Self-adaptive projection and boundary element methods for contact problems with Tresca friction

Zhang, Shougui; Li, Xin; Ran, Ruisheng

doi:10.1016/j.cnsns.2018.05.001

Cited by 14 publications

(9 citation statements)

References 19 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: 74%

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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: 74%

“…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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“…Elastic frictional contact is a multiple nonlinear problem [1,2], and it is necessary to accurately track the motion of the object before contact and the interaction between objects after contact, which includes the correct simulation of friction and deformation behavior between contact surfaces and the analysis of the possible energy conversion problem. For the contact problems, only very few of them can be solved by analytical methods, and most of them need to be simulated by numerical methods such as the Finite Element Method (FEM) [3,4] and the Boundary Element Method (BEM) [5,6].…”

Section: Introductionmentioning

confidence: 99%

A Kind of FM-BEM Penalty Function Method for a 3D Elastic Frictional Contact Nonlinear System

Jing

et al. 2021

Journal of Mathematics

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In this paper, a kind of node_face frictional contact FM-BEM penalty function method is presented for 3D elastic frictional contact nonlinear problems. According to the principle of minimum potential energy, nonpenetrating constraints are introduced into the elastic frictional contact system as a penalty term. By using the least square method and penalty function method, an optimization mathematical model and a mathematical programming model with a penalty factor are established for the node_face frictional contact nonlinear system. For the two models, a penalty optimization IGMRES (m) algorithm is proposed, and the influences of different penalty factors on the solution of the whole system are analyzed. Finally, a numerical simulation is carried out for two elastic frictional contact objects, and some important results including displacements, pressures, friction forces, and friction slips in the contact area are presented. Theoretical analysis and numerical experiment show that the newly presented FM-BEM penalty function method not only is efficient and practical but also has much superiority. It is easy to implement, and it is fast convergent with good stability.

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“…Most of the time, the mathematical formulation of the frictional contact problem is reformulated as a minimization problem or a variational inequality of the second kind. Theory of contact problems and their numerical approximations has been extensively developed during the past decades [3][4][5][6][7][8][9][10]. Among the most popular methods we mention semi-smooth Newton methods and projection methods.…”

Section: Introductionmentioning

confidence: 99%

“…In these two methods, the key unknowns of frictional contact problems are displacement and stress on the contact boundary, which are considered primary variables and can be related in a linear system by the boundary element method (BEM) [9,10,17,18]. Besides, the BEM significantly reduces expense mesh generation because the formulation of the problem is concluded to the boundary of the domain.…”

Section: Introductionmentioning

confidence: 99%

Comparison of two projection methods for the solution of frictional contact problems

Zhang

Ran

2019

Bound Value Probl

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Frictional contact problems in linear elasticity are considered in this paper. The contact constraint is imposed in the weak sense using the fixed point method, which leads to a variational equation problem. For solving such a nonlinear variational problem, we study two projection methods using different self-adaptive rules. Based on the self-adaptive projection method, we propose a modified self-adaptive rule which is more effective to update the parameter. The methods can be implemented easily in conjunction with the boundary element method for the solution. Numerical experiments are reported to illustrate theoretical results.

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Self-adaptive projection and boundary element methods for contact problems with Tresca friction

Cited by 14 publications

References 19 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

A Kind of FM-BEM Penalty Function Method for a 3D Elastic Frictional Contact Nonlinear System

Comparison of two projection methods for the solution of frictional contact problems

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