The Contact Problem Studied by Pseudocaustics Formed at the Vicinity of the Contact Zone

1984 ◽  
Vol 106 (3) ◽  
pp. 211-215 ◽  
Author(s):  
P. S. Theocaris ◽  
C. A. Stassinakis
Keyword(s):  
Contact Problem ◽  
Contact Zone ◽  
Contact Area ◽  
The Other ◽  
Tangential Stresses ◽  
Elastic Bodies ◽  
First Case ◽  
Reflected Light ◽  
Spline Polynomial ◽  
Distribution Of Stresses

The method of caustics is applied to formulate the normal and tangential stresses developed in the contact zone of two elastic bodies, and also for one elastic and the other plastic. The stresses are represented by a cubic spline polynomial, its coefficients calculated by pseudocaustics from reflected light around the contact zone. The method is applied to determine the stresses along the boundary of a half-plane and the stresses along the contact area of two disks. The deviation of calculated stresses from the applied ones, in the first case was small, while in the second case it was found that the normal distribution of stresses was similar to a Hertzian distribution. This experimental method can be used to accurately obtain contact stresses.

scholarly journals FFT-ASSISTED ALGORITHMS FOR 3D LINE-CONTACT PROBLEMS

2021 ◽  
Vol 13 (2) ◽  
pp. 124-129
Author(s):  
Sergiu Spinu ◽  
◽  
Keyword(s):  
Fourier Transform ◽  
Contact Problem ◽  
Fast Fourier Transform ◽  
Contact Area ◽  
Contact Problems ◽  
Contact Length ◽  
The Other ◽  
Line Contact ◽  
Contact Width ◽  
Length Direction

The line-contact is a particular type of contact with a contact length much greater than its width. Such contact scenarios can be treated in the frame of a two-dimensional plane-strain problem if the contacting surfaces can be considered nominally smooth. However, surface irregularities inherent to any manufacturing technique lead to a discontinuous contact area that differs from the one derived on the basis of the smooth profile assumption. It is therefore tantalizing to pursue the solution of a line-contact problem using an intrinsically three-dimensional (3D) model, which can only be numerical due to lack of general analytical solutions in contact mechanics. Considering the geometry of the line-contact, a major challenge in its numerical modelling is that the expected contact area is orders of magnitude larger in one direction compared to the other. This may lead to an unreasonably large number of grids in the contact length direction, which translates to a prohibitive computational burden. An alternative approach, employed in this paper, is to treat the line-contact as non-periodic in the contact width direction, but periodic in the contact length direction, with a period equal to the window required to capture and replicate the surface specific texture. This periodicity encourages the contact problem solution by spectral methods based on the fast Fourier transform (FFT) algorithm. Based on this idea, two methods are derived in this paper from the existing Discrete Convolution Fast Fourier Transform (DCFFT) technique, which was previously developed for purely non-periodic contact problems. A first algorithm variant employs a special padding technique for pressure, whereas a second one mimics the contribution of multiple pressure periods by summation of the influence coefficients over a domain a few times larger than the target domain. Both techniques are validated against the existing analytical Hertz solution for the line-contact and a good agreement is found. The advanced methods seem well adapted to the simulation of contact problems that can be approximated as periodic in one direction and non-periodic in the other.

scholarly journals Contact problem on indentation of an elastic half-plane with functionally-graded coating in presence of tangential stresses on the surface

2018 ◽  
Vol 226 ◽  
pp. 03018 ◽  
Author(s):  
Sergei S. Volkov ◽  
Andrey S. Vasiliev ◽  
Evgeniy V. Sadyrin
Keyword(s):  
Fourier Series ◽  
Contact Problem ◽  
Half Plane ◽  
Contact Area ◽  
Functionally Graded ◽  
Dual Integral Equations ◽  
Normal Contact ◽  
Functionally Graded Coating ◽  
Tangential Stresses ◽  
Graded Coating

Plane contact problem on indentation of an elastic half-plane with functionally graded coating by a parabolic punch is considered. The surface of the half-plane is additionally subjected to distributed tangential stresses in a certain region different from contact area. The contact area is assumed to be asymmetric with respect to the center of the punch. Tangential stresses are represented in the form of Fourier series. The problem is reduced to the solution of two dual integral equations over even and odd functions describing distribution of normal contact stresses. The bilateral asymptotic method is used to solve these equations. Approximated analytical solutions asymptotically exact for both the small and large values of relative coating thickness are constructed.

scholarly journals Solution of Contact Problem for Supporting Node of Beam Hinged Plate

2019 ◽  
Vol 18 (4) ◽  
pp. 274-283
Author(s):  
S. V. Bosakov ◽  
P. D. Skachok
Keyword(s):  
Contact Problem ◽  
Contact Zone ◽  
Contact Area ◽  
Concrete Slab ◽  
Bending Moment ◽  
Rigid Base ◽  
Concentrated Load ◽  
Rigid Stamp ◽  
Quarter Plane ◽  
Flexibility Index

The paper considers a solution of contact problem for hinged supporting node of beam floor slab (coating). The main goal is to determine a stress state of the area where a plate rests on the wall. In this case, a number of problems are solved: construction of reactive pressure diagrams in the area of direct plate and wall contact, clarification of the calculated plate span, influence of contact zone size on a value of maximum bending moment in the middle of the plate, determination of contact area at various indices of flexibility and comparison of the obtained results with the known solution of rigid stamp and elastic quarter-plane interaction. The calculation has been carried out by the Zhemochkin method, its implementation for the given task corresponds to a mixed method of structural mechanics. As an illustration, the calculation has been performed on a concentrated load applied in the middle of the plate span. In the course of the study, it has been established that when a reinforced concrete slab rests on concrete and brick walls, the contact zone reduces itself to two Zhemochkin sections. When a flexibility index is decreased that corresponds to slab support on a less rigid base, the contact area is increased, and that, in its turn, has an influence on an increase of the calculated slab span and the bending moment in the middle of the slab. In the case of an absolutely rigid plate support (flexibility index is equal to zero), the contact stresses reach their maximum value at the point of plate edge contact and elastic quarter-plane. The nature of the diagram is confirmed by an analytical dependence of contact stress distribution obtained by Aleksandrov V. M. when solving a problem of pressing a rigid stamp into an edge of an elastic wedge.

scholarly journals Johnson–Kendall–Roberts adhesive contact for a toroidal indenter

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160218 ◽  
Author(s):  
Ivan Argatov ◽  
Qiang Li ◽  
Roman Pohrt ◽  
Valentin L. Popov
Keyword(s):  
Asymptotic Solution ◽  
Contact Problem ◽  
Half Space ◽  
Elastic Properties ◽  
Contact Area ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
The Other ◽  
Leading Order

The unilateral axisymmetric frictionless adhesive contact problem for a toroidal indenter and an elastic half-space is considered in the framework of the Johnson–Kendall–Roberts theory. In the case of a semi-fixed annular contact area, when one of the contact radii is fixed, while the other varies during indentation, we obtain the asymptotic solution of the adhesive contact problem based on the solution of the corresponding unilateral non-adhesive contact problem. In particular, the adhesive contact problem for Barber’s concave indenter is considered in detail. In the case when both contact radii are variable, we construct the leading-order asymptotic solution for a narrow annular contact area. It is found that for a v-shaped generalized toroidal indenter, the pull-off force is independent of the elastic properties of the indented solid.

A NEW APPROACH TO THE STUDY OF COORDINATIVE CONSTRUCTIONS

2019 ◽  
pp. 175-187
Author(s):  
Anna Varnayeva
Keyword(s):  
Characteristic Property ◽  
Mathematical Concept ◽  
The Other ◽  
New Approach ◽  
Logical Aspect ◽  
First Case

Coordinative constructions are traditionally opposed to subordinative constructions. However, this opposition comes down to denial of dependence in coordinative constructions. Thereby the parity of these two constructions does not come to light: subordinative construction can be described without coordinative one. This situation is not improved by detection of a coordinative triangle in all coordinative constructions. The article shows a new approach in the study of coordinative constructions: a coordinative construction is a system; there are not only specific relations – a coordinative triangle, – but also specific elements. Novelty of the study consists in the address to extralinguistic facts, viz. a mathematical concept of a set and its elements. There are a lot of similarities between them. A set in mathematics includes generalizing elements and the composed row in coordinative constructions; in the first case the set is not partitioned, in the second case it is partitioned. In mathematics equivalent components in coordinative constructions correspond to the set elements. A characteristic property in mathematics is homogeneity in coordinative constructions and etc. It is firstly demonstrated, that coordinative and subordinative constructions are correlative and the study of one construction is impossible without the study of the other one. Their parity is shown in coordinative constructions with elements of one set, in subordinative ones with elements of different sets. Cf.: roses and tulips –red roses. In the coordinatiму construction elements of one set are called: «flowers »; in the subordinative construction there are elements of different sets: «flowers » and «colors». It should be noted that the mathematical concept of a set relates to so called logical aspect in linguistics or thinking about reality.

scholarly journals On the contact problem of layered elastic bodies

1967 ◽  
Vol 25 (3) ◽  
pp. 233-242 ◽  
Author(s):  
Ting-Shu Wu ◽  
Y. P. Chiu
Keyword(s):  
Contact Problem ◽  
Elastic Bodies

On Slip Inception and Static Friction for Smooth Dry Contact

2014 ◽  
Vol 81 (12) ◽  
Author(s):  
Xi Shi
Keyword(s):  
Shear Strength ◽  
Contact Area ◽  
Material Properties ◽  
Static Friction ◽  
Friction Model ◽  
Interfacial Bonding ◽  
The Other ◽  
Material Failure ◽  
Bonding Failure ◽  
Dry Contact

Slip inception mechanism is very important for modeling of static friction and understanding of some experimental observations of friction. In this work, slip inception was treated as a local competence of interfacial bonding failure and weaker material failure. At any contacting point, if bond shear strength is weaker than softer material shear strength, slip inception is governed by interfacial bonding failure. Otherwise, it is governed by softer material failure. Considering the possible co-existence of these two slip inception mechanisms during presliding, a hybrid static friction model for smooth dry contact was proposed, which indicates that the static friction consists of two components: one contributed by contact area where bonding failure is dominant and the other contributed by contact area where material failure is dominant. With the proposed static friction model, the effects of contact pressure, the material properties, and the contact geometry on static friction were discussed.

Tribological Study of Polymer Composite Forming Using Model Experiments and Real Composites

2014 ◽  
Vol 611-612 ◽  
pp. 300-305 ◽  
Author(s):  
Olga Smerdova ◽  
Michael P.F. Sutcliffe
Keyword(s):  
Experimental Study ◽  
Polymer Composites ◽  
Viscous Liquid ◽  
Polymer Composite ◽  
Contact Area ◽  
Essential Feature ◽  
The Other ◽  
Carbon Fabric ◽  
Simultaneous Application ◽  
Composite Forming

This experimental study is focused on identification of tribological mechanisms acting during forming of polymer composites. The range of relevant processes includes fibre placement, tape lay-up, moulding, draping, and RTM. Two types of tribological experiments, relying both on simultaneous application of compression and shear loadings, are carried out. Firstly, model macromechanical tests are undertaken on plastic rods of millimetric diameter immersed in a viscous liquid, representing composite fibres and matrix, respectively. By careful simulation of forming conditions, this experiment helps to identify the friction phenomena occurring in real composites. On the other hand, the micromechanics of forming processes is studied through a microscopic experiment on real carbon fabric. This material is clamped between two glass plates and pulled in opposing directions in the plane of the fabric. It is hypothesized that the evolution of contact area due to shearing that can be measured in this experiment is an essential feature of the tribology of forming processes, a topic which hitherto has not been investigated.

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