Coupled FEM-BEM for elastoplastic contact problems using Lagrange multipliers

The coupling of the elastoplastic finite element and elastic boundary element methods for two-dimensional frictionless contact stress analysis is presented. Interface traction matching (boundary element approach), which involves the force terms in the finite element analysis being transformed to tractions, is chosen for the coupling method. The analysis at the contact region is performed by the finite element method, and the Lagrange multiplier approach is used to apply the contact constraints. Since the analyses of elastoplastic problems are non-linear and involve iterative solution, the reduced size of the final system of equations introduced by combining the two methods is very advantageous, especially for contact problems where the nature of the problem also involves an iterative scheme.     

Dynamic analysis and passive control of viscoelastically damped nonlinear dynamic contacts

This paper presents an analytical and finite element study on nonlinear contact dynamics and controls. Nonlinear dynamic contacts between eccentrically supported masses and simply supported beams are studied. Passive control of the dynamic contacts using viscoelastic dampers is also proposed and evaluated. A nonlinear contact finite element is modeled by a set of nonlinear stiffness and damping polynomial functions; and a nonlinear viscoelastic finite element is modeled by a Standard Linear Model with frequency-dependent nonlinear stiffness and damping functions. Analyses show that the dynamic contact force increases as the initial gap increases. Application of viscoelastic dampers can effectively reduce contact loads and prevent dynamic contacts. A simple design equation is also proposed.     

Simulation and analysis of rotary forging a ring workpiece using finite element method

The methods of dealing with some key problems in analyzing a rotary forging process with a finite element method are given. The presented mechanical model of the finite element analysis is in accordance with the actual conditions of the rotary forging process. A three-dimensional rigid–plastic finite element analysis code is developed in FORTRAN language and used to analyze the rotary forging process of a ring workpiece. Velocity fields and stress–strain fields of both contact and non-contact zones of the ring workpiece in the rotary forging are obtained. The deformation mechanism and metal flow laws of the contact zone surface of the ring workpiece in the rotary forging process are revealed. The pressure distributions of the contact surface along the radial and tangential directions and effects of rotary forging parameters on deformation characteristics are given.     

Simulation of the Physiological Contact Pressure Distribution in the Human Hip Joint

In this contribution a finite element analysis of the proximal femur and the acetabulum regarding the physiological contact pressure distribution is presented. Using a detailed 3D finite element model obtained from CT data, the contact pressure in the human hip will be analysed and a summary with respect to different movement situations will be shown. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional simulation of flat rolling through a combined finite element–boundary element approach

This paper presents an innovative approach for analysing three-dimensional flat rolling. The proposed approach is based on a solution resulting from the combination of the finite element method with the boundary element method. The finite element method is used to perform the rigid–plastic numerical modelling of the workpiece allowing the estimation of the roll separating force, rolling torque and contact pressure along the surface of the rolls. The boundary element method is applied for computing the elastic deformation of the rolls. The combination of the two numerical methods is made using the finite element solution of the contact pressure along the surface of the rolls to define the boundary conditions to be applied on the elastic analysis of the rolls. The validity of the proposed approach is discussed by comparing the theoretical predictions with experimental data found in the literature.     

A posteriori error analysis for the normal compliance problem

In this work, a contact problem between a linear elastic material and a deformable obstacle is numerically analyzed. The contact is modeled using the well-known normal compliance contact condition. The weak formulation leads to a nonlinear variational equation which is approximated by using the finite element method. A priori error estimates are recalled. Then, we define an a posteriori error estimator of residual type to evaluate the accuracy of the finite element approximation of the problem. Upper and lower bounds of the discretization error are proved for this estimator.     

一个第二类变分不等式的有限元逼近

本短文讨论下述第二类变分不等式（见 ［２, ４］）的有限元逼近及其误差分析：其中是平面凸多边形区域的的边界, 且而 ． 诸如热量控制问题,流体通过半可透性壁的扩散问题以及简化库仑摩擦接触问题的正则化方法等均可归为上述变分不等式（１）（见［２,３］）．在文［２］中给出了上述变分不等式的有限元逼近格式,作出了收敛性分析及误差估计．本文的目的是进一步用数值积分简化上述有限元逼近格式并改进原有的估计误差． 设Ｔｈ是的拟一致三角形部分,Ｖｈ是对应的线性元空间,且使得ｖｈ＝０在上．［２］中用数值积分代替其中 Ｍｉ…     

A finite element method for granular flow through a frictional boundary

A finite element method for the flow of dry granular solids through a domain involving a frictional contact boundary is formulated. The granular material is assumed as a compressible viscous-elastic–plastic continuum. Based on the principles of continuum mechanics, a complete set of equations is developed. The resulting boundary value problem is solved by the finite element method in space and by the finite difference method in time. The derivation of the finite element equations and the mathematical framework of the numerical technique are presented, together with two illustrative examples to demonstrate the validity of the technique.     

A propos d'approximation par elements finis optimale pour les problèmes de contact unilatéral

We consider a interpolation type operator and a projection type operator with values in a finite element function set, defined for continuous functions and keeping positiveness. We prove with a counter-example that the two operators do not verify optimal approximation results with respect to a dual norm. This counter-example yields some predicted results concerning optimality of the mortar element method and finite element analysis for unilateral contact problems.     

Accurate modeling of contact using cubic splines

In this paper, we develop and implement a new method for the accurate representation of contact surfaces. This approach overcomes the difficulties arising from the use of traditional node-to-linear surface contact algorithms. In our proposed method, contact surfaces were modeled accurately using C¹-continuous cubic splines, which interpolate the finite element nodes. In this case, the unit normal vectors are defined uniquely at any point on the contact surfaces. These splines preserve the local deformation of the nodes on each flexible contact surface. Consequently, a consistent linearization of the kinematic contact constraints, based on the spline interpolation, was derived. Moreover, the gap between two contact surfaces was modeled accurately using an efficient surface-to-surface contact search algorithm. Since the continuity of the splines is not affected by the number of nodes, accurate stress distribution can be obtained with less finite elements at the contact surface than that using the traditional linear discretization of the contact surface. Two numerical examples are used to illustrate the advantages of the proposed representation. They show a significant improvement in accuracy compared to traditional piecewise element-based surface interpolation. This approach overcomes the problem of mismatch in a finite element mesh. This is very useful, since most realistic engineering problems involve contact areas that are not known a priori.     

Load share and finite element stress analysis for double circular-arc helical gears

The authors analyze the tooth surface contact and stresses for double circular-arc helical gear drives. The geometry of such gear drives has been represented by the authors in their previous paper [1]. The proposed approach is based on application of (i) computerized simulation of meshing and contact of loaded gear drives, and (ii) the finite element method. Load share between the neighboring pairs of teeth is based on the analysis of position errors caused by surface mismatch and elastic deformation of teeth. The authors have investigated the conditions of load share under a load and determined the real contact ratio for aligned and misaligned gear drives, respectively. Elastic deformation of teeth and the stress analysis of the double circular-arc helical gears are accomplished by using the finite element method. The finite element models for the pinion and gear are constructed, respectively. Contact pressure is spread over elliptical area. The stress analysis for aligned and misaligned gear drives, respectively, has been performed. The numerical results have been compared with those obtained by other approaches.     

Pre-Tensioned Belts Overhanging Elastic Rollers

Subject of this paper are deformation mechanisms in pre-tensioned elastic belts, which are wrapped around rollers carrying elastic layers that support the belts over part of their width. By means of analytical models and the finite element method the corresponding deformations of the belts are predicted. Special emphasis is put on the effects of the nonlinear (contact) boundary conditions in the vicinity of the lateral edges of the roller. The continuum finite element simulations provide reference solutions, and, furthermore, serve as an accurate means for predicting the contact stress distribution, whereas the semi-analytical solutions allow for an inexpensive and quick investigation of several parameter combinations. The high quality of the semi-analytical model can be judged by the excellent agreement of the obtained results with the reference finite element results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element analysis of fir-tree region in turbine discs

Comprehensive 2D and 3D finite element analysis is undertaken of the fir-tree region in aeroengine turbine disc assemblies. The study examines the effect of the critical geometrical features, such as the number of teeth, flank length and flank angle upon the stress field in the disc. The two-dimensional finite element predictions are verified using photoelastic-stress-freezing technique. The study is further extended to account for the effect of the skew angle and the interfacial friction between the disc and attached blades upon the resulting contact stresses at the interface and through the disc thickness. The results reveal that aeroengine disc designers must treat the two-dimensional finite element results with caution. This is due to the fact that two-dimensional results do not account for the large stress variations at the contact region and through the thickness due to the presence of skew slots in the disc.     

Plate Contact问题的混合有限元逼近

论文考虑了Plate Contact问题的混合有限元逼近,其变分问题为第二类四阶椭圆变分不等问题.首先,根据正则化方法,得到原问题的正则化问题.再根据网格依赖范数技巧,考虑了正则化问题的Ciarlet-Raviart混合有限元逼近,并证明了真解与逼近解之间的误差估计.最后通过数值算例验证了理论分析的结果.     

Éléments finis non conformes pour un problème de contact unilatéral avec frottement

In a previous study, we considered it nonconforming finite element method for a frictionless contact problem. The aim of this note is to establish the convergence of the method for a frictional contact problem between two deformable bodies.     

Isogeometrical approach for cable type structures allowing large sliding contact

A special combination of two finite elements approaches is considered in order to derive a formulation suitable for cable type structures. First, a finite beam element allowing arbitrarily large rotations together with a high order approximation technique including a C¹-continuous approximation is used to model cable behavior. Afterwards, a covariant approach for a curve-to-curve contact is exploited to incorporate contact between a pair of cable elements. This leads to a cable type element with contact. In numerical examples both “soft” and “hard” cables are represented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

接触表面的边界条件奇异性及其随机扰动

碰撞表面的随机边界条件反映了粘弹性材料在不同碰撞条件下的复杂性质.数值的不确定性和确定模型的渐近估计都可以利用计算机系统来计算.运用有限元方法来模拟碰撞表面的变形,得出远离接触表面部分的结构保持稳定.     

Deterministic particle method approximation of a contact inhibition cross-diffusion problem

We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations.According to the values of the diffusion parameters related to the intra- and inter-population repulsion intensities, the system may be classified in terms of an associated matrix. When the matrix is definite positive, the problem is well posed and the finite element approximation produces convergent approximations to the exact solution.A particularly important case arises when the matrix is only positive semi-definite and the initial data are segregated: the contact inhibition problem. In this case, the solutions may be discontinuous and hence the (conforming) finite element approximation may exhibit instabilities in the neighborhood of the discontinuity.In this article we deduce the particle method approximation to the general cross-diffusion problem and apply it to the contact inhibition problem. We then provide some numerical experiments comparing the results produced by the finite element and the particle method discretizations.