View in EDS PDF Full Text

Hermite polynomial smoothing in beam-to-beam frictional contact.

Saved in:
Bibliographic Details
Title: Hermite polynomial smoothing in beam-to-beam frictional contact.
Authors: Litewka, Przemysław1 przemyslaw.litewka@ikb.poznan.pl
Source: Computational Mechanics. Oct2007, Vol. 40 Issue 5, p815-826. 12p. 11 Diagrams, 1 Chart, 6 Graphs.
Subjects: Published errata, Paper, Polynomials, Finite element method, Hermite polynomials, Matrices (Mathematics), Friction
Abstract: In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Links:
  – Type: pdflink
Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 26284267
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Hermite polynomial smoothing in beam-to-beam frictional contact.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Litewka%2C+Przemysław%22">Litewka, Przemysław</searchLink><relatesTo>1</relatesTo><i> przemyslaw.litewka@ikb.poznan.pl</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Computational+Mechanics%22">Computational Mechanics</searchLink>. Oct2007, Vol. 40 Issue 5, p815-826. 12p. 11 Diagrams, 1 Chart, 6 Graphs.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Published+errata%22">Published errata</searchLink><br /><searchLink fieldCode="DE" term="%22Paper%22">Paper</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Hermite+polynomials%22">Hermite polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Friction%22">Friction</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=26284267
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s00466-006-0143-9
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 12
        StartPage: 815
    Subjects:
      – SubjectFull: Published errata
        Type: general
      – SubjectFull: Paper
        Type: general
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Hermite polynomials
        Type: general
      – SubjectFull: Matrices (Mathematics)
        Type: general
      – SubjectFull: Friction
        Type: general
    Titles:
      – TitleFull: Hermite polynomial smoothing in beam-to-beam frictional contact.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Litewka, Przemysław
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 15
              M: 10
              Text: Oct2007
              Type: published
              Y: 2007
          Identifiers:
            – Type: issn-print
              Value: 01787675
          Numbering:
            – Type: volume
              Value: 40
            – Type: issue
              Value: 5
          Titles:
            – TitleFull: Computational Mechanics
              Type: main
ResultId 1