A finite element solution method for contact problems with friction
01 Mar 1987-International Journal for Numerical Methods in Engineering (Wiley)-Vol. 24, Iss: 3, pp 477-495
TL;DR: In this article, a finite element solution method for the analysis of frictional contact problems is presented, which is solved by imposing geometric constraints on the pseudo equilibrium configuration, defined as a configuration at which the compatibility conditions are violated.
Abstract: A new finite element solution method for the analysis of frictional contact problems is presented. The contact problem is solved by imposing geometric constraints on the pseudo equilibrium configuration, defined as a configuration at which the compatibility conditions are violated. The algorithm does not require any a priori knowledge of the pairs of contactor nodes or segments. The contact condition of sticking, slipping, rolling or tension release is determined from the relative magnitudes of the normal and tangential global nodal forces. Contact iterations are in general found to converge within one or two iterations. The analysis method is applied to selected problems to illustrate the applicability of the solution procedure.
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TL;DR: In this article, a geometric nonlinear finite element method is used to analyze fabric deformation characterized by large displacements and rotations, but small strains, using shell/plate elements.
Abstract: Fabric deformation characterized by large displacements and rotations but small strains is analyzed using a geometric nonlinear finite element method. The fabrics are modeled by shell/plate elements. Special considerations for applying the finite element method to fabric analysis are discussed and several examples of fabric deformation presented. The results from the finite element model are compared with experimental data and are in good agreement.
84 citations
TL;DR: A simulation-based comparison between deformable grasping and rigid body grasping reveals why soft objects are easier to pick up than hard ones, and demonstrates how a rigid body grasped strategy may fail on soft objects in certain situations.
Abstract: This paper describes a strategy for a robotic hand to pick up deformable 3D objects on a table. Inspired by human hand behavior, the robotic hand employs two rigid fingers to first squeeze such an object until it ?feels? the object to be liftable. Such ?feeling? is provided by a virtual liftability test that is repeatedly conducted during the squeeze. Passing of the test then triggers a lifting action. Throughout the manipulation the object's deformation and its state of contact with the fingers and the table are being tracked based on contact events. Deformable modeling uses the finite element method FEM while slip computation employs the homotopy continuation method to determine the contact displacements induced by finger movements. The experiment was conducted for everyday items ranging from vegetables to a toy. A simulation-based comparison between deformable grasping and rigid body grasping reveals why soft objects are easier to pick up than hard ones, and demonstrates how a rigid body grasping strategy may fail on soft objects in certain situations.
61 citations
Cites methods from "A finite element solution method fo..."
...Within the FEM framework, the problem of elastic contact with friction had iterative solutions (Sachdeva and Ramakrishnan, 1981; Chandrasekaran et al., 1987), which relied on updating the contact zone and the modes of individual nodes....
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TL;DR: In this paper, a unified PQP (Parametric quadratic programming) model related to contact problems as well as to elasto-plastic structures is constructed.
Abstract: In this paper, the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force. The contact condition and the flow rule are expressed by the same form as in a non-associated plastic flow problem. A unified PQP (Parametric Quadratic Programming) model related to contact problems as well as to elasto-plastic structures is constructed. A series of PQP formulae for contact problems and elastic-plastic structures is derived in the text, and some numerical examples are illustrated as well.
57 citations
TL;DR: In this paper, the application of the finite element method to dynamic contact buckling problems is discussed, where the penalty function method is applied to incorporate the contact conditions in the equation of motion and a trial-and-error method is employed to obtain the converged contact state.
Abstract: The present paper deals with the application of the finite element method to dynamic contact buckling problems. The penalty function method is applied to incorporate the contact conditions in the equation of motion and a trial-and-error method is employed to obtain the converged contact state. Numerical examples are analysed to show the effectiveness and the validity of the method, and it is applied to a dynamic buckling problem involving contact phenomena.
54 citations
TL;DR: This paper presents a grasping strategy that squeezes the object with two fingers under specified displacements rather than forces, and states that a ‘stable’ squeeze minimizes the potential energy for the same amount of squeezing, while a 'pure' squeeze ensures that the object undergoes no rigid body motion as it deforms.
Abstract: Robotic grasping of deformable objects is difficult and under-researched, not simply due to the high computational cost of modeling. More fundamentally, several issues arise with the deformation of an object being grasped: a changing wrench space, growing finger contact areas, and pointwise varying contact modes inside these areas. Consequently, contact constraints needed for deformable modeling are hardly established at the beginning of the grasping operation. This paper presents a grasping strategy that squeezes the object with two fingers under specified displacements rather than forces. A 'stable' squeeze minimizes the potential energy for the same amount of squeezing, while a 'pure' squeeze ensures that the object undergoes no rigid body motion as it deforms. Assuming linear elasticity, a finite element analysis guarantees equilibrium and the uniqueness of deformation during a squeeze action. An event-driven algorithm tracks the contact regions as well as the modes of contact in their interiors under Coulomb friction, which in turn serve as the needed constraints for deformation update. Grasp quality is characterized as the amount of work performed by the grasping fingers in resisting a known push by some adversary finger. Simulation and multiple experiments have been conducted to validate the results over solid and ring-like 2D objects.
52 citations
Cites background or methods from "A finite element solution method fo..."
...Algorithm 1 is similar in its iterative updating of contact status to previous FEM-based solutions to elastic contact problems (Okamoto and Nakazawa, 1979; Sachdeva and Ramakrishnan, 1981; Chandrasekaran et al., 1987)....
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...This event-based approach was extended by Chandrasekaran et al. (1987) to handle geometric and physical nonlinearities as well as node-edge contacts in solving for the exact loading condition from prescribed displacements....
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References
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01 Jan 1982
TL;DR: Elements finis Reference Record created on 2004-09-07, modified on 2016-08-08.
Abstract: Keywords: Methode des elements finis ; Mathematique ; Elements finis Reference Record created on 2004-09-07, modified on 2016-08-08
5,049 citations
TL;DR: In this paper, an incremental approach to the solution of buckling and snapping problems is explored, where the authors use the length of the equilibrium path as a control parameter, together with the second order iteration method of Newton.
1,821 citations
TL;DR: In this article, a modified version of the Newton-Raphson method is proposed to overcome limit points in the finite element method with a fixed load level and a constraint equation.
1,581 citations
TL;DR: In this article, the concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced, and the relationship between local smoothing and the reduced integration technique is established.
Abstract: The concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced.
The relationship between local smoothing and the ‘reduced’ integration' technique is established.
Examples are presented to illustrate the application of the two smoothing techniques to the finite element stresses from several structural analysis problems.
The paper concludes with some practical recommendations for discontinuous finite element function smoothing.
613 citations
TL;DR: The aim in this research is the development of a solution algorithm for analysis of general contact conditions which shall include the possibilities to analyse: contact between flexible-flexible and rigid--flexible bodies; sticking or sliding conditions; large relative motions between bodies; repeated contact and separation between the bodies.
Abstract: SUMMARY A solution procedure for the analysis of planar and axisymmetric contact problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure arc the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm. Much progress has been made during recent years in the development of computational capabilities for general analysis of certain nonlinear effects in solids and structures. In each of these developments, quite naturally, the first step was the demonstration of some ideas and possibilities for the analyses under consideration, and then the research and development for reliable and general techniques was undertaken. The second step proved in many cases much more difficult, and in the case of capabilities for analysis of contact problems has yielded few general results. Although some of the first complex contact problems have been solved using the finite element method quite some time ago,'- and much interest exists in the research and solution of contact problems (see, for example, References 4-1 5), there is still a great deaiwf effort necessary for the development of a reliable, general and cost-effective algorithm for the practical analysis of such problems. This is largely due to the fact that the analysis of contact problems is computationally extremely difficult, even for the simplest constitutive relations used. Much of the difficulty lies in that the boundary conditions of the bodies under consideration are not known prior to the analysis, but they depend on the solution variables. The aim in our research is the development of a solution algorithm for analysis of general contact conditions which shall include the possibilities to analyse: contact between flexible-flexible and rigid--flexible bodies; sticking or sliding conditions (with or without friction); large relative motions between bodies; repeated contact and separation between the bodies. Since the large deformation motion of the individual bodies can in many cases be analysed already quite effectively,'6 an algorithm of the above nature will certainly enlarge, very
474 citations