Geometrically exact covariant approach for contact between curves

Konyukhov, Alexander; Schweizerhof, Karl

doi:10.1016/j.cma.2010.04.012

Cited by 59 publications

(70 citation statements)

References 24 publications

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“…The need to combine exact geometrical descriptions with contact constraints may arise in attempting to achieve convenient and theoretically robust parametrizations [33,34] or in attempting to virtually manipulate such exact descriptions in the presence of contact constraints [41,6]. Isogeometric analysis [27,9] is a computational mechanics technology which uses basis functions emanating from computer aided geometric design, such as B-Splines, NURBS, T-splines or subdivision surfaces instead of traditional and provides a general framework towards this purpose.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

Temizer

Wriggers

Hughes

2012

Computer Methods in Applied Mechanics and Engineering

159

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a b s t r a c tA three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS is presented in the finite deformation regime. Within a setting where the NURBS discretization of the contact surface is inherited directly from the NURBS discretization of the volume, the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities. The formulation delivers a non-negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative Lagrange discretizations independent of the discretization order. These enable the achievement of improved smoothness in global contact forces and moments through higher-order geometrical descriptions. It is concluded that the presented mortar-based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

Temizer

Wriggers

Hughes

2012

Computer Methods in Applied Mechanics and Engineering

159

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“…[7]. A rigorous approach to the question of point-wise contact was also suggested by Konyukhov and Schweizerhof in [5]. There the authors focused their interest on the closest-point projection procedure, which for the beam-to-beam contact leads to the orthogonality conditions, see [11].…”

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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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“…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. 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].…”

Section: Introductionmentioning

confidence: 99%

“…1. The issues related to the existence and uniqueness of the closest points location were discussed in detail in [7,10].…”

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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Geometrically exact covariant approach for contact between curves

Cited by 59 publications

References 24 publications

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

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

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

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