The Boundary Element Method applied to Two-Dimensional Contact Problems with Friction

Andersson, Torbjörn

doi:10.1007/978-3-662-11270-0_16

Cited by 47 publications

(31 citation statements)

References 3 publications

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“…block Toeplitz matrix with Toeplitz blocks. 1 Combining equations (2.3) and (2.7), and considering the discretization of the contact conditions (2.1) and (2.2), we obtain a linear complementarity problem LCP(h, A), which aims to find the pressures, p, and contact area, C, satisfying e = h + Ap, (2.8) 10) where I is the element index with I = (iy − 1)mx + ix, 1 ≤ I ≤ n, and E is the exterior area. Note that the constraints on the deformed distance e are the primary constraints: e I = 0 defines the active set, i.e.…”

Section: Discretizationmentioning

confidence: 99%

“…The boundary element method (BEM), e.g. [1,17] is efficient for solving homogeneous elastic problems, when assuming small deformations and deformation gradients. This method transforms a 3D boundary value problem into a 2D boundary integral equation and then solves it only at the discrete boundary, which reduces the computational work significantly.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Full Multigrid Method for Linear Complementarity Problems Arising From Elastic Normal Contact Problems

Zhao

Vollebregt

Oosterlee

2014

Mathematical Modelling and Analysis

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Abstract. This paper presents a full multigrid (FMG) technique, which combines a multigrid method, an active set algorithm and a nested iteration technique, to solve a linear complementarity problem (LCP) modeling elastic normal contact problems. The governing system in this LCP is derived from a Fredholm integral of the first kind, and its coefficient matrix is dense, symmetric and positive definite. One multigrid cycle is applied to solve this system approximately in each active set iteration. Moreover, this multigrid solver incorporates a special strategy to handle the complementarity conditions, including restricting both the defect and the contact area (active set) to the coarse grid, and setting all quantities outside contact to zero. The smoother is chosen by some analysis based on the eigenvectors of the iteration matrix. This method is applied to a Hertzian smooth contact and a rough surface contact problem.

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Section: Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Full Multigrid Method for Linear Complementarity Problems Arising From Elastic Normal Contact Problems

Zhao

Vollebregt

Oosterlee

2014

Mathematical Modelling and Analysis

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“…To calculate these slip velocities at the contact nodes, two di erent approximations can be adopted: the material formulation based on (17), or the convective-local formulation based on (18).…”

Section: The Elastic Equationsmentioning

confidence: 99%

Solving 2D transient rolling contact problems using the BEM and mathematical programming techniques

González

Abascal

2001

Numerical Meth Engineering

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SUMMARYThis work presents a new approach to the transient rolling contact of two-dimensional elastic bodies. A solution will be obtained by minimizing a general B-di erentiable function representing the equilibrium equations and the contact conditions at each time step. Inertial e ects are not taken into account and the boundary element method is used to compute the elastic in uence coe cients of the surface points involved in contact (equilibrium equations). The contact conditions are represented with the help of variational inequalities and projection functions. Finally, the minimization problem is solved using the Generalized Newton's Method with line search. The results are compared with some example problems and the in uence of discretization and integration time step on the results is discussed.

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“…One is the finite element method (FEM) [14,17,38], which is widely used, especially for problems involving large deformation and nonlinear materials. The other is the boundary element method (BEM) [1,13,22], which is applied for homogeneous material, under the assumption of small deformation and deformation gradients. This method particularly suits the concentrated contact problem well.…”

Section: Introductionmentioning

confidence: 99%

Extending the Bem for Elastic Contact Problems Beyond the Half-Space Approach

Zhao

Vollebregt

Oosterlee

2016

Mathematical Modelling and Analysis

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Abstract. The boundary element method (BEM) is widely used in fast numerical solvers for concentrated elastic contact problems arising from the wheel-rail contact in the railway industry. In this paper we extend the range of applicability of BEM by computing the influence coefficients (ICs) numerically. These ICs represent the Green's function of the problem, i.e. the surface deformation due to unit loads. They are not analytically available when the half-space is invalid, for instance in conformal contact. An elastic model is proposed to compute these ICs numerically, by the finite element method (FEM). We present a detailed investigation to find proper strategies of FEM meshing and element types, considering accuracy and computational cost. Moreover, the effects of computed ICs to contact solutions are examined for a Cattaneo shift contact problem. The work in this paper provides a guidance to study fast solvers for the conformal contact.

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The Boundary Element Method applied to Two-Dimensional Contact Problems with Friction

Cited by 47 publications

References 3 publications

A Full Multigrid Method for Linear Complementarity Problems Arising From Elastic Normal Contact Problems

A Full Multigrid Method for Linear Complementarity Problems Arising From Elastic Normal Contact Problems

Solving 2D transient rolling contact problems using the BEM and mathematical programming techniques

Extending the Bem for Elastic Contact Problems Beyond the Half-Space Approach

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