A mortared finite element method for frictional contact on arbitrary interfaces

This work concerns finite-element algorithms for imposing frictional contact constraints on intra-element, or embedded surfaces. Existing techniques typically rely on the underlying bulk mesh to implicitly partition the surface, a strategy that can give rise to overconstraint. In the present work, we first apply a mortaring algorithm to the modeling of frictional contact conditions on arbitrary interfaces. The algorithm is based upon a projection of the bulk and surface fields onto independent mortar fields at the interface. We examine the advantages of this approach when combined with extended finite-element approximations to the bulk fields. In particular, the method allows for bulk and surface domains to be partitioned separately, as well as enforce nonlinear contact constraints on surfaces that are not explicitly “fitted” to the bulk mesh. Results from several benchmark problems in frictional contact are provided to demonstrate the accuracy and efficacy of the method, as well as the improvement in robustness compared to existing techniques. We also provide an example that illustrates the effectiveness of the approach in high-speed machining simulation.     

A finite element method for contact using a third medium

The numerical simulation of contact problems is nowadays a standard procedure in many engineering applications. The contact constraints are usually formulated using either the Lagrange multiplier, the penalty approach or variants of both methodologies. The aim of this paper is to introduce a new scheme that is based on a space filling mesh in which the contacting bodies can move and interact. To be able to account for the contact constraints, the property of the medium, that imbeds the bodies coming into contact, has to change with respect to the movements of the bodies. Within this approach the medium will be formulated as an isotropic/anisotropic material with changing characteristics and directions. In this paper we will derive a new finite element formulation that is based on the above mentioned ideas. The formulation is presented for large deformation analysis and frictionless contact.     

Numerical solution of the point contact problem using the finite element method

The elastohydrodynamic lubrication problem, in which the lubricant pressure and film thickness are sensitive to surface deformation, is solved by using a finite element procedure and the Newton method. The numerical procedure is applied to the point contact problem, in which a thin lubricant film is maintained between two balls loaded together by a high load under conditions of pure rolling. The present analysis shows that pressure spikes are formed near the outlet region, a result which has been found in the line contact problem and which has been conjectured in the present problem.     

A mixed finite element model for the elastic contact problem

The static elastic contact problem is approached using Lagrange multipliers, leading to a mixed finite element problem. A non-linear friction law is introduced explicitly and the non-local character of the friction phenomena is implicitly assumed. In order to avoid stress oscillations near singular points, a perturbed Lagrangian functional is considered. The algorithms herein proposed do not impose nodal dependencies over the contact surfaces, allowing for the independent discretization of both bodies. The method is able to model simultaneous contact over different regions of any geometrical shape. Computer code, examples and results presented here are restricted to axisymmetrical and bidimensional cases.     

Reducing computational costs using a multi-region finite element method for electromagnetic scattering

Electromagnetic scattering problems involving multiple scatterers can be solved by the finite element method using a single domain truncated with an absorbing boundary condition, but often it is more efficient to separate the single domain into several subdomains, separated by free-space, and to solve the set of subdomains iteratively. This multi-region method has been reported in the literature. Its relative computational cost is investigated and formulas for determining are provided when it is advantageous to use a multi-region against a single-region method.     

A finite element solution method for contact problems with friction

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.     

A computational procedure for flexible beams with frictional contact constraints

This paper deals with the application of a parametric quadratic programming (PQP) method to the numerical solution of large-deflection beams involving frictional contact constraints. The flexibility of the structure is modelled by an intrinsic spatial beam theory which is approximated by transverse-shear deformable linear beam elements. The linear complementary problem (LCP) without the penalty function resulting from PQP is made part of a Newton-Raphson search. The tool for solving the complementary equations is Lemke's algorithm, in which frictional contact conditions are enforced and new contact surfaces are updated during iteration. Applying the resulting contact element, a more accurate approximation of the contact point can be guaranteed, and the contact force can be directly computed by the adjacent beam elements. Three numerical examples are analysed to show the effectiveness and validity of the method.     

Symmetric Galerkin boundary element method for quasi-brittle-fracture and frictional contact problems

The analysis of elastic quasi-brittle structures containing cohesive cracks and contacts with friction is given a unitary formulation in the framework of incremental plasticity. Integral equations for displacements and tractions are enforced by a weighted-residual Galerkin approach so that symmetry is preserved in the key operators (in contrast to collocation BE approaches) and cracks (either internal or edge cracks) can be dealt with by a single-domain BE formulation. The space-discrete problem in rates is expressed as a linear complementarity problem centered on a symmetric matrix or, equivalently, as a quadratic programming problem in variables pertaining to the displacement discontinuity locus only. Criteria for overall instabilities and bifurcations are derived from this formulation. The BE approach proposed and implemented by a suitable time-stepping technique, is comparatively tested by numerical solutions of cohesive-crack propagation problems.     

A finite element method for contact problems related to fracture mechanics

A finite element method for contact problems in crack mechanics is developed on the basis of the penalty function method. The method is successfully applied to three important problems in fracture mechanics: a crack propagated from a pin hole, a two-point supported specimen with an edge crack loaded by a stamp, and a thick plate with a through-wall crack under bending force.     

A combined surface integral and finite element solution for a three-dimensional contact problem

A method is described to determine contact stresses and deformation using a combination of the finite element method and a surface integral form of the Bousinesq solution. Numerical examples of contacting hypoid gears are presented.     

A second order finite element method for the one-dimensional Stefan problem

We describe a finite element method for the one-dimensional Stefan problem. The elements are quadrilaterals of the space-time plane which are determined at each time-step in relation with the position of the free boundary. The method appears as a generalization of the classical Crank-Nicolson scheme, since it is identical to this scheme in the case of rectangular elements; it has the advantage of providing a simple and accurate determination of the free boundary. Numerical experiments show that the order of accuracy is equal to 2.     

A computational investigation and smooth-shaped defect synthesis for eddy current testing problems using the subregion finite element method

Eddy Current Testing (ECT) plays a key role in detecting cracks and defects in conductors. The present study examines for the first time how the subregion method as an effective mathematical and computational technique can be admixed with Finite Element Method (FEM) to study multiple defects parameters for ECT issues. Separating a defect region from the entire domain in any computational technique will save both time and storage space. Examples of different types of defects are presented in this article . A tangible result of processing time reduction by 90% has been achieved which has led us to consider the subregion FEM method as an effective method in solving different Nondestructive Evaluation (NDE) problems. An agreement between our results and others using classical FEM has been achieved which could lead to using this technique in online and field testing problems. The presented subregion FEM algorithm was verified experimentally with good agreement by testing Aluminum (T6061-T6) samples with defects. A Tunneling Magnetoresistive (TMR) sensor was used to measure the component of the magnetic field from normal to the sample top surface. A major component of minimizing processing time was achieved, which could lead to using this technique in online and field testing problems.     

An error indicator for the generalized eigenvalue problem using the hierarchical finite element method

The hierarchical concept applied to eigenvalue problems is considered. An error indicator is derived from the pertinent Rayleigh quotient. The indicator serves as an estimation ‘a posteriori’ of the relative change in an eigenvalue for a hierarchical refinement. A numerical example is included.     

A contact algorithm for 3D discrete and finite element contact problems based on penalty function method

A contact algorithm in the context of the combined discrete element (DE) and finite element (FE) method is proposed. The algorithm, which is based on the node-to-surface method used in finite element method, treats each spherical discrete element as a slave node and the surfaces of the finite element domain as the master surfaces. The contact force on the contact interface is processed by using a penalty function method. Afterward, a modification of the combined DE/FE method is proposed. Following that, the corresponding numerical code is implemented into the in-house developed code. To test the accuracy of the proposed algorithm, the impact between two identical bars and the vibration process of a laminated glass plate under impact of elastic sphere are simulated in elastic range. By comparing the results with the analytical solution and/or that calculated by using LS-DYNA, it is found that they agree with each other very well. The accuracy of the algorithm proposed in this paper is proved.     

On a finite element method for dynamic contact/impact problems

This paper addresses the formulation and discrete approximation of dynamic contact/impact initial-value problems. The continuous problem is presented in the context of non-linear kinematics. Standard semi-discrete time integrators are introduced and are shown to be unsuccessful in modelling the kinematic constraints imposed on the interacting bodies during persistent contact. A procedure that bypasses the aforementioned difficulty is proposed by means of a novel variational formulation. Numerical simulations are conducted and the results are reported and discussed.     

A general finite element approach for contact stress analysis

This paper presents a general finite element approach for the treatment of contact stress problems. Stanctard shape function routines are used for the detection of contact between previously separate meshes and for the application of displacement constraints where contact has been identified. The mesh contact routines are installed in an incremental approach whereby the contact constraints are imposed by using either penalty functions or Lagrange multipliers.     

A novel finite element formulation for frictionless contact problems

This article advocates a new methodology for the finite element solution of contact problems involving bodies that may undergo finite motions and deformations. The analysis is based on a decomposition of the two-body contact problem into two simultaneous sub-problems, and results naturally in geometrically unbiased discretization of the contacting surfaces. A proposed two-dimensional contact element is specifically designed to unconditionally allow for exact transmission of constant normal traction through interacting surfaces.