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Contact Problems (contact + problem)
Kinds of Contact Problems Selected AbstractsSteady-state 3D rolling-contact using boundary elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2007R. Abascal Abstract This work presents a new approach to the steady-state rolling contact problem for 3D elastic bodies. The problem solution is achieved by minimizing a general function representing the equilibrium equation and the rolling-contact restrictions. The boundary element method is used to compute the elastic influence coefficients of the surface points involved in the contact (equilibrium equations); while the contact conditions are represented with the help of projection functions. Finally, the minimization problem is solved by the generalized Newton's method with line search. Classic rolling problems are also solved and commented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Numerical derivation of contact mechanics interface laws using a finite element approach for large 3D deformationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Alex Alves Bandeira Abstract In this work a homogenization method is presented to obtain by numerical simulation interface laws for normal contact pressure based on statistical surface models. For this purpose and assuming elastic behaviour of the asperities, the interface law of Kragelsky et al. (Friction and Wear,Calculation Methods, Pergamon, 1982) is chosen for comparison. The non-penetration condition and interface models for contact that take into account the surface micro-structure are investigated in detail. A theoretical basis for the three-dimensional contact problem with finite deformations is shortly presented. The augmented Lagrangian method is then used to solve the contact problem with friction. The algorithms for frictional contact are derived based on a slip rule using backward Euler integration like in plasticity. Special attention was dedicated to the consistent derivation of the contact equations between finite element surfaces. A matrix formulation for a node-to-surface contact element is derived consisting of a master surface segment with four nodes and a contacting slave node. It was also necessary to consider the special cases of node-to-edge contact and node-to-node contact in order to achieve the desired asymptotic quadratic convergence in the Newton method. A numerical example is selected to show the ability of the contact formulation and the algorithm to represent interface law for rough surfaces. Copyright © 2003 John Wiley & Sons, Ltd. [source] Improvement of a frictional contact algorithm for strongly curved contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003M. C. Oliveira Abstract One of the challenges in contact problems is the prediction of the actual contact surface and the kind of contact that is established in each region. In numerical simulation of deep drawing problems the contact conditions change continuously during the forming process, increasing the importance of a correct evaluation of these parameters at each load step. In this work a new contact search algorithm devoted to contact between a deformable and a rigid body is presented. The rigid body is modelled by parametric Bézier surfaces, whereas the deformable body is discretized with finite elements. The numerical schemes followed rely on a frictional contact algorithm that operates directly on the parametric Bézier surfaces. The algorithm is implemented in the deep drawing implicit finite element code DD3IMP. This code uses a mechanical model that takes into account the large elastoplastic strains and rotations. The Coulomb classical law models the frictional contact problem, which is treated with an augmented Lagrangian approach. A fully implicit algorithm of Newton,Raphson type is used to solve within a single iterative loop the non-linearities related with the frictional contact problem and the elastoplastic behaviour of the deformable body. The numerical simulations presented demonstrate the performance of the contact search algorithm in an example with complex tools geometry. Copyright © 2003 John Wiley & Sons, Ltd. [source] Boundary elements for half-space problems via fundamental solutions: A three-dimensional analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001J. Liang Abstract An efficient solution technique is proposed for the three-dimensional boundary element modelling of half-space problems. The proposed technique uses alternative fundamental solutions of the half-space (Mindlin's solutions for isotropic case) and full-space (Kelvin's solutions) problems. Three-dimensional infinite boundary elements are frequently employed when the stresses at the internal points are required to be evaluated. In contrast to the published works, the strongly singular line integrals are avoided in the proposed solution technique, while the discretization of infinite elements is independent of the finite boundary elements. This algorithm also leads to a better numerical accuracy while the computational time is reduced. Illustrative numerical examples for typical isotropic and transversely isotropichalf-space problems demonstrate the potential applications of the proposed formulations. Incidentally, the results of the illustrative examples also provide a parametric study for the imperfect contact problem. Copyright © 2001 John Wiley & Sons, Ltd. [source] Complementarity methods for multibody friction contact problems in finite deformationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2001Patrick Chabrand Abstract This paper deals with the frictional contact occurring between deformable elastoplastic bodies subjected to large displacements and finite deformations. Starting from a standard slave/master formulation we have developed a symmetrical formulation with which the unilateral contact conditions and the friction law are satisfied for each body. From the continuum equations, the discretized frictional contact problem is set as a complementarity problem and solved using Lemke's mathematical programming method. The efficiency of the method is illustrated in the case of several examples. Copyright © 2001 John Wiley & Sons, Ltd. [source] A class of implicit variational inequalities and applications to frictional contactMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2009Anca Capatina Abstract This paper deals with the mathematical and numerical analysis of a class of abstract implicit evolution variational inequalities. The results obtained here can be applied to a large variety of quasistatic contact problems in linear elasticity, including unilateral contact or normal compliance conditions with friction. In particular, a quasistatic unilateral contact problem with nonlocal friction is considered. An algorithm is derived and some numerical examples are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source] hp -Mortar boundary element method for two-body contact problems with frictionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2008Alexey Chernov Abstract We construct a novel hp -mortar boundary element method for two-body frictional contact problems for nonmatched discretizations. The contact constraints are imposed in the weak sense on the discrete set of Gauss,Lobatto points using the hp -mortar projection operator. The problem is reformulated as a variational inequality with the Steklov,Poincaré operator over a convex cone of admissible solutions. We prove an a priori error estimate for the corresponding Galerkin solution in the energy norm. Due to the nonconformity of our approach, the Galerkin error is decomposed into the approximation error and the consistency error. Finally, we show that the Galerkin solution converges to the exact solution as ,,((h/p)1/4) in the energy norm for quasiuniform discretizations under mild regularity assumptions. We solve the Galerkin problem with a Dirichlet-to-Neumann algorithm. The original two-body formulation is rewritten as a one-body contact subproblem with friction and a one-body Neumann subproblem. Then the original two-body frictional contact problem is solved with a fixed point iteration. Copyright © 2008 John Wiley & Sons, Ltd. [source] Global existence for a contact problem with adhesionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2008Elena Bonetti Abstract In this paper, we analyze a contact problem with irreversible adhesion between a viscoelastic body and a rigid support. On the basis of Frémond's theory, we detail the derivation of the model and of the resulting partial differential equation system. Hence, we prove the existence of global in time solutions (to a suitable variational formulation) of the related Cauchy problem by means of an approximation procedure, combined with monotonicity and compactness tools, and with a prolongation argument. In fact the approximate problem (for which we prove a local well-posedness result) models a contact phenomenon in which the occurrence of repulsive dynamics is allowed for. We also show local uniqueness of the solutions, and a continuous dependence result under some additional assumptions. Copyright © 2007 John Wiley & Sons, Ltd. [source] Fixed point strategies for elastostatic frictional contact problemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2008Patrick Laborde Abstract Several fixed point strategies and Uzawa algorithms (for classical and augmented Lagrangian formulations) are presented to solve the unilateral contact problem with Coulomb friction. These methods are analysed, without introducing any regularization, and a theoretical comparison is performed. Thanks to a formalism coming from convex analysis, some new fixed point strategies are presented and compared with known methods. The analysis is first performed on continuous Tresca problem and then on the finite dimensional Coulomb problem derived from an arbitrary finite element method. Copyright © 2007 John Wiley & Sons, Ltd. [source] Simulation of Rayleigh waves in cracked platesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2007M. T. Cao Abstract The aim of this paper is to develop new numerical procedures to detect micro cracks, or superficial imperfections, in thin plates using excitation by Rayleigh waves. We shall consider a unilateral contact problem between the two sides of the crack in an elastic plate subjected to suitable boundary conditions in order to reproduce a single Rayleigh wave cycle. An approximate solution of this problem will be calculated by using one of the Newmark methods for time discretization and a finite element method for space discretization. To deal with the nonlinearity due to the contact condition, an iterative algorithm involving one multiplier will be used; this multiplier will be approximated by using Newton's techniques. Finally, we will show numerical simulations for both cracked and non-cracked plates. Copyright © 2006 John Wiley & Sons, Ltd. [source] Modeling and numerical analysis of masonry structuresNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2007Mark Ainsworth Abstract We model masonry structures as elastodynamic systems assembled from a large number of elastic bodies (bricks or stone-blocks) in unilateral, frictional contact. The problem is formulated as a quasi-variational inequality and discretised using piecewise polynomial finite elements in conjunction with an energy consistent time integration scheme. At each time-step, the quasi-variational inequality is reformulated as a nonlinear complementarity problem. An iterative splitting of the contact problem into normal contact and frictional contact, together with a primal-dual active-set method is employed to calculate deformations and openings in the model structures. Numerical results are presented to illustrate the efficiency of the resulting approach in predicting the mechanical behaviour of a bidimensional arch-ring made of bricks, deformed due to body forces and surface tractions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 798,816, 2007 [source] Total FETI for contact problems with additional nonlinearitiesPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008í Dobiá The paper is concerned with application of a new variant of the Finite Element Tearing and Interconnecting (FETI) method, referred to as the Total FETI (TFETI), to the solution to contact problems with additional nonlinearities. While the standard FETI methods assume that the prescribed Dirichlet conditions are inherited by subdomains, TFETI enforces both the compatibility between subdomains and the prescribed displacements by the Lagrange multipliers. If applied to the contact problems, this approach not only transforms the general nonpenetration constraints to the bound constraints, but it also generates an enriched natural coarse grid defined by the a priori known kernels of the stiffness matrices of the subdomains exhibiting rigid body modes. We combine our in a sense optimal algorithms for the solution to bound and equality constrained problems with geometric and material nonlinearities. The section on numerical experiments presents results of solution to bolt and nut contact problem with additional geometric and material nonlinear effects. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Thermoelastic rolling contact problem with temperature dependent frictionPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Andrzej Chudzikiewicz The paper is concerned with the numerical solution of a thermoelastic rolling contact problem with wear. The friction between the bodies is governed by Coulomb law. A frictional heat generation and heat transfer across the contact surface as well as Archard's law of wear in contact zone are assumed. The friction coefficient is assumed to depend on temperature. In the paper quasistatic approach to solve this contact problem is employed. This approach is based on the assumption that for the observer moving with the rolling body the displacement of the supporting foundation is independent on time. The original thermoelastic contact problem described by the hyperbolic inequality governing the displacement and the parabolic equation governing the heat flow is transformed into elliptic inequality and elliptic equation, respectively. In order to solve numerically this system we decouple it into mechanical and thermal parts. Finite element method is used as a discretization method. Numerical examples showing the influence of the temperature dependent friction coefficient on the temperature distribution and the length of the contact zone are provided. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Thermomechanical modeling and simulation of aluminum alloys during extrusion processPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Farhad Parvizian The purpose of this work is to simulate the microstructure development of aluminum alloys during hot metal forming processes such as extrusion with the help of the Finite Element Method (FEM). To model the thermomechanical coupled behavior of the material during the extrusion process an appropriate material model is required. In the current work a Johnson,Cook like thermoelastic viscoplastic material model is used. To overcome the numerical difficulties during simulation of extrusion such as contact problem and element distortion an adaptive meshing system is developed and applied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A new update procedure for internal variables in an ALE-description of rolling contactPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005M. Ziefle In FEM analysis of rolling contact problems Arbitrary Lagrangian-Eulerian (ALE) methods are the state of the art. These methods allow mesh refinements concentrated to the contact region and offer a time independent formulation of stationary elastic rolling. The relative-kinematic description of rolling leads to a relative motion between the finite element mesh and the material points. Thus in the case of inelastic material behavior history dependent constitutive equations contain convective terms. The handling of these convective terms is performed by a so called fractional step method. A material step is followed by a convection step. In the first step the nonlinear solid contact problem is resolved by neglecting the convective terms. In the following step the internal variables are transported on the streamlines of the material particles by solving the advection equation via a time-discontinuous Galerkin method. This update procedure is demonstrated on a typical FEM-tire model. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Elastoplastic modelling of subsurface crack growth in rail/wheel contact problemsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 10 2007R. LUNDÉN ABSTRACT Propagation of small subsurface cracks subjected to shear under repeated rolling contact load is studied. An analytical crack model (Dugdale) with plastic strips at the two crack tips is employed. Compressive stresses promoting crack closure and friction between crack faces are considered. The triaxial stress state is used in the yield criterion. A damage criterion is suggested based on experimental LCF data. In a numerical study, critical crack lengths are found below which propagation of an existing crack should be effectively suppressed. [source] Finite element modelling of frictional instability between deformable rocksINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2003H. L. Xing Abstract Earthquakes are recognized as resulting from a stick,slip frictional instability along faults. Based on the node-to-point contact element strategy (an arbitrarily shaped contact element strategy applied with the static-explicit algorithm for modelling non-linear frictional contact problems proposed by authors), a finite element code for modelling the 3-D non-linear friction contact between deformable bodies has been developed and extended here to analyse the non-linear stick,slip frictional instability between deformable rocks with a rate- and state-dependent friction law. A typical fault bend model is taken as an application example to be analysed here. The variations of the normal contact force, the frictional force, the transition of stick,slip instable state and the related relative slip velocity along the fault between the deformable rocks and the stress evolution in the total bodies during the different stages are investigated, respectively. The calculated results demonstrate the usefulness of this code for simulating the non-linear frictional instability between deformable rocks. Copyright © 2003 John Wiley & Sons, Ltd. [source] Large displacement FEM modelling of the cone penetration test (CPT) in normally consolidated sandINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2003Endra Susila Abstract A new finite element model based on a large strain formulation has been developed to study cone penetration in normally consolidated sand. An auto-adaptive remeshing technique was utilized for handling the very large distortion of sand surrounding the cone tip. A frictional contact interface utilizing Mohr,Coulomb's theory was chosen to represent interactions between the surface of the cone and sand. To model the sand behaviour, the non-associated Drucker,Prager constitutive model was selected. ABAQUS, a commercial finite element software package, was used to implement the model. The explicit solution algorithm was chosen due to its effectiveness for complicated contact problems. Analysis results proved that the model successfully captured the cone penetration behavior in sand. In addition, a chart to predict internal friction angles based on cone tip resistance for different vertical effective stresses was provided. This paper also shows a typical distribution of sleeve resistance, tip resistance,penetration relationship, and typical contours of vertical, horizontal, and shear stresses in normally consolidated sand. Finally, a non-uniform resistance was found along the length of the friction sleeve. Copyright © 2003 John Wiley & Sons, Ltd. [source] An adaptive multigrid iterative approach for frictional contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2006S. A. Mohamed Abstract The objective of this paper is the construction of a robust strategy towards adaptively solving Signorini's frictional contact problems. The frictional contact problem between a linearly elastic body and rigid foundation is formulated as a classical boundary value problem of the elastic body but associated with special inequality conditions on the contact surface. A new iterative approach is presented to solve the problem on a given mesh. In the first iteration the candidate nodes are assumed to be in micro-slip contact and then proceeding to update the contact status according to the actual displacements and stresses obtained at the end of each increment. An efficient multigrid method is developed to solve the discrete problems of different iterations. The proposed iterative procedure is integrated with an error indicator and automatic grid generator to construct an adaptive multigrid method. Numerical results of the convergence rates, automatically generated grid sequence, contact stresses and strains as well as two parametric studies are presented to prove the efficiency of the proposal. Copyright © 2005 John Wiley & Sons, Ltd. [source] Optimal time integration parameters for elastodynamic contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2001A. Czekanski Abstract In this paper, we employ the generalized- , time integration scheme for treating elastodynamic contact problems. The criteria invoked for the selection of the four time integration parameters are motivated by our desire to ensure that the solution is unconditionally stable, second-order accurate, provides optimal high-frequency dissipation and preserves the energy and momentum transfer in dynamic rigid impact problems. New closed-form expressions for the time integration parameters are determined in terms of user-specified high-frequency spectral radius. The selected parameters help in avoiding the spurious high-frequency modes, which are present in the traditional Newmark method. Copyright © 2001 John Wiley & Sons, Ltd. [source] Asymptotic numerical methods for unilateral contactINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2006W. Aggoune Abstract New algorithms based upon the asymptotic numerical method (ANM) are proposed to solve unilateral contact problems. ANM leads to a representation of a solution path in terms of series or Padé approximants. To get a smooth solution path, a hyperbolic relation between contact forces and clearance is introduced. Three key points are discussed: the influence of the regularization of the contact law, the discretization of the contact force by Lagrange multipliers and prediction,correction algorithms. Simple benchmarks are considered to evaluate the relevance of the proposed algorithms. Copyright © 2006 John Wiley & Sons, Ltd. [source] Application of piece-wise linear weight functions for 2D 8-node quadrilateral element in contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Chouping Luo Abstract The present study is a continuation of our previous work with the aim to reduce problems caused by standard higher order elements in contact problems. The difficulties can be attributed to the inherent property of the Galerkin method which gives uneven distributions of nodal forces resulting in oscillating contact pressures. The proposed remedy is use of piece-wise linear weight functions. The methods to establish stiffness and/or mass matrix for 8-node quadrilateral element in 2D are presented, i.e. the condensing and direct procedures. The energy and nodal displacement error norms are also checked to establish the convergence ratio. Interpretation of calculated contact pressures is discussed. Two new 2D 8-node quadrilateral elements, QUAD8C and QUAD8D, are derived and tested in many examples, which show their good performance in contact problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Improvement of a frictional contact algorithm for strongly curved contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003M. C. Oliveira Abstract One of the challenges in contact problems is the prediction of the actual contact surface and the kind of contact that is established in each region. In numerical simulation of deep drawing problems the contact conditions change continuously during the forming process, increasing the importance of a correct evaluation of these parameters at each load step. In this work a new contact search algorithm devoted to contact between a deformable and a rigid body is presented. The rigid body is modelled by parametric Bézier surfaces, whereas the deformable body is discretized with finite elements. The numerical schemes followed rely on a frictional contact algorithm that operates directly on the parametric Bézier surfaces. The algorithm is implemented in the deep drawing implicit finite element code DD3IMP. This code uses a mechanical model that takes into account the large elastoplastic strains and rotations. The Coulomb classical law models the frictional contact problem, which is treated with an augmented Lagrangian approach. A fully implicit algorithm of Newton,Raphson type is used to solve within a single iterative loop the non-linearities related with the frictional contact problem and the elastoplastic behaviour of the deformable body. The numerical simulations presented demonstrate the performance of the contact search algorithm in an example with complex tools geometry. Copyright © 2003 John Wiley & Sons, Ltd. [source] FFS contact searching algorithm for dynamic finite element analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2001Fujun Wang Abstract A new contact searching algorithm for general contact systems is proposed in this paper. Due to that the smooth and accurate geometry description is crucial to the contact stress analysis, we have worked out a free-formed-surface (FFS) algorithm specialized to model the contacting surface with the C1 boundary continuity and the exact boundary condition definition. Moreover, the geometrical description using the FFS produces those data required for determining the actual contact direction and calculating the exact contact penetration. Numerical simulation results demonstrate that our contact searching algorithm is robust and capable to simulate three-dimensional contact problems accurately. Copyright © 2001 John Wiley & Sons, Ltd. [source] Complementarity methods for multibody friction contact problems in finite deformationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2001Patrick Chabrand Abstract This paper deals with the frictional contact occurring between deformable elastoplastic bodies subjected to large displacements and finite deformations. Starting from a standard slave/master formulation we have developed a symmetrical formulation with which the unilateral contact conditions and the friction law are satisfied for each body. From the continuum equations, the discretized frictional contact problem is set as a complementarity problem and solved using Lemke's mathematical programming method. The efficiency of the method is illustrated in the case of several examples. Copyright © 2001 John Wiley & Sons, Ltd. [source] A numerically scalable domain decomposition method for the solution of frictionless contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2001D. Dureisseix Abstract We present a domain decomposition method with Lagrange multipliers for solving iteratively frictionless contact problems. This method, which is based on the FETI method and therefore is named here the FETI-C method, incorporates a coarse contact system that guides the iterative prediction of the active zone of contact. We demonstrate numerically that this method is numerically scalable with respect to both the problem size and the number of subdomains. Copyright © 2001 John Wiley & Sons, Ltd. [source] A class of implicit variational inequalities and applications to frictional contactMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2009Anca Capatina Abstract This paper deals with the mathematical and numerical analysis of a class of abstract implicit evolution variational inequalities. The results obtained here can be applied to a large variety of quasistatic contact problems in linear elasticity, including unilateral contact or normal compliance conditions with friction. In particular, a quasistatic unilateral contact problem with nonlocal friction is considered. An algorithm is derived and some numerical examples are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source] hp -Mortar boundary element method for two-body contact problems with frictionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2008Alexey Chernov Abstract We construct a novel hp -mortar boundary element method for two-body frictional contact problems for nonmatched discretizations. The contact constraints are imposed in the weak sense on the discrete set of Gauss,Lobatto points using the hp -mortar projection operator. The problem is reformulated as a variational inequality with the Steklov,Poincaré operator over a convex cone of admissible solutions. We prove an a priori error estimate for the corresponding Galerkin solution in the energy norm. Due to the nonconformity of our approach, the Galerkin error is decomposed into the approximation error and the consistency error. Finally, we show that the Galerkin solution converges to the exact solution as ,,((h/p)1/4) in the energy norm for quasiuniform discretizations under mild regularity assumptions. We solve the Galerkin problem with a Dirichlet-to-Neumann algorithm. The original two-body formulation is rewritten as a one-body contact subproblem with friction and a one-body Neumann subproblem. Then the original two-body frictional contact problem is solved with a fixed point iteration. Copyright © 2008 John Wiley & Sons, Ltd. [source] Fixed point strategies for elastostatic frictional contact problemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2008Patrick Laborde Abstract Several fixed point strategies and Uzawa algorithms (for classical and augmented Lagrangian formulations) are presented to solve the unilateral contact problem with Coulomb friction. These methods are analysed, without introducing any regularization, and a theoretical comparison is performed. Thanks to a formalism coming from convex analysis, some new fixed point strategies are presented and compared with known methods. The analysis is first performed on continuous Tresca problem and then on the finite dimensional Coulomb problem derived from an arbitrary finite element method. Copyright © 2007 John Wiley & Sons, Ltd. [source] Analysis of a time discretization for an implicit variational inequality modelling dynamic contact problems with frictionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2001Jean-Marc Ricaud Abstract Some dynamic contact problems with friction can be formulated as an implicit variational inequality. A time discretization of such an inequality is given here, thus giving rise to a so-called incremental solution. The convergence of the incremental solution is established, and then the limit is shown to be the unique solution of the variational inequality. This paper contains therefore not only some new results concerning the numerical aspect of some models of contact and friction but also a constructive existence result. Copyright © 2001 John Wiley & Sons, Ltd. [source] | |||||||||||||