On Contact Between Three-Dimensional Beams Undergoing Large Deflections

Wriggers, Peter; Zavarise, Giorgio

doi:10.1002/(sici)1099-0887(199706)13:6<429::aid-cnm70>3.0.co;2-x

Cited by 131 publications

(135 citation statements)

References 3 publications

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“…in [11] and continued in [9,10,12] where contact without and with Coulomb friction for beams of circular and rectangular cross-sections was covered. The further development concerned inclusion of thermal and electric coupling, see [1].…”

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confidence: 99%

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

Litewka

2013

Comput Mech

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In this paper a new contact finite element for beams with circular cross-sections is presented. The element is an enhancement of the previously formulated point-wise beam-to-beam contact finite elements to be used in cases when beams get in contact at very acute angles. In such situation, if beam deformations in the vicinity of the contact zone are taken into account, the contact is not 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. The central pair is determined using the orthogonality conditions for the beam axes and the positions of two extra points are defined on one beam axis by a shift of the local co-ordinate. This shift depends on beams geometry and the current angle between tangent vectors at the central contact point. The appropriate kinematic variables for normal contact together with their finite element approximation are derived. Basing on the weak form for normal contact and its linearisation, the tangent stiffness matrix and the residual vector are derived. The new element is tested using author's computer programs and comparisons with the point-wise contact elements are made.

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confidence: 99%

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

Litewka

2013

Comput Mech

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“…In the suggested multiplepoint beam-to-beam contact element three pairs of contact points are considered-the central contact points C mn − C sn and two additional ones. The central points are found using the orthogonality conditions, as described in [1,3] where the minimisation of the axes distance d N yields the local coordinates of the closest points on each beam −ξ mn and ξ sn (−1 ≤ ξ in ≤ 1, i = s or m). Hence, the normal contact gap function is…”

Section: Additional Contact Pairsmentioning

confidence: 99%

“…Generally, each of the conditions (6) and (7) represents a non-linear equation, which can be solved iteratively using the Newton-Raphson method. Following the lines of the solution for the central points with a set of orthogonality conditions (see [1]) with the use of the following expressions for the position vectors and their derivatives with respect to local co-ordinates, determined at the additional points…”

Section: Additional Contact Pairsmentioning

confidence: 99%

“…The efforts to analyze it numerically were started by Wriggers and Zavarise in [1] B Przemysław Litewka przemyslaw.litewka@gmail.com 1 Institute of Structural Engineering, Poznań University of Technology, ul. Piotrowo 5, 60-965 Poznan, Poland and subsequently continued in [2][3][4] where contact without and with Coulomb friction for beams of circular and rectangular cross-sections was considered.…”

Section: Introductionmentioning

confidence: 99%

“…Since then further developments appeared and they included inclusion of thermal and electric coupling [5], smoothing procedures for 3D curves representing axes of beams in contact, e.g., [6] as well as a rigorous approach to the question of solution existence and uniqueness in the point-wise contact formulation, which was presented by Konyukhov and Schweizerhof in [7]. These authors focused their interest on the closest-point projection procedure, which in the particular case of the beam-to-beam contact leads to the orthogonality conditions, see [1]. The same authors used their approach to analyse the problem of rope wound around a cylinder and the question of knottightening [8].…”

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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Re-visiting the contact patch test

Crisfield

2000

Int. J. Numer. Meth. Engng.

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The paper uses the contact patch test to assess both linear and quadratic elements in relation to straight and curved contact surfaces. A new contact formulation is proposed which uses a combination of linear and quadratic shape functions. The potential advantages of the new formulation are demonstrated. a mid-side node on one side of the interface close to (here coincident with) a corner node on the other side. A new contact formulationThe previous tests have pointed the way for an improved formulation. The problems appear to be associated with the higher-order shape functions that produce the non-uniform distribution of forces (or Lagrange multipliers) at the interface. A possible solution could be to derive higherorder continuum elements that are speci"cally designed to produce smoother force distributions at the boundaries. However, for the present, we will duck this challenge and work with linear 444 M. A. CRISFIELD

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On Contact Between Three-Dimensional Beams Undergoing Large Deflections

Cited by 131 publications

References 3 publications

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

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

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

Re-visiting the contact patch test

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