Enhanced multiple-point beam-to-beam frictionless contact finite element

Litewka, Przemysław

doi:10.1007/s00466-013-0881-4

Cited by 30 publications

(35 citation statements)

References 11 publications

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“…Here the latter term only will be discussed. It is assumed that the contact model is independent of the beam model itself, as was assumed in previous research (e.g., in [17]), while the normal contact component was analyzed in detail in [16]. For the case with three contact pairs as introduced in Sect.…”

Section: Friction Contribution To the Weak Formmentioning

confidence: 99%

“…The multiple-point beam-to-beam contact finite element was developed in [16] to model in a more precise way the situations, when contact between beams cannot be considered as point-wise. The frictionless interaction between beams was considered therein.…”

Section: Introductionmentioning

confidence: 99%

“…The adopted interpretation of the contact zone between two cylinders as a curved line is valid, if the assumption of small strains and undeformable cross-sections is kept, as was assumed in the previous papers [3,4,16].…”

Section: Introductionmentioning

confidence: 99%

“…2 a brief introduction of geometrical considerations regarding the two additional contact pairs is presented repeating the ideas from [16]. To this end also some results of the finite element discretisation for the frictionless case are summarised in Appendix 3.…”

Section: Introductionmentioning

confidence: 99%

“…In this way the components due to friction of the residual vector and the consistent tangent stiffness matrix for the contact element are determined. Combined with the normal contact components from [16] they yield the complete frictional contact finite element formulation, which was embedded in the author's computer program.…”

Section: Introductionmentioning

confidence: 99%

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Frictional beam-to-beam multiple-point contact finite element

Litewka

2015

Comput Mech

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The present paper is the extension of author's earlier research devoted to more accurate numerical modelling of beam-to-beam contact in the cases when beam axes form acute angles in the contact zone. In such situation with beam deformations taken into account, the contact cannot be considered as point-wise but it extends to a certain area. To cover such a case in a more realistic way, two additional pairs of contact points are introduced to accompany the original single pair of contact points from the point-wise formulation. The Coulomb friction model is introduced and advantage is taken from the analogy to plasticity. The penalty method is used to enforce the contact and friction constraints. The appropriate kinematic variables for tangential contact and their finite element approximation are derived. Basing on the weak form for frictional contact and its linearisation, the tangent stiffness matrix and the residual vector are derived. The enhanced element is tested using author's computer programs and comparisons with the point-wise contact elements are made.

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Section: Friction Contribution To the Weak Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Frictional beam-to-beam multiple-point contact finite element

Litewka

2015

Comput Mech

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Geometrically exact theory of contact interactions – a general approach with a special focus on curve‐tosurface contact

Konyukhov

Schweizerhof

2014

GAMM-Mitteilungen

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Geometrically exact theory of contact interactions is aiming on the development of the unified geometrical formulation of computational contact algorithms for various geometrical situations of contacting bodies leading to contact pairs: surface‐to‐surface, curve‐to‐surface, point‐to‐surface, curve‐to‐curve, point‐to‐curve, point‐to‐point. The construction of the corresponding computational contact algorithms is considered in accordance with the geometry of contacting bodies in covariant and closed forms. These forms can be easily discretized within finite element methods independently of the order of approximation and, therefore, the result is straightforwardly applied within any further method: high order finite element methods, iso‐geometric finite element methods etc. Application for contact between bodies with iso‐ and anisotropic surface, for contact between cables and curvilinear beams is straightforward. Recent developments include the various approaches to describe the ”Curve‐to‐Surface” contact pair; and the “Solid Beam‐to‐Solid Beam” contact algorithm, fully resolving the problem of “parallel tangents” of “Curve‐to‐Curve” contact algorithm. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Consistent development of a beam‐to‐beam contact algorithm via the curve‐to‐solid beam contact: Analysis for the nonfrictional case

Konyukhov

Mrenes

Schweizerhof

2017

Numerical Meth Engineering

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Beam-to-beam contact can be dually described depending on the scale as contact between curves or contact between surfaces. The surface-to-surface algorithm requires a computationally expensive continuum description of the beams. The curve-to-curve contact algorithm is generated from the corresponding closest point projection procedure determining a minimal distance between curves and involves less expensive beam finite elements.The existence and uniqueness criterion of the closest point projection procedure formulated already in earlier publications is analyzed in detail, especially in the case of multiple solutions for "parallel curves." It is shown that the curve-to-curve contact algorithm cannot be applied for general parallel curves, which can be generated in an arbitrary range of angles between the tangent lines.A new curve-to-solid beam contact algorithm is here developed. This algorithm requires a special solid-beam finite element and is combining the advantages of surface contact together with the flexibility of the application to beam-to-beam contact.Further, a special case with "parallel tangent" vectors is considered from the classical Hertzian contact problem. It is found numerically that the corresponding length of a contact zone is well correlated with the Hertz theory. A possible application of the developed strategy for wire ropes is analyzed numerically.

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Enhanced multiple-point beam-to-beam frictionless contact finite element

Cited by 30 publications

References 11 publications

Frictional beam-to-beam multiple-point contact finite element

Frictional beam-to-beam multiple-point contact finite element

Geometrically exact theory of contact interactions – a general approach with a special focus on curve‐tosurface contact

Consistent development of a beam‐to‐beam contact algorithm via the curve‐to‐solid beam contact: Analysis for the nonfrictional case

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