A variational characterization of a hyperelastic rod with hard self-contact

We consider an elastic rod, modeled as a curve in space with an impenetrable surrounding tube of radius ρ , subject to a general class of boundary conditions. The impossibility of self-intersection is then imposed as a family of scalar constraints on the physical separation of nonlocal pairs of poi...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Nonlinear analysis Ročník 74; číslo 16; s. 5388 - 5401
Hlavní autori:	Hoffman, Kathleen A., Seidman, Thomas I.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier Ltd 01.11.2011 Elsevier
Predmet:	Calculus of variations and optimal control Contact Derivation Elastic rod Energy of formation Exact sciences and technology Homotopy class Mathematical analysis Mathematical models Mathematics Non-smooth optimization Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Optimization Regularity Scalars Sciences and techniques of general use Tubes Elastic rod Homotopy class Non-smooth optimization Necessary condition Homotopy Nonlinear analysis Optimization method Optimality condition Boundary condition Mathematical model
ISSN:	0362-546X, 1873-5215
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	We consider an elastic rod, modeled as a curve in space with an impenetrable surrounding tube of radius ρ , subject to a general class of boundary conditions. The impossibility of self-intersection is then imposed as a family of scalar constraints on the physical separation of nonlocal pairs of points on the rod. Thus, the usual variational formulation of energy minimization is considered in a context of nonconvex, nonsmooth optimization. We show the existence of minimizers within suitably defined homotopy classes associated with both the centerline and the frame along the rod. The principle results are then concerned with derivation of first-order necessary conditions for optimality and some consequences of these for the contact forces and for regularity.
AbstractList	We consider an elastic rod, modeled as a curve in space with an impenetrable surrounding tube of radius [rho], subject to a general class of boundary conditions. The impossibility of self-intersection is then imposed as a family of scalar constraints on the physical separation of nonlocal pairs of points on the rod. Thus, the usual variational formulation of energy minimization is considered in a context of nonconvex, nonsmooth optimization. We show the existence of minimizers within suitably defined homotopy classes associated with both the centerline and the frame along the rod. The principle results are then concerned with derivation of first-order necessary conditions for optimality and some consequences of these for the contact forces and for regularity. We consider an elastic rod, modeled as a curve in space with an impenetrable surrounding tube of radius ρ , subject to a general class of boundary conditions. The impossibility of self-intersection is then imposed as a family of scalar constraints on the physical separation of nonlocal pairs of points on the rod. Thus, the usual variational formulation of energy minimization is considered in a context of nonconvex, nonsmooth optimization. We show the existence of minimizers within suitably defined homotopy classes associated with both the centerline and the frame along the rod. The principle results are then concerned with derivation of first-order necessary conditions for optimality and some consequences of these for the contact forces and for regularity.
Author	Seidman, Thomas I. Hoffman, Kathleen A.
Author_xml	– sequence: 1 givenname: Kathleen A. surname: Hoffman fullname: Hoffman, Kathleen A. email: khoffman@umbc.edu, khoffman@math.umbc.edu – sequence: 2 givenname: Thomas I. surname: Seidman fullname: Seidman, Thomas I. email: seidman@math.umbc.edu
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24327781$$DView record in Pascal Francis
BookMark	eNp9kM1LHTEUR0Ox0KftvstsBDcz5mOSzLgT6YcouFFwF-5kbnh5jMlrEi3613f0iYuCri5czvktzj7ZiykiId85aznj-njTRmgF47xlqmVCfCIr3hvZKMHVHlkxqUWjOn37heyXsmGMcSP1ilyc0gfIAWpIEWbq1pDBVczh6eVFk6dA149bzDhDqcHRnCb6N9Q1XdCJFpx941Ksi_WVfPYwF_z2eg_Izc8f12e_m8urX-dnp5eNk8rUZhzENHQjVxKE6PRoOCrocdRguBHeKz6hkHrsBo-9QQ9iGPph4BKZR-xRHpCj3e42pz_3WKq9C8XhPEPEdF8s14ZLoVWvF_TwFYXiYPYZogvFbnO4g_xoRSeFMT1fOLbjXE6lZPRvCGf2ua_d2Aj2ua9lyi59F0X_p7hQX6LVDGH-SDzZibg0egiYbXEBo8MpZHTVTim8L_8Du86Vtg
CODEN	NOANDD
CitedBy_id	crossref_primary_10_1007_s10915_024_02487_4 crossref_primary_10_1016_j_cma_2024_116832 crossref_primary_10_1007_s00211_020_01156_6 crossref_primary_10_1016_j_jsv_2025_119151 crossref_primary_10_1007_s10957_022_02002_5
Cites_doi	10.1016/j.na.2010.01.008 10.1007/s002050050062 10.1007/s005260100089 10.1007/s00209-007-0117-4 10.1007/s00205-004-0341-6 10.1007/s00205-003-0253-x 10.1007/s00205-010-0368-9 10.1023/A:1010911113919 10.1103/PhysRevE.61.759 10.1016/S0020-7403(02)00183-2
ContentType	Journal Article
Copyright	2011 Elsevier Ltd 2015 INIST-CNRS
Copyright_xml	– notice: 2011 Elsevier Ltd – notice: 2015 INIST-CNRS
DBID	AAYXX CITATION IQODW 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D
DOI	10.1016/j.na.2011.05.022
DatabaseName	CrossRef Pascal-Francis Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	Civil Engineering Abstracts
DeliveryMethod	fulltext_linktorsrc
Discipline	Applied Sciences Engineering Mathematics
EISSN	1873-5215
EndPage	5401
ExternalDocumentID	24327781 10_1016_j_na_2011_05_022 S0362546X11003075
GroupedDBID	--K --M -~X .~1 0R~ 123 1B1 1RT 1~. 1~5 29N 4.4 457 4G. 5VS 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABLJU ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFS ACIWK ACNNM ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD ADTZH AEBSH AECPX AEKER AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 GBLVA HMJ HVGLF HZ~ IHE J1W JJJVA KOM M26 M41 MHUIS MO0 MVM N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SDF SDG SDP SES SEW SME SPC SPCBC SST SSW SSZ T5K TN5 WUQ XPP YQT ZMT ~G- 9DU AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACLOT ACRPL ADNMO AEIPS AFJKZ AGQPQ AIIUN ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D
ID	FETCH-LOGICAL-c357t-b92d94b153a2246b71e5a8eb6a7172ff51de236b49fe87efa29989913e0fee8e3
ISICitedReferencesCount	6
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000292035500014&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0362-546X
IngestDate	Sun Sep 28 03:06:48 EDT 2025 Mon Jul 21 09:15:11 EDT 2025 Sat Nov 29 02:58:02 EST 2025 Tue Nov 18 21:45:46 EST 2025 Fri Feb 23 02:29:48 EST 2024
IsPeerReviewed	true
IsScholarly	true
Issue	16
Keywords	Elastic rod Homotopy class Non-smooth optimization Necessary condition Homotopy Nonlinear analysis Optimization method Optimality condition Boundary condition Mathematical model
Language	English
License	https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c357t-b92d94b153a2246b71e5a8eb6a7172ff51de236b49fe87efa29989913e0fee8e3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
PQID	1671326586
PQPubID	23500
PageCount	14
ParticipantIDs	proquest_miscellaneous_1671326586 pascalfrancis_primary_24327781 crossref_primary_10_1016_j_na_2011_05_022 crossref_citationtrail_10_1016_j_na_2011_05_022 elsevier_sciencedirect_doi_10_1016_j_na_2011_05_022
PublicationCentury	2000
PublicationDate	2011-11-01
PublicationDateYYYYMMDD	2011-11-01
PublicationDate_xml	– month: 11 year: 2011 text: 2011-11-01 day: 01
PublicationDecade	2010
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	Nonlinear analysis
PublicationYear	2011
Publisher	Elsevier Ltd Elsevier
Publisher_xml	– name: Elsevier Ltd – name: Elsevier
References	Schuricht, von der Mosel (br000030) 2003; 168 vander Heijden, Neukirch, Goss, Thompson (br000045) 2003; 45 Antman (br000060) 2005 Coleman, Swigon, Tobias (br000035) 2000; 61 Antman, Seidman (br000070) 2005; 175 Mordukhovich (br000015) 2006 Seidman (br000020) 2010; 72 Strzelecki, von der Mosel (br000050) 2007; 257 Gonzalez, Maddocks, Schuricht, von der Mosel (br000025) 2002; 14 Mordukhovich (br000010) 2006 Coleman, Swigon (br000040) 2000; 60 Schuricht (br000065) 1997; 140 Clarke (br000055) 1983 Hoffman, Seidman (br000005) 2010; 200 Mordukhovich (10.1016/j.na.2011.05.022_br000010) 2006 Antman (10.1016/j.na.2011.05.022_br000070) 2005; 175 Seidman (10.1016/j.na.2011.05.022_br000020) 2010; 72 vander Heijden (10.1016/j.na.2011.05.022_br000045) 2003; 45 Gonzalez (10.1016/j.na.2011.05.022_br000025) 2002; 14 Coleman (10.1016/j.na.2011.05.022_br000040) 2000; 60 Schuricht (10.1016/j.na.2011.05.022_br000065) 1997; 140 Schuricht (10.1016/j.na.2011.05.022_br000030) 2003; 168 Hoffman (10.1016/j.na.2011.05.022_br000005) 2010; 200 Antman (10.1016/j.na.2011.05.022_br000060) 2005 Coleman (10.1016/j.na.2011.05.022_br000035) 2000; 61 Strzelecki (10.1016/j.na.2011.05.022_br000050) 2007; 257 Mordukhovich (10.1016/j.na.2011.05.022_br000015) 2006 Clarke (10.1016/j.na.2011.05.022_br000055) 1983
References_xml	– volume: 175 start-page: 85 year: 2005 end-page: 150 ident: br000070 article-title: Parabolic–hyperbolic systems governing the spatial motion of nonlinearly viscoelastic rods publication-title: Arch. Ration. Mech. Anal. – year: 2006 ident: br000010 article-title: Variational Analysis and Generalized Differentiation I – volume: 60 start-page: 171 year: 2000 end-page: 221 ident: br000040 article-title: Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids publication-title: J. Elasticity – volume: 45 start-page: 161 year: 2003 end-page: 196 ident: br000045 article-title: Instability and self-contact phenomena in the writhing of clamped rods publication-title: Int. J. Mech. Sci. – volume: 140 start-page: 103 year: 1997 end-page: 159 ident: br000065 article-title: A variational approach to obstacle problems for shearable nonlinearly elastic rods publication-title: Arch. Ration. Mech. Anal. – volume: 168 start-page: 35 year: 2003 end-page: 82 ident: br000030 article-title: Euler–Lagrange equations for nonlinearly elastic rods with self-contact publication-title: Arch. Rational Mech. Anal. – year: 2006 ident: br000015 article-title: Variational Analysis and Generalized Differentiation II – volume: 14 start-page: 29 year: 2002 end-page: 68 ident: br000025 article-title: Global curvature and self-contact of nonlinearly elastic curves and rods publication-title: Calc. Var. Partial Differential Equations – volume: 72 start-page: 3911 year: 2010 end-page: 3917 ident: br000020 article-title: Normal cones to infinite intersections publication-title: Nonlinear Anal. – volume: 61 start-page: 759 year: 2000 end-page: 770 ident: br000035 article-title: Elastic stability of DNA configurations: II. Supercoiled plasmids with self-contact publication-title: Phys. Rev. E – volume: 200 start-page: 255 year: 2010 end-page: 284 ident: br000005 article-title: A variational rod model with a singular nonlocal potential publication-title: Arch. Ration. Mech. Anal. – year: 1983 ident: br000055 article-title: Optimization and Nonsmooth Analysis – volume: 257 start-page: 107 year: 2007 end-page: 130 ident: br000050 article-title: On rectifiable curves with publication-title: Math. Z. – year: 2005 ident: br000060 article-title: Nonlinear Problems in Elasticity – volume: 72 start-page: 3911 year: 2010 ident: 10.1016/j.na.2011.05.022_br000020 article-title: Normal cones to infinite intersections publication-title: Nonlinear Anal. doi: 10.1016/j.na.2010.01.008 – year: 2006 ident: 10.1016/j.na.2011.05.022_br000015 – volume: 140 start-page: 103 year: 1997 ident: 10.1016/j.na.2011.05.022_br000065 article-title: A variational approach to obstacle problems for shearable nonlinearly elastic rods publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s002050050062 – volume: 14 start-page: 29 year: 2002 ident: 10.1016/j.na.2011.05.022_br000025 article-title: Global curvature and self-contact of nonlinearly elastic curves and rods publication-title: Calc. Var. Partial Differential Equations doi: 10.1007/s005260100089 – volume: 257 start-page: 107 year: 2007 ident: 10.1016/j.na.2011.05.022_br000050 article-title: On rectifiable curves with Lp bounds on global curvature: self-avoidance, regularity, and minimizing knots publication-title: Math. Z. doi: 10.1007/s00209-007-0117-4 – volume: 175 start-page: 85 year: 2005 ident: 10.1016/j.na.2011.05.022_br000070 article-title: Parabolic–hyperbolic systems governing the spatial motion of nonlinearly viscoelastic rods publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-004-0341-6 – volume: 168 start-page: 35 year: 2003 ident: 10.1016/j.na.2011.05.022_br000030 article-title: Euler–Lagrange equations for nonlinearly elastic rods with self-contact publication-title: Arch. Rational Mech. Anal. doi: 10.1007/s00205-003-0253-x – volume: 200 start-page: 255 issue: 1 year: 2010 ident: 10.1016/j.na.2011.05.022_br000005 article-title: A variational rod model with a singular nonlocal potential publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-010-0368-9 – volume: 60 start-page: 171 year: 2000 ident: 10.1016/j.na.2011.05.022_br000040 article-title: Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids publication-title: J. Elasticity doi: 10.1023/A:1010911113919 – year: 2005 ident: 10.1016/j.na.2011.05.022_br000060 – volume: 61 start-page: 759 year: 2000 ident: 10.1016/j.na.2011.05.022_br000035 article-title: Elastic stability of DNA configurations: II. Supercoiled plasmids with self-contact publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.61.759 – volume: 45 start-page: 161 year: 2003 ident: 10.1016/j.na.2011.05.022_br000045 article-title: Instability and self-contact phenomena in the writhing of clamped rods publication-title: Int. J. Mech. Sci. doi: 10.1016/S0020-7403(02)00183-2 – year: 1983 ident: 10.1016/j.na.2011.05.022_br000055 – year: 2006 ident: 10.1016/j.na.2011.05.022_br000010
SSID	ssj0001736
Score	2.002962
Snippet	We consider an elastic rod, modeled as a curve in space with an impenetrable surrounding tube of radius ρ , subject to a general class of boundary conditions.... We consider an elastic rod, modeled as a curve in space with an impenetrable surrounding tube of radius [rho], subject to a general class of boundary...
SourceID	proquest pascalfrancis crossref elsevier
SourceType	Aggregation Database Index Database Enrichment Source Publisher
StartPage	5388
SubjectTerms	Calculus of variations and optimal control Contact Derivation Elastic rod Energy of formation Exact sciences and technology Homotopy class Mathematical analysis Mathematical models Mathematics Non-smooth optimization Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Optimization Regularity Scalars Sciences and techniques of general use Tubes
Title	A variational characterization of a hyperelastic rod with hard self-contact
URI	https://dx.doi.org/10.1016/j.na.2011.05.022 https://www.proquest.com/docview/1671326586
Volume	74
WOSCitedRecordID	wos000292035500014&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-5215 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001736 issn: 0362-546X databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bb9MwFLaqjQcQ4jKYKJfJSLygKiOO4zh5rKAVA1aQNlDfLCexBVOVVktXTfv1O64vSwcMeOAlatM6iXK-nFvO-Q5Cr6q4zkrT-SupjqOUyjoqc6ajuqoJ11ka1-spEd8-8ckkn06LL73eke-FWc140-Tn58Xiv4oa9oGwTevsP4g7HBR2wGcQOmxB7LD9K8EPByuIf32OrwqEzBfBOZSD7xB9mi6Wds3gPHcV6KYBa9CqmY5MATus6nquE8upIU3NpeUxCYj4PB4fDifd2oyrDOnR6OCd-9HWIrk0bR0yp2Qj0eA7YDoKynRcsXQ9iTBoUztzx6OmqxtBteYdOwuuIvmlDrfphJP9RjqGVbYf297lTbrsa2YsFBcmKU04N-342wlnBWjr7eHBaPohGGjCaeZZxczlu7fXtuxv86y_81buLmQLz5C2w09-suNr5-T4Abrnogo8tGh4iHqq2UH3XYSBnf5ud9CdDv0kfDsMnL3tI_RxiDvAwdeBg-caS9wFDgbgYAMcbICDu8B5jL6OR8dv30du1EZUUcaXUVkkdZGWYP6kYRgsOVFM5qrMJIT7idaM1CqhWZkWWuVcaQleDETqhKpYK5Uruou2mnmjniDMUqrhrmcQDxUprSEglgkzZflE1yWhpI_e-FsqKsdDb8ahzIQvODwRjRRGCCJmAoTQR6_DioXlYLnhv9RLSTgf0vqGAuB1w6q9DYGG03gs9dFLL2EB-te8VJONmp-1gmScQAjE8uzpnw7yDN2-eq6eo63l6Zl6gW5Vq-WP9nTPofQSj2ykkQ
linkProvider	Elsevier
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+variational+characterization+of+a+hyperelastic+rod+with+hard+self-contact&rft.jtitle=Nonlinear+analysis&rft.au=HOFFMAN%2C+Kathleen+A&rft.au=SEIDMAN%2C+Thomas+I&rft.date=2011-11-01&rft.pub=Elsevier&rft.issn=0362-546X&rft.volume=74&rft.issue=16&rft.spage=5388&rft.epage=5401&rft_id=info:doi/10.1016%2Fj.na.2011.05.022&rft.externalDBID=n%2Fa&rft.externalDocID=24327781
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0362-546X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0362-546X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0362-546X&client=summon