Boundary augmented Lagrangian method for contact problems in linear elasticity

Zhang, Shougui; Li, Xin

doi:10.1016/j.enganabound.2015.07.006

Cited by 8 publications

(3 citation statements)

References 39 publications

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“…e proof can be found in [22,[35][36][37]. For the friction condition, we also have the following result according to [23,37].…”

Section: Setting Of the Problemmentioning

confidence: 75%

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Boundary Element and Augmented Lagrangian Methods for Contact Problem with Coulomb Friction

Zhang

2020

Mathematical Problems in Engineering

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In this paper, boundary element and augmented Lagrangian methods for Coulomb friction contact problems are presented. Based on the projection technique, both unilateral contact and Coulomb friction conditions are reformulated as fixed point problems. The original problem is deduced to a variational formulation with boundary integral operators. Then, we propose a new augmented Lagrangian method which can be dealt with the semismooth Newton method. Short theoretical results and the algorithm description are given. Numerical simulations show the performance of the method proposed.

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“…e proof can be found in [22,[35][36][37]. For the friction condition, we also have the following result according to [23,37].…”

Section: Setting Of the Problemmentioning

confidence: 75%

“…For contact problems, the key unknowns are displacement and stress on the contact boundary, which are considered as primary variables and can be obtained directly in the BEM [28][29][30]. erefore, the BEM seems to be the natural way for these problems [6][7][8][9][10][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Boundary Element and Augmented Lagrangian Methods for Contact Problem with Coulomb Friction

Zhang

2020

Mathematical Problems in Engineering

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“…with various boundary values [7], mechanics [7] [8] [9], medical imaging and computational biology [10], geophysics [11], ontology regarding big data representation and storage [12], and elastica theory [13], to name just a few.…”

Section: Introductionmentioning

confidence: 99%

Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential Equations

Li¹

2017

JAMP

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A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions to engineering problems. These engineering problems are described by differential equations with boundary values and are formulated as optimization of some functionals. The algorithm achieves its simplicity and versatility by choosing linear equality relations recursively for the augmented Lagrangian associated with an optimization problem. We demonstrate the formulation of an optimization functional for a 4th order nonlinear differential equation with boundary values. We also derive the associated augmented Lagrangian for this 4th order differential equation. Numerical test results are included that match up with well-established experimental outcomes. These numerical results indicate that the new algorithm is fully capable of producing accurate and stable solutions to differential equations.

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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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Boundary augmented Lagrangian method for contact problems in linear elasticity

Cited by 8 publications

References 39 publications

Boundary Element and Augmented Lagrangian Methods for Contact Problem with Coulomb Friction

Boundary Element and Augmented Lagrangian Methods for Contact Problem with Coulomb Friction

Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential Equations

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

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