],"determining":[31],"equations":[33,158],"motion":[35],"for":[36,80],"single":[38,82],"element.":[40],"paper":[42],"presents":[43],"an":[44],"alternative":[45],"calculation":[48],"theses":[49],"using":[50,134],"Gibbs\u2013Appell":[52,136],"(GA)":[53],"formulation,":[54],"which":[55,87,147],"requires":[56],"smaller":[58,139,151],"number":[59,129,152],"calculations":[61],"and,":[62],"as":[63],"result,":[65],"easier":[67],"to":[68,103,149,155],"apply":[69],"in":[70,92,101,113,122],"practice.":[71],"For":[72],"this":[73],"purpose,":[74],"energy":[76],"accelerations":[79],"one":[81],"calculated,":[86],"will":[88],"be":[89],"then":[91],"GA":[94],"This":[96],"can":[98],"have":[99,121],"advantages":[100],"applying":[102],"study":[105],"systems":[108],"elements":[111],"and":[112,118],"case":[115],"robots":[117],"manipulators":[119],"that":[120],"their":[123],"composition":[124],"some":[125],"elements.":[127],"differentiation":[131],"required":[132],"than":[140],"if":[141],"Lagrange":[143],"leads":[148],"operations":[154],"obtain":[156],"motion.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":29},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":8}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}