Least-squares stabilized augmented Lagrangian multiplier method for elastic contact

Hansbo, Peter; Rashid, Asim; Salomonsson, Kent

doi:10.1016/j.finel.2016.03.005

Cited by 18 publications

(13 citation statements)

References 14 publications

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“…where H g and J g are the respective quadrature weight and Jacobian of the transformation, and κ E h = (κ 1 + κ 2 ) with E being the Young's modulus and h the mesh size. This result is similar to the one obtained in[18] with the advantage of having less integrals to evaluate as no derivatives of the…”

supporting

confidence: 87%

“…Stabilized formulations have been recently adapted to embedded domains. In [18] a stabilized augmented Lagrange formulation is developed for frictionless contact. A stabilized formulation based on the Nitsche method is presented in [4,5] for small sliding contact in 2D and 3D respectively.…”

mentioning

confidence: 99%

“…The terms ∆ξ , ∆η are considered for the calculation of ∆δg N and ∆δg. Therefore, starting from (18) and (25) these increments are respectively written as ∆δg N = (δs (2) ξ • n (1) )∆ξ + (δs (2) η • n (1) )∆η + (δu (2) − δu (1) ) • ∆n (1)…”

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confidence: 99%

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Large deformation frictional contact analysis with immersed boundary method

et al. 2018

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This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method.

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confidence: 87%

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confidence: 99%

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Large deformation frictional contact analysis with immersed boundary method

et al. 2018

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“…In this paper, a stabilized augmented Lagrange multiplier method for the finite element solution of small deformation elastic contact problems is used. Application of augmented Lagrangian method in contact problem modeling is presented by Hansboet al In this method expression

σ_{n}

( u ) is replaced by a Lagrange multiplier p which indicates contact pressure. It has an influence on a form of boundary conditions on

Γ_{C}

.…”

Section: Mathematical Model Of the Problemmentioning

confidence: 99%

Finite Element Analysis of the Influence of the Covering Auxetic Layer of Plate on the Contact Pressure

Stręk

Matuszewska

Jopek

2017

Physica Status Solidi (b)

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The contact problem between two bodies: plate and semi‐cylindrical bar is studied in this paper. The analysis concerns the contact pressure distribution along the contact region, as well as the deflection of the plate. Furthermore, the case of a composite plate covered with the auxetic layer is also considered. The influence of the Poisson's ratio of the layer on the behavior of the plate is studied. The contact pressure distribution along the contact area is analyzed using finite element analysis.

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“…Nitsche's method is a particular case of Lagrange multiplier method [2], [3] and [4]. We know that imposing boundary conditions is a key issue in study solutions of problems not only in fluid dynamics but in all scientific problems.…”

Section: Introductionmentioning

confidence: 99%