A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems

Hüeber, S.; Mair, Michael; Wohlmuth, Barbara

doi:10.1016/j.apnum.2004.09.019

Cited by 42 publications

(29 citation statements)

References 20 publications

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“…Hüeber et al [12] also presented numerical examples confirming the theoretical result and illustrating the performance of the algorithm. We also refer the reader to other work of Hüeber et al [10,11,13,14].…”

Section: Resultsmentioning

confidence: 99%

Contact Problems for Nonlinearly Elastic Materials: Weak Solvability Involving Dual Lagrange Multipliers

Matei¹,

Ciurcea²

2010

ANZIAM J.

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A class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.2000 Mathematics subject classification: primary 74M10; secondary 74M15, 35J50, 35J66.

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Section: Resultsmentioning

confidence: 99%

Contact Problems for Nonlinearly Elastic Materials: Weak Solvability Involving Dual Lagrange Multipliers

Matei¹,

Ciurcea²

2010

ANZIAM J.

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“…In particular, the oscillatory response at coarse discretizations has been observed earlier in various settings [32,15,58]. While a p N P 0 requirement, although physically sound, may not be deemed critical and even restrictive since the contact constraints are satisfied only by the projected quantities, the need for an explicit treatment of higher-order L p -discretizations is clear and has been pursued mostly for the case of L 2 [24,14,55,50]. Nevertheless, in all upcoming investigations a common treatment of all L p -discretizations will be pursued.…”

Section: Local Quality: Contact Tractionsmentioning

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

153

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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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“…In the literature, we can find a dual application of the Lagrange multipliers which consists in succeeding the integration of the multipliers on the slave surface then on the master surface or the invers. We can find more detail of this technique in the works of [19][20][21][22][23][24][25][26]. The shape functions adopted by Wohlmouth [19] and presented in (62) do not express a maximal value of the multiplier in the extremities.…”

Section: Lagrange Multipliers Methodsmentioning

confidence: 99%

“…In this problem of contact with large displacement [20][21][22][23][24][25][26][27], a solid disk interacts with a half-crown (basis) with a vertical translation ∆ y =80 UL (Figure 14). The radios of the disk and the contact surface of the basis is R=50 UL, whereas the external radios of the basis is R e =125 UL.…”

Section: Example Of Validationmentioning

confidence: 99%

2d Frictional B-Spline Smoothed Mortar Contact Problems Part II: Resolution Phase

Kallel¹,

Bouabdallah²

2017

J Appl Mech Eng

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We detailed in this paper three formulations for the resolution of a contact problem by mortar method. The penalty method is a simple technique which does not introduce new unknowns which can increase the size of the system to be solved. But this formulation suffers of conditioning problems especially when the penalty coefficient becomes very high. The Lagrange multipliers method is more accurate than the penalty formulation. The multiplier λ N represents in the contact surface the exact value of the normal contact effort. This approach requires additional variables which are the Lagrange multiplier in the contact interface nodes. The augmented Lagrange method is a combination between the penalty formulation and the Lagrange multipliers method. The contact constraints are applied by a Lagrange multiplier approached without increasing the problem size. The penalty coefficient in this method has less influence on the quality of the result and the robustness of the solution than in the penalty formulation.

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A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems

Cited by 42 publications

References 20 publications

Contact Problems for Nonlinearly Elastic Materials: Weak Solvability Involving Dual Lagrange Multipliers

Contact Problems for Nonlinearly Elastic Materials: Weak Solvability Involving Dual Lagrange Multipliers

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

2d Frictional B-Spline Smoothed Mortar Contact Problems Part II: Resolution Phase

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