Contact self-dual geometry of quasi-Sasakian 5-manifolds

We construct a self-dual geometry of quasi-Sasakian 5-manifolds. Namely, we intrinsically define the notion of contact conformally semiflat (i.e., contact self-dual or contact antiself-dual) almost contact metric manifolds and also obtain a number of results concerning contact conformally semiflat quasi-Sasakian 5-manifolds. Themost important results concerning Sasakian and cosymplectic manifolds reveal interesting relationships between the characteristics of these manifolds such as contact self-duality and constancy of the Φ-holomorphic sectional curvature, contact anti-self-duality and Ricci flatness, etc.     

Connections on contact manifolds and contact twistor space

In this paper we generalize the definition of symplectic connection to the contact case. It turns out that any odd-dimensional manifold equipped with a contact form admits contact connections and that any Sasakian structure induces a canonical contact connection. Furthermore (as in the symplectic case), any contact connection induces an almost CR structure on the contact twistor space which is integrable if and only if the curvature of the connection is of Ricci-type.     

Conformal quaternionic contact curvature and the local sphere theorem

A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern–Moser tensor in CR geometry. It is shown that a quaternionic contact manifold is locally quaternionic contact conformal to the standard flat quaternionic contact structure on the quaternionic Heisenberg group, or equivalently, to the standard 3-Sasakian structure on the sphere iff the quaternionic contact conformal curvature vanishes.     

Elastic-plastic halfspace simulation

Due to the roughness of technical surfaces only the surface peaks are in contact for moderate contact pressures. Thus, the real contact area is smaller than the apparent contact area. Contact forces can only occur in the real contact area. Consequently it is necessary to determine the deformation of surface asperities in order to analyse the tribological properties of surfaces. The real contact area is usually small in initial contact. This leads to large contact pressures which in turn lead to the plastic deformation of surface roughness peaks. Therefore an elastic-plastic model is necessary. The halfspace model seems to be beneficial because there is only a system of equations on a surface mesh to be solved and not on a volume mesh like in the Finite-Element-Method. This leads to a much smaller system of equations which should allow reasonable calculation times even for large contact surfaces. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

高速铁路旅客满意度研究:服务接触理论视角

作为旅客重要的出行方式,高速铁路既面临着市场竞争,又面临着旅客不断增长的服务质量要求。基于服务接触理论形成高速铁路客运服务接触链,从理论上构建高速铁路旅客满意度模型,研究影响旅客满意度的关键接触点。运用SEM定量分析潜变量间的路径系数,对该理论模型的路径假设进行检验。结果表明:四个阶段的服务接触直接影响旅客满意度,间接影响旅客忠诚度;四个服务接触阶段对旅客满意度的影响效应从高到低依次是列车、候车、出站、进站;各服务接触阶段对旅客忠诚度的影响存在明显差异。     

A Two Dimensional Model for the Dynamical Contact of Elastic Rough Surfaces

To model the contact behavior including dynamical effects, a two dimensional mechanical model of elastic rough contact is developed. This model can simulate the contact behaviour between two rough surfaces depending on normal pressure, sliding speed and roughness profiles. The contact between two rough surfaces is reduced to a rough rigid and a rough elastic layer. The elastic layer is modeled by point masses connected by spring-damper elements. The total system is described by coupled ODEs. The number of ODEs and thus the degree of freedom of the model depends on the varying contact conditions. The contact conditions are monitored during the simulation and the simulation interrupts, in case the contact conditions change. The equations of motion are then adapted with respect to the contact constraints. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

CONTACT ALGORITHMS FOR CONTACT DYNAMICAL SYSTEMS

1.IntroductionContactstructureisananalogofasymplecticoneforodd-dimensionalmanifolds,itstemsfrommanifoldsofcontactelementsofconfigurationspacesinmechanicsand,therefore,itisalsoofbasicimportanceinphysicalandengineeringsciences.Weapplytinthispaperttheideasof…     

Mathematical modeling of contact problems of plastic flow

The nonstationary space contact problems of plastic flow in the comparatively thin layer between surfaces of external bodies have been analysed in the present paper. Earlier encountered in mathematical modeling peculiarities characterized for considered processes (as the slipping of layer material along contact, high - comparatively with shears - contact pressures, normal elastic movements commensurable with thickness of the layer, the formation of hardened layers near contact) are noted. Other characterized peculiarities, such as the property of anisotropy of friction forces on contact, the possibility of preserving the intermediate lubricant volumes on contact and contact friction faces control, the influence of initial nonhomogeneity on the formation of plastic flow are also considered. In each caw the induced qualitative effects by them are represented.     

A solution approach for contact problems based on the dual interpolation boundary face method

The recently proposed dual interpolation boundary face method (DiBFM) has been shown to have a much higher accuracy and improved convergence rates compared with the traditional boundary element method. In addition, the DiBFM has the ability to approximate both continuous and discontinuous fields, and this provides a way to approximate the discontinuous pressure at a contact boundary. This paper presents a solution approach for two dimensional frictionless and frictional contact problems based on the DiBFM. The solution approach is divided into outer and inner iterations. In the outer iteration, the size of the contact zone is determined. Then the elements near the contact boundary are updated to approximate the discontinuous pressure. The inner iteration is used to determine the contact state (sticking or sliding), and is only performed for frictional contact problems. To make the system of equations solvable, the contact constraints and some supplementary equations are also given. Several numerical examples demonstrate the validity and high accuracy of the proposed approach. Furthermore, due to the continuity of elements in DiBFM and the detection of the contact boundary, the pressure oscillations near the contact boundary can be treated.     

Spatial contact problems for rough elastic bodies under elastoplastic deformations of the unevenness

On the basis of /1, 2/, a model is constructed for the contact between a rigid stamp and a rough body taking elastoplastic deformations of the unevenness into account. The contact model for rough bodies with elastic deformations of the unevenness is a special case. A classical approach utilizing boundary integral equations is applied in the mathematical formulation of the contact problem. Under quite general assumptions (for instance, the multiconnectedness of the contact domain desired), the uniqueness and existence of the solution are investigated. A method is developed to determine the contact pressure, the closure of the bodies, and also the contact area which consists of two parts in the general case, a zone of elastoplastic deformation of the unevenness and a zone of their elastic deformation. The efficiency of the method is shown in examples of new contact problems. The solution is represented in a convenient form for analysing the influence of the roughness. This is of considerable value for material testing by a contact method. A fairly complete survey of research on contact problems for rough bodies can be found in /1–4/.     

A comparison between elastohydrodynamic and dry hertzian line contacts with regard to their nonlinear vibration behaviour

The nonlinear dynamic behaviour of a simple system employing two different types of contact is compared: elastohydrodynamic line contact and Hertzian line contact with appropriate damping. The elastohydrodynamic problem is solved with finite elements. For the Hertzian line contact problem an analytical solution is known. It is found that for highly loaded cases Hertzian and elastohydrodynamic contacts lead to very similar frequency response curves. This means that instead of solving the computational expensive elastohydrodynamic problem the Hertzian contact can be used. However, considering weakly loaded contacts the two types of contact show very different behaviour. In particular the natural frequencies are different and the elastohydrodynamic contact exhibits rich nonlinear dynamic behaviour including jump phenomena as well as sub- and superharmonic bifurcations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contact open books with exotic pages

We consider a fixed contact 3-manifold that admits infinitely many compact Stein fillings which are all homeomorphic but pairwise non-diffeomorphic. Each of these fillings gives rise to a closed contact 5-manifold described as a contact open book whose page is the filling at hand and whose monodromy is the identity symplectomorphism. We show that the resulting infinitely many contact 5-manifolds are all diffeomorphic but pairwise non-contactomorphic. Moreover, we explicitly determine these contact 5-manifolds.     

Künneth formula in Rabinowitz Floer homology

Rabinowitz Floer homology has been investigated on submanifolds of contact type. The contact condition, however, is quite restrictive. For example, a product of contact hypersurfaces is rarely of contact type. In this article, we study Rabinowitz Floer homology for product manifolds which are not necessarily of contact type. We show for a class of product manifolds that there are infinitely many leafwise intersection points by proving the Künneth formula for Rabinowitz Floer homology.     

3D dynamic modeling of powder forming processes via a simple and efficient node-to-surface contact algorithm

In this paper, a simple and efficient contact algorithm is presented for the evaluation of density distribution in three-dimensional dynamic modeling of powder compaction processes. The contact node-to-surface algorithm is employed to impose the contact constraints in large deformation frictional contact, and the contact frictional slip is modified by the Coulomb friction law to simulate the frictional behavior between the rigid punch and the work-piece. The 3D nonlinear contact friction algorithm is employed together with a double-surface cap plasticity model within the framework of large finite element deformation in order to predict the non-uniform relative density distribution during the dynamic simulation of powder die-pressing. The accuracy and robustness of contact algorithm is verified by the impact analysis of two elastic rods, which is compared with the analytical solution. Finally, the performance of computational schemes is illustrated in dynamic modeling of a set of powder components.     

Homotopy classification of contact foliations on open contact manifolds

We give a homotopy classification of foliations on open contact manifolds whose leaves are contact submanifolds of the ambient space. The result is an extension of Haefliger’s classification of foliations on open manifold in the contact setting. While proving the main theorem, we also prove a result on equidimensional isocontact immersions on open contact manifolds.     

Modeling of jointed structures using zero thickness interface elements

An important contribution to global damping of mechanical devices is structural damping due tomicroslip effects with friction in joint interfaces. In order to investigate the mechanical behaviour in these contact interfaces numerically, a contact element in the context of Finite Element Method (FEM) is presented. The suggested element is an isoparametric zero thickness element which is well suited for the present problem because the contact area is known and only small relative displacements occur. Arbitrary linear or nonlinear constitutive contact models for normal and tangential contact behaviour can be implemented. Using a proper parametrisation of the contact area, it is possible to apply the element in contact interfaces lying arbitrarily in space and in interfaces discretized with distorted elements. This method is described before a numerical example is compared with experimental results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contact handle decompositions

We review Giroux's contact handles and contact handle attachments in dimension three and show that a bypass attachment consists of a pair of contact 1 and 2-handles. As an application we describe explicit contact handle decompositions of infinitely many pairwise non-isotopic overtwisted 3-spheres. We also give an alternative proof of the fact that every compact contact 3-manifold (closed or with convex boundary) admits a contact handle decomposition, which is a result originally due to Giroux.     

Inequivalent contact structures on Boothby–Wang five-manifolds

We consider contact structures on simply-connected five-manifolds which arise as circle bundles over simply-connected symplectic four-manifolds and show that invariants from contact homology are related to the divisibility of the canonical class of the symplectic structure. As an application we find new examples of inequivalent contact structures in the same equivalence class of almost contact structures with non-zero first Chern class.