{"id":"https://openalex.org/W7224915829","doi":"https://doi.org/10.68381/jca34027","title":"A Snowpiercer Model: Dynamic Beam Solution for Highly Nonlinear Reaction, Energy Inequality, and Granular Foundation","display_name":"A Snowpiercer Model: Dynamic Beam Solution for Highly Nonlinear Reaction, Energy Inequality, and Granular Foundation","publication_year":2026,"publication_date":"2026-10-30","ids":{"openalex":"https://openalex.org/W7224915829","doi":"https://doi.org/10.68381/jca34027"},"language":"en","primary_location":{"id":"doi:10.68381/jca34027","doi":"https://doi.org/10.68381/jca34027","is_oa":true,"landing_page_url":"https://doi.org/10.68381/jca34027","pdf_url":"https://journalofconvexanalysis.com/articles/jca34027/jca34027.pdf","source":{"id":"https://openalex.org/S163398844","display_name":"Journal of convex analysis","issn_l":"0944-6532","issn":["0944-6532","2363-6394"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Convex Analysis","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://journalofconvexanalysis.com/articles/jca34027/jca34027.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061705141","display_name":"Victor A. Kovtunenko","orcid":"https://orcid.org/0000-0001-5664-2625","observed_orcids":["https://orcid.org/0000-0001-5664-2625"]},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]},{"id":"https://openalex.org/I4210108044","display_name":"Nawi Graz","ror":"https://ror.org/01mm16571","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210108044"]},{"id":"https://openalex.org/I4210151517","display_name":"Lavrentyev Institute of Hydrodynamics","ror":"https://ror.org/04t5w6b17","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210127387","https://openalex.org/I4210151517","https://openalex.org/I4210164537"]}],"countries":["AT","RU"],"is_corresponding":true,"raw_author_name":"Victor A. Kovtunenko","raw_affiliation_strings":["Dept. of Mathematics and Scientific Computing, Karl-Franzens University, NAWI Graz, Graz, Austria","Lavrent'ev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, Novosibirsk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics and Scientific Computing, Karl-Franzens University, NAWI Graz, Graz, Austria","institution_ids":["https://openalex.org/I15766117","https://openalex.org/I4210108044"]},{"raw_affiliation_string":"Lavrent'ev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210151517"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061705141"],"corresponding_institution_ids":["https://openalex.org/I15766117","https://openalex.org/I4210108044","https://openalex.org/I4210151517"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.85852382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"1","first_page":"408","last_page":"414"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9603999853134155,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9603999853134155,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.010099999606609344,"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/T10842","display_name":"Railway Engineering and Dynamics","score":0.009800000116229057,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/euler-bernoulli-beam","display_name":"Euler-Bernoulli beam","score":0.9319999814033508},{"id":"https://openalex.org/keywords/energy-inequality","display_name":"energy inequality","score":0.7839999794960022},{"id":"https://openalex.org/keywords/variational-solutions","display_name":"variational solutions","score":0.75},{"id":"https://openalex.org/keywords/semilinear-evolution-equations","display_name":"semilinear evolution equations","score":0.6600000262260437},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.8270000219345093},{"id":"https://openalex.org/keywords/high-speed-vehicles","display_name":"high-speed vehicles","score":0.5950000286102295},{"id":"https://openalex.org/keywords/plasticity","display_name":"plasticity","score":0.675000011920929},{"id":"https://openalex.org/keywords/aging-materials","display_name":"aging materials","score":0.7049999833106995},{"id":"https://openalex.org/keywords/hardening","display_name":"hardening","score":0.921999990940094}],"concepts":[{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.7598000168800354},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6972000002861023},{"id":"https://openalex.org/C2781355719","wikidata":"https://www.wikidata.org/wiki/Q2080698","display_name":"Deflection (physics)","level":2,"score":0.5954999923706055},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5630999803543091},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49619999527931213},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.4884999990463257},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.47510001063346863},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.4740999937057495},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.47290000319480896},{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.447299987077713},{"id":"https://openalex.org/C44255700","wikidata":"https://www.wikidata.org/wiki/Q978423","display_name":"Hardening (computing)","level":3,"score":0.43220001459121704},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3849000036716461},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3840999901294708},{"id":"https://openalex.org/C32568104","wikidata":"https://www.wikidata.org/wiki/Q1155083","display_name":"Granular material","level":2,"score":0.37540000677108765},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.3646000027656555},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C153919410","wikidata":"https://www.wikidata.org/wiki/Q9993851","display_name":"Weak formulation","level":3,"score":0.30979999899864197},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26269999146461487},{"id":"https://openalex.org/C84551667","wikidata":"https://www.wikidata.org/wiki/Q155640","display_name":"Potential energy","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.68381/jca34027","doi":"https://doi.org/10.68381/jca34027","is_oa":true,"landing_page_url":"https://doi.org/10.68381/jca34027","pdf_url":"https://journalofconvexanalysis.com/articles/jca34027/jca34027.pdf","source":{"id":"https://openalex.org/S163398844","display_name":"Journal of convex analysis","issn_l":"0944-6532","issn":["0944-6532","2363-6394"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Convex Analysis","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.68381/jca34027","doi":"https://doi.org/10.68381/jca34027","is_oa":true,"landing_page_url":"https://doi.org/10.68381/jca34027","pdf_url":"https://journalofconvexanalysis.com/articles/jca34027/jca34027.pdf","source":{"id":"https://openalex.org/S163398844","display_name":"Journal of convex analysis","issn_l":"0944-6532","issn":["0944-6532","2363-6394"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Convex Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320325582","display_name":"Karl-Franzens-Universit\u00e4t Graz","ror":"https://ror.org/01faaaf77"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224915829.pdf","grobid_xml":"https://content.openalex.org/works/W7224915829.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W84946493","https://openalex.org/W648349353","https://openalex.org/W1589352600","https://openalex.org/W1596635901","https://openalex.org/W1978531073","https://openalex.org/W1986122208","https://openalex.org/W2003221092","https://openalex.org/W2006957478","https://openalex.org/W2031367896","https://openalex.org/W2038081132","https://openalex.org/W2042794102","https://openalex.org/W2060256160","https://openalex.org/W2069052857","https://openalex.org/W2092519665","https://openalex.org/W2134167120","https://openalex.org/W2225049010","https://openalex.org/W2475444157","https://openalex.org/W2774033079","https://openalex.org/W2929580147","https://openalex.org/W3015495736","https://openalex.org/W3027447781","https://openalex.org/W3205718342","https://openalex.org/W4200368386","https://openalex.org/W4225265316","https://openalex.org/W4242998625","https://openalex.org/W4251803873","https://openalex.org/W4297201185","https://openalex.org/W4313271706","https://openalex.org/W4322580360","https://openalex.org/W4381786177","https://openalex.org/W4390174571","https://openalex.org/W4393338569","https://openalex.org/W4396810119","https://openalex.org/W4400662036","https://openalex.org/W4400662354","https://openalex.org/W4407853171","https://openalex.org/W4408516182","https://openalex.org/W4410282421","https://openalex.org/W4412449638","https://openalex.org/W4415671286"],"related_works":["https://openalex.org/W4412449638","https://openalex.org/W2793385706","https://openalex.org/W4315651597","https://openalex.org/W7100761613","https://openalex.org/W2016431017","https://openalex.org/W1160158988","https://openalex.org/W3164013021","https://openalex.org/W6990619624","https://openalex.org/W2373966358","https://openalex.org/W2912099084"],"abstract_inverted_index":{"The":[0,51],"dynamic":[1],"contact":[2],"problem":[3],"for":[4,59],"Euler-Bernoulli":[5],"beam":[6,61],"equation":[7,48],"with":[8],"highly":[9],"nonlinear":[10],"reaction":[11,52],"term":[12],"is":[13,49,57],"formulated":[14],"to":[15,43],"model":[16],"deflection":[17],"of":[18,28,53],"a":[19,23,29],"rail":[20],"road":[21],"on":[22,34],"granular":[24,55],"foundation":[25,56],"under":[26],"motion":[27],"high-speed":[30],"vehicle":[31],"(snowpiercer).":[32],"Based":[33],"the":[35,44,54],"energy":[36],"inequality":[37],"and":[38,67],"Galerkin":[39],"approximation,":[40],"variational":[41],"solution":[42],"evolutionary":[45],"semi-linear":[46],"differential":[47],"proved.":[50],"presented":[58],"periodic":[60],"vibrations,":[62],"which":[63],"illustrate":[64],"plastic,":[65],"ageing,":[66],"hardening":[68],"phenomena.":[69]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2026-10-31T00:00:00"}
