Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2126135062', 'doi': 'https://doi.org/10.1002/(sici)1097-0207(19970215)40:3<473::aid-nme75>3.0.co;2-u', 'title': 'A UNIFIED TIMOSHENKO BEAM B-SPLINE RAYLEIGH-RITZ METHOD FOR VIBRATION AND BUCKLING ANALYSIS OF THICK AND THIN BEAMS AND PLATES', 'display_name': 'A UNIFIED TIMOSHENKO BEAM B-SPLINE RAYLEIGH-RITZ METHOD FOR VIBRATION AND BUCKLING ANALYSIS OF THICK AND THIN BEAMS AND PLATES', 'publication_year': 1997, 'publication_date': '1997-02-15', 'ids': {'openalex': 'https://openalex.org/W2126135062', 'doi': 'https://doi.org/10.1002/(sici)1097-0207(19970215)40:3<473::aid-nme75>3.0.co;2-u', 'mag': '2126135062'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/(sici)1097-0207(19970215)40:3<473::aid-nme75>3.0.co;2-u', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S165651092', 'display_name': 'International Journal for Numerical Methods in Engineering', 'issn_l': '0029-5981', 'issn': ['0029-5981', '1097-0207'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5082823113', 'display_name': 'Simon Wang', 'orcid': 'https://orcid.org/0000-0002-8860-2078'}, 'institutions': [{'id': 'https://openalex.org/I143804889', 'display_name': 'Loughborough University', 'ror': 'https://ror.org/04vg4w365', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I143804889']}], 'countries': ['GB'], 'is_corresponding': True, 'raw_author_name': 'S. WANG', 'raw_affiliation_strings': ['Department of AAETS, Loughborough University, Loughborough LE11 3TU, U.K.'], 'affiliations': [{'raw_affiliation_string': 'Department of AAETS, Loughborough University, Loughborough LE11 3TU, U.K.', 'institution_ids': ['https://openalex.org/I143804889']}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5082823113'], 'corresponding_institution_ids': ['https://openalex.org/I143804889'], 'apc_list': {'value': 5050, 'currency': 'USD', 'value_usd': 5050, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 5.189, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 42, 'citation_normalized_percentile': {'value': 0.944354, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 90, 'max': 91}, 'biblio': {'volume': '40', 'issue': '3', 'first_page': '473', 'last_page': '491'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10221', 'display_name': 'Modeling and Analysis of Functionally Graded Plates', 'score': 0.9999, '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': 'Modeling and Analysis of Functionally Graded Plates', 'score': 0.9999, '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/T10713', 'display_name': 'Developments and Applications of Concrete-Filled Steel Tubes', 'score': 0.9979, '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'}}, {'id': 'https://openalex.org/T12206', 'display_name': 'Analysis and Control of Axially Moving Dynamics', 'score': 0.9954, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/timoshenko-beam-theory', 'display_name': 'Timoshenko beam theory', 'score': 0.824484}, {'id': 'https://openalex.org/keywords/rayleigh–ritz-method', 'display_name': 'Rayleigh–Ritz method', 'score': 0.7242569}, {'id': 'https://openalex.org/keywords/shear-deformation-theory', 'display_name': 'Shear Deformation Theory', 'score': 0.563157}, {'id': 'https://openalex.org/keywords/vibration-analysis', 'display_name': 'Vibration Analysis', 'score': 0.556909}, {'id': 'https://openalex.org/keywords/buckling-behavior', 'display_name': 'Buckling Behavior', 'score': 0.545737}, {'id': 'https://openalex.org/keywords/ritz-method', 'display_name': 'Ritz method', 'score': 0.52507466}, {'id': 'https://openalex.org/keywords/plate-theory', 'display_name': 'Plate theory', 'score': 0.5229543}, {'id': 'https://openalex.org/keywords/viscoelastic-beams', 'display_name': 'Viscoelastic Beams', 'score': 0.517223}, {'id': 'https://openalex.org/keywords/multilayered-structures', 'display_name': 'Multilayered Structures', 'score': 0.506721}], 'concepts': [{'id': 'https://openalex.org/C190699663', 'wikidata': 'https://www.wikidata.org/wiki/Q2435044', 'display_name': 'Timoshenko beam theory', 'level': 3, 'score': 0.824484}, {'id': 'https://openalex.org/C146996283', 'wikidata': 'https://www.wikidata.org/wiki/Q165618', 'display_name': 'Rotary inertia', 'level': 3, 'score': 0.75765675}, {'id': 'https://openalex.org/C70940138', 'wikidata': 'https://www.wikidata.org/wiki/Q852247', 'display_name': 'Rayleigh–Ritz method', 'level': 3, 'score': 0.7242569}, {'id': 'https://openalex.org/C198394728', 'wikidata': 'https://www.wikidata.org/wiki/Q3695508', 'display_name': 'Vibration', 'level': 2, 'score': 0.5752376}, {'id': 'https://openalex.org/C85476182', 'wikidata': 'https://www.wikidata.org/wiki/Q693104', 'display_name': 'Buckling', 'level': 2, 'score': 0.5699366}, {'id': 'https://openalex.org/C66938386', 'wikidata': 'https://www.wikidata.org/wiki/Q633538', 'display_name': 'Structural engineering', 'level': 1, 'score': 0.5474551}, {'id': 'https://openalex.org/C168834538', 'wikidata': 'https://www.wikidata.org/wiki/Q3705329', 'display_name': 'Beam (structure)', 'level': 2, 'score': 0.52860093}, {'id': 'https://openalex.org/C21575042', 'wikidata': 'https://www.wikidata.org/wiki/Q905132', 'display_name': 'Ritz method', 'level': 3, 'score': 0.52507466}, {'id': 'https://openalex.org/C16826683', 'wikidata': 'https://www.wikidata.org/wiki/Q2098720', 'display_name': 'Plate theory', 'level': 3, 'score': 0.5229543}, {'id': 'https://openalex.org/C184050105', 'wikidata': 'https://www.wikidata.org/wiki/Q273163', 'display_name': 'Isotropy', 'level': 2, 'score': 0.5002754}, {'id': 'https://openalex.org/C96035792', 'wikidata': 'https://www.wikidata.org/wiki/Q43606218', 'display_name': 'Shear (geology)', 'level': 2, 'score': 0.42242903}, {'id': 'https://openalex.org/C192562407', 'wikidata': 'https://www.wikidata.org/wiki/Q228736', 'display_name': 'Materials science', 'level': 0, 'score': 0.4038295}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.28706643}, {'id': 'https://openalex.org/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.21902314}, {'id': 'https://openalex.org/C135628077', 'wikidata': 'https://www.wikidata.org/wiki/Q220184', 'display_name': 'Finite element method', 'level': 2, 'score': 0.20435414}, {'id': 'https://openalex.org/C159985019', 'wikidata': 'https://www.wikidata.org/wiki/Q181790', 'display_name': 'Composite material', 'level': 1, 'score': 0.13996124}, {'id': 'https://openalex.org/C120665830', 'wikidata': 'https://www.wikidata.org/wiki/Q14620', 'display_name': 'Optics', 'level': 1, 'score': 0.12642759}, {'id': 'https://openalex.org/C24890656', 'wikidata': 'https://www.wikidata.org/wiki/Q82811', 'display_name': 'Acoustics', 'level': 1, 'score': 0.0776597}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/(sici)1097-0207(19970215)40:3<473::aid-nme75>3.0.co;2-u', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S165651092', 'display_name': 'International Journal for Numerical Methods in Engineering', 'issn_l': '0029-5981', 'issn': ['0029-5981', '1097-0207'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 24, 'referenced_works': ['https://openalex.org/W185715123', 'https://openalex.org/W1969878894', 'https://openalex.org/W2009993675', 'https://openalex.org/W2012078052', 'https://openalex.org/W2024321552', 'https://openalex.org/W2030911466', 'https://openalex.org/W2066285031', 'https://openalex.org/W2068847877', 'https://openalex.org/W2072106333', 'https://openalex.org/W2077640448', 'https://openalex.org/W2077801132', 'https://openalex.org/W2077924899', 'https://openalex.org/W2083345508', 'https://openalex.org/W2084871066', 'https://openalex.org/W2087991437', 'https://openalex.org/W2088315668', 'https://openalex.org/W2089405062', 'https://openalex.org/W2090114470', 'https://openalex.org/W2117713971', 'https://openalex.org/W2128978199', 'https://openalex.org/W2132782245', 'https://openalex.org/W2143749428', 'https://openalex.org/W2261621682', 'https://openalex.org/W2266285536'], 'related_works': ['https://openalex.org/W4387449185', 'https://openalex.org/W4313420248', 'https://openalex.org/W4235532775', 'https://openalex.org/W307745419', 'https://openalex.org/W3046292589', 'https://openalex.org/W2809618120', 'https://openalex.org/W2490793394', 'https://openalex.org/W2221593332', 'https://openalex.org/W2126135062', 'https://openalex.org/W2057691046'], 'abstract_inverted_index': {'First,': [0], 'the': [1, 5, 10, 24, 32, 37, 72, 81, 89, 94, 106, 109], 'shear-locking': [2, 11, 25], 'phenomenon': [3], 'in': [4, 15, 116], 'wψBkSRRM1–3': [6], 'is': [7, 46, 87, 103, 130], 'investigated': [8], 'and': [9, 19, 30, 58, 60, 112, 123, 136, 139], 'terms': [12], 'are': [13, 28, 121], 'identified': [14], 'both': [16, 134], 'one-dimensional': [17], 'beam': [18, 39, 56, 96], 'two-dimensional': [20], 'plate': [21, 76, 100], 'analyses.': [22], 'Subsequently': [23], 'free': [26], 'conditions': [27, 36], 'proposed': [29], 'under': [31], 'guidance': [33], 'of': [34, 51, 63, 83, 85], 'these': [35], 'Timoshenko': [38, 55], 'B-spline': [40], 'Rayleigh–Ritz': [41], 'method,': [42], 'designated': [43], 'as': [44, 91], 'TBkSRRM,': [45], 'formulated': [47], 'for': [48, 133], 'vibration': [49, 59], 'analysis': [50, 62], 'beams': [52, 138], 'based': [53, 70], 'on': [54, 71], 'theory': [57, 77, 97, 101], 'buckling': [61], 'isotropic': [64], 'plates': [65], 'or': [66, 98], 'fibre-reinforced': [67], 'composite': [68], 'laminates': [69], 'first-order': [73], 'shear': [74], 'deformation': [75], '(SDPT).': [78], 'In': [79], 'TBkSRRM': [80, 107], 'number': [82], 'degrees': [84], 'freedom': [86], 'exactly': [88], 'same': [90], 'that': [92, 126], 'when': [93], 'Bernoulli–Euler': [95], 'classical': [99], '(CPT)': [102], 'used.': [104], 'However,': [105], 'includes': [108], 'through-thickness': [110], 'shearing': [111], 'rotary': [113], 'inertia': [114], 'effects': [115], 'full.': [117], 'Several': [118], 'numerical': [119], 'applications': [120], 'presented': [122], 'they': [124], 'show': [125], 'this': [127], 'unified': [128], 'approach': [129], 'extremely': [131], 'efficient': [132], 'thick': [135], 'thin': [137], 'plates.': [140], '©': [141], '1997': [142], 'by': [143], 'John': [144], 'Wiley': [145], '&': [146], 'Sons,': [147], 'Ltd.': [148]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2126135062', 'counts_by_year': [{'year': 2022, 'cited_by_count': 2}, {'year': 2021, 'cited_by_count': 1}, {'year': 2019, 'cited_by_count': 1}, {'year': 2018, 'cited_by_count': 3}, {'year': 2017, 'cited_by_count': 3}, {'year': 2016, 'cited_by_count': 1}, {'year': 2015, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 4}, {'year': 2012, 'cited_by_count': 2}], 'updated_date': '2024-08-15T09:54:49.523299', 'created_date': '2016-06-24'}