Assessing the complete solution set of the planar frictional wedging problem (original) (raw)
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A complementarity problem formulation for two-dimensional frictional contact problems
Computers & Structures, 1988
A numerical procedure is developed for the solution of contact problems with Coulomb friction based on a complementarity problem formulation. Two-dimensional elasticity problems discretized by the boundary element method are used for detailed derivation of the complementarity equations for an incremental step. The dependency of the contact stress state on loading path is clearly shown and illustrated by examples.
International Journal for Numerical Methods in Engineering, 1991
A Newton method for solution of frictionless contact problems is presented. A finite element discretization is performed and the contact constraints are given as complementarity conditions. The resulting equations, which represent the equilibrium of the system, are formulated as a generalized equation. Generalized equations, from the discipline of Mathematical Programming, are a way of writing multi-valued relations, such as complementarity conditions, in a way that is similar to ordinary equations. Newton's method is then used, in a straightforward way, to solve the present non-linear generalized equation, resulting in a sequence of Linear Complementarity Problems (LCP's).
A boundary element and mathematical programming approach for frictional contact problems
Computers & Structures, 1992
A general solution method for three-dimensional quasistatic frictional contact problems is presented. It is based on the direct boundary element formulation with substructuring and a particular mathematical programming technique identified as the parametric linear complementarity problem (PLCP) with mixed complementary conditions. A solution algorithm that deals with the special form of PLCP is presented and allows one to define and check a criterion assessing the algorithm convergence. The frictional law is represented by a piecewise linear approximation of the Coulomb's friction cone which, when combined with the spatial discretization, yields a solution process that is linear in 'time' and thus not requiring an explicit time discretization of the original problem.
Numerical implementation of three-dimensional frictional contact by a linear complementarity problem
KSME Journal
The complementarity principle recently derived for a general three dimensional frictional contact is explicitly implemented as a linear complementarity problem (LCP). The inherent nonlinearity in the three dimensional friction condition has been treated by introducing a polyhedral law instead of elliptic law. The two-dimensional formulation previously derived is shown to be a special case of this three-dimensional formaulation in LCP.
Complementarity methods for multibody friction contact problems in finite deformations
International Journal for Numerical Methods in Engineering, 2001
This paper deals with the frictional contact occurring between deformable elastoplastic bodies subjected to large displacements and ÿnite 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 satisÿed 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 e ciency of the method is illustrated in the case of several examples.
International Journal of Mechanical Sciences, 2001
The computation of the collapse loads of discrete rigid block systems, characterized by frictional (nonassociative) and tensionless contact interfaces, is formulated and solved as a special constrained optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC). In the present instance, some of the essential constraints are defined by a complementarity system involving the orthogonality of two sign-constrained vectors. Due to its intrinsic complexity, MPECs are computationally very hard to solve. In this paper, we investigate a simple numerical scheme, involving appropriate relaxation of the complementarity term, to solve this nonstandard limit analysis problem. Some computational results are presented to illustrate potentialities of the method.
Constitutive model for 2D analysis of iso-kinematic frictional contact problems
abcm.org.br
During contact between two surfaces, a part the normal pressure between the surfaces, tangential forces that involve dissipative phenomena related to friction, occur. Modeling the interface friction involves adherence and slipping. This last effect may include evolution equations considering displacement hardening with isotropic or kinematic surfaces involved. Isotropic conditions are generally considered, what may be inadequate to cyclic loadings. Kinematic models address this difficulty and should handle these cases better. Here a kinematic model is formulated, developed and implemented for two-dimensional problems. Corotational measures are used in the setting of the constitutive incremental equations for quasi-static conditions, without thermal coupling. An implicit numerical scheme is used to develop the solution procedure. A few cyclic cases are used to verify the model, followed by an application problem. Results are compared to available solutions with acceptable agreement.
A complementarity problem formulation of the frictional grasping problem
Computer Methods in Applied Mechanics and Engineering, 2000
The problem of secure grasping in the presence of unilateral contact and friction eects is formulated as a nonlinear complementarity problem (NCP). This approach, in comparison with other methods which involve piecewise linear approximations, is very natural and applicable. The proposed formulation covers isotropic and orthotropic friction conditions. Numerical examples which illustrate the developed method are included. Ó
IEEE Transactions on Robotics and Automation, 1994
If an admittance control law is properly designed, a workpiece can be guided into a fixture using only the contact forces for guidance (force-assembly). Previously, we have shown that: 1) a space of accommodation control laws that will ensure force-assembly without friction always exists, and 2) as friction is increased, a control law that allows force-assembly can be obtained as long as the forces associated with positional misalignment are characteristic. A single accommodation control law that allows force-assembly at the maximum value of friction can be obtained by an optimization procedure.