scholarly journals NUMERICAL SIMULATION OF TRI-LAYERED MATERIALS UNDER CONTACT LOAD

2021 ◽  
Vol 13 (3) ◽  
pp. 164-170
Author(s):  
Sergiu Spinu ◽  
◽  
Keyword(s):  
Contact Problem ◽  
Frequency Domain ◽  
Frictional Coefficient ◽  
Analytical Techniques ◽  
Contact Problems ◽  
Layered Materials ◽  
Boundary Element Methods ◽  
Contact Load ◽  
Wear Protection ◽  
Influence Coefficients

Various biomedical components, such as dental crowns and hip prostheses, data processing devices, and other numerous mechanical components that transmit load through a mechanical contact, may benefit from a tri-layer design. The coating may be optimized for wear protection and corrosion prevention, whereas the intermediate layer provides increased adhesion between the outer layer and the substrate, and confines the crack propagation. The solution to the contact problem involving tri-layered materials can be pursued numerically with the finite element or the boundary element methods, but semi-analytical techniques benefitting from the efficiency of the fast Fourier transform (FFT) technique have also been successfully applied. At the heart of the FFT-assisted approach lie the frequency response functions (FRFs), which are analytical solutions for fundamental problems of elasticity such as the Boussinesq and Cerruti problems, but expressed in the frequency domain. Considering recent efforts and results in application of FFT to convolution calculations in contact problems, the displacement arising in a tri-layer configuration is computed in the frequency domain, and the contact problem is subsequently solved in the space domain using a state-of-the-art algorithm based on the conjugate gradient method. The method relies on the FRFs derived in the literature for tri-layered materials, and the efficiency and accuracy of computations in the frequency domain is assured by using the Discrete Convolution Fast Fourier Technique (DCFFT) with influence coefficients derived from the FRFs. The computer program reproduces well-known results for bi-layered materials. Numerical simulations are performed for various configurations in which the elastic properties of the layers, as well as the frictional coefficient, are varied. By using the newly advanced simulation technique, design recommendations may be advanced for the optimal configuration of tri-layered materials under contact load.

scholarly journals The Indentation Rolling Resistance in Belt Conveyors: A Model for the Viscoelastic Friction

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 58 ◽  
Author(s):  
Nicola Menga ◽  
Francesco Bottiglione ◽  
Giuseppe Carbone
Keyword(s):  
Contact Problem ◽  
Finite Thickness ◽  
Numerical Procedure ◽  
Contact Problems ◽  
Accurate Solution ◽  
Rolling Contact ◽  
Viscoelastic Layer ◽  
Force Coefficient ◽  
Belt Conveyors ◽  
Energy Dissipated

In this paper, we study the steady-state rolling contact of a linear viscoelastic layer of finite thickness and a rigid indenter made of a periodic array of equally spaced rigid cylinders. The viscoelastic contact model is derived by means of Green’s function approach, which allows solving the contact problem with the sliding velocity as a control parameter. The contact problem is solved by means of an accurate numerical procedure developed for general two-dimensional contact geometries. The effect of geometrical quantities (layer thickness, cylinders radii, and cylinders spacing), material properties (viscoelastic moduli, relaxation time) and operative conditions (load, velocity) are all investigated. Physical quantities typical of contact problems (contact areas, deformed profiles, etc.) are calculated and discussed. Special emphasis is dedicated to the viscoelastic friction force coefficient and to the energy dissipated per unit time. The discussion is focused on the role played by the deformation localized at the contact spots and the one in the bulk of the thin layer, due to layer bending. The model is proposed as an accurate solution for engineering applications such as belt conveyors, in which the energy dissipated on the rolling contact of idle rollers can, in some cases, be by far the most important contribution to their energy consumption.

3-D Elasto-Plastic Contact Finite Element Analysis for Bearings Design

1990 ◽  
Author(s):  
Wang Shigang ◽  
Yu Jun ◽  
Zhou Ji ◽  
Li Mingzhang
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Geometrical Nonlinearity ◽  
Contact Problems ◽  
Plastic State ◽  
Element Analysis ◽  
Surface Pressure Distribution ◽  
Tangential Stiffness ◽  
Stiffness Method ◽  
Error Method

Abstract In this paper, A 3-D elasto-plastic contact problem in bearings is studied by Finite Element Method (FEM). A computer program has been developed for this purpose. A trial-error method is employed to cope with the geometrical nonlinearity and a tangential stiffness method is employed to tackle the material nonlinearity appeared in elasto-plastic contact problems. A frictionless contact problem of roller bearings is analysed, the result reveals that in 3-D elasto-plastic state the trend of the contact surface pressure distribution is similar to Hertz problem’s but flater.

A comparative study of the methods for calculation of surface elastic deformation

2003 ◽  
Vol 217 (2) ◽  
pp. 145-154 ◽  
Author(s):  
W-Z Wang ◽  
H Wang ◽  
Y-C Liu ◽  
Y-Z Hu ◽  
D Zhu
Keyword(s):  
Surface Deformation ◽  
Contact Problems ◽  
Piecewise Constant Function ◽  
Bilinear Interpolation ◽  
Numerical Accuracy ◽  
Piecewise Constant ◽  
Computation Efficiency ◽  
Influence Coefficients ◽  
Grid Points

A fundamental issue of lubrication analysis is the calculation of surface deformation, which includes two major steps: determination of influence coefficients and multiplication and summation. There are various interpolation schemes, such as the bilinear interpolation, the piecewise constant function or Green's function, available for determining the influence coefficients, while the summation operation may be performed by using one of the following methods: direct summation (DS), multilevel multi-integration (MLMI) or the discrete convolution and fast Fourier transform (DC-FFT) method. To limit the periodical errors, the proper way to implement the DC-FFT method is described in detail. The computation efficiency and numerical accuracy are compared by applying the different methods to typical contact problems. The results show that the three methods can achieve comparable numerical accuracy, but the DC-FFT method shows much higher computation efficiency than the others, especially when a great number of grid points are involved. It is concluded that the DC-FFT method has great potential in applications to the numerical analysis of, for example, surface deformations and temperature rises.

scholarly journals SOLUTION OF ADHESIVE CONTACT PROBLEM ON THE BASIS OF THE KNOWN SOLUTION FOR NON-ADHESIVE ONE

2018 ◽  
Vol 16 (1) ◽  
pp. 93 ◽  
Author(s):  
Valentin L. Popov
Keyword(s):  
Contact Problem ◽  
Material Properties ◽  
Present Method ◽  
Additional Assumption ◽  
Short Communication ◽  
Contact Problems ◽  
Adhesive Contact ◽  
Contact Shape

The well-known procedure of reducing an adhesive contact problem to the corresponding non-adhesive one is generalized in this short communication to contacts with an arbitrary contact shape and arbitrary material properties (e.g. non homogeneous or gradient media). The only additional assumption is that the sequence of contact configurations in an adhesive contact should be exactly the same as that of contact configurations in a non-adhesive one. This assumption restricts the applicability of the present method. Nonetheless, the method can be applied to many classes of contact problems exactly and also be used for approximate analyses.

Some Criteria for Coating Effectiveness in Heavily Loaded Line Elastohydrodynamically Lubricated Contacts—Part II: Lubricated Contacts

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Ilya I. Kudish ◽  
Sergey S. Volkov ◽  
Andrey S. Vasiliev ◽  
Sergey M. Aizikovich
Keyword(s):  
Analytical Solution ◽  
Contact Problem ◽  
Half Space ◽  
Contact Problems ◽  
Functionally Graded ◽  
Elastic Solids ◽  
Elastic Materials ◽  
Lubricated Contacts ◽  
Dry Contact ◽  
Appl Math

Contacts of indentors with functionally graded elastic solids may produce pressures significantly different from the results obtained for homogeneous elastic materials (Hertzian results). It is even more so for heavily loaded line elastohydrodynamically lubricated (EHL) contacts. The goal of the paper is to indicate two distinct ways the functionally graded elastic materials may alter the classic results for the heavily loaded line EHL contacts. Namely, besides pressure, the other two main characteristics which are influenced by the nonuniformity of the elastic properties of the contact materials are lubrication film thickness and frictional stress/friction force produced by lubricant flow. The approach used for analyzing the influence of functionally graded elastic materials on parameters of heavily loaded line EHL contacts is based on the asymptotic methods developed earlier by the authors such as Kudish (2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman & Hall/CRC Press, Boca Raton, FL), Kudish and Covitch (2010, Modeling and Analytical Methods in Tribology, Chapman & Hall/CRC Press, Boca Raton, FL), Aizikovich et al. (2002, “Analytical Solution of the Spherical Indentation Problem for a Half-Space With Gradients With the Depth Elastic Properties,” Int. J. Solids Struct., 39(10), pp. 2745–2772), Aizikovich et al. (2009, “Bilateral Asymptotic Solution of One Class of Dual Integral Equations of the Static Contact Problems for the Foundations Inhomogeneous in Depth,” Operator Theory: Advances and Applications, Birkhauser Verlag, Basel, p. 317), Aizikovich and Vasiliev (2013, “A Bilateral Asymptotic Method of Solving the Integral Equation of the Contact Problem for the Torsion of an Elastic Halfspace Inhomogeneous in Depth,” J. Appl. Math. Mech., 77(1), pp. 91–97), Volkov et al. (2013, “Analytical Solution of Axisymmetric Contact Problem About Indentation of a Circular Indenter Into a Soft Functionally Graded Elastic Layer,” Acta Mech. Sin., 29(2), pp. 196–201), Vasiliev et al. (2014, “Axisymmetric Contact Problems of the Theory of Elasticity for Inhomogeneous Layers,” Z. Angew. Math. Mech., 94(9), pp. 705–712), Aizikovich et al. (2008, “The Deformation of a Half-Space With a Gradient Elastic Coating Under Arbitrary Axisymmetric Loading,” J. Appl. Math. Mech., 72(4), pp. 461–467), and Aizikovich et al. (2010, “Inverse Analysis for Evaluation of the Shear Modulus of Inhomogeneous Media in Torsion Experiments,” Int. J. Eng. Sci., 48(10), pp. 936–942). More specifically, it is based on the analysis of contact problems for dry contacts of functionally graded elastic solids and the lubrication mechanisms in the inlet and exit zones as well as in the central region of heavily loaded lubricated contacts. The way the solution of the EHL problem for coated/functionally graded materials is obtained provides a very clear structure of the solution. The solution of the EHL problem in the Hertzian region is very close to the solution of the dry contact problem while in the inlet and exit zones the solutions of the EHL problem with the right asymptotes coming from the solution of the dry contact problem can be related to the solutions of the classic EHL problem for homogeneous materials.

Optimization of Contact Problem by Genetic Algorithm Method

2011 ◽  
Vol 105-107 ◽  
pp. 386-391 ◽  
Author(s):  
Jan Szweda ◽  
Zdenek Poruba
Keyword(s):  
Genetic Algorithm ◽  
Contact Problem ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Optimization Technique ◽  
Contact Problems ◽  
Global Optimum ◽  
Genetic Algorithm Method ◽  
Characteristic Features ◽  
Contact Shape

In this paper is discussed the way of suitable numerical solution of contact shape optimization problem. The first part of the paper is focused on method of global optimization field among which the genetic algorithm is chosen for computer processing and for application on contact problem optimization. The brief description of this method is done with emphasis of its characteristic features. The experiment performed on plane structural problem validates the ability of genetic algorithm in search the area of the global optimum. On the base of the research described in this work, it is possible to recommend optimization technique of genetic algorithm to use for shape optimization of engineering contact problems in which it is possible for any shape to achieve successful convergence of contact task solution.

Solution of contact problems for Gao beam and elastic foundation

2017 ◽  
Vol 23 (3) ◽  
pp. 473-488 ◽  
Author(s):  
Jitka Machalová ◽  
Horymír Netuka
Keyword(s):  
Contact Problem ◽  
Elastic Foundation ◽  
Variational Equation ◽  
Main Idea ◽  
Axial Loading ◽  
Elastic Beam ◽  
Beam Theory ◽  
Contact Problems ◽  
Problem Formulations ◽  
Nonlinear Elastic

This paper presents mathematical formulations and a solution for contact problems that concern the nonlinear beam published by Gao (Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech Res Commun 1996; 23: 11–17) and an elastic foundation. The beam is subjected to a vertical and also axial loading. The elastic deformable foundation is considered at a distance under the beam. The contact is modeled as static, frictionless and using the normal compliance contact condition. In comparison with the usual contact problem formulations, which are based on variational inequalities, we are able to derive for our problem a nonlinear variational equation. Solution of this problem is realized by means of the so-called control variational method. The main idea of this method is to transform the given contact problem to an optimal control problem, which can provide the requested solution. Finally, some results including numerical examples are offered to illustrate the usefulness of the presented solution method.

scholarly journals A fast multipole accelerated BEM for 3-D elastic wave computation

2008 ◽  
pp. 701-712
Author(s):  
Stéphanie Chaillat ◽  
Marc Bonnet ◽  
Jean- François Semblat
Keyword(s):  
Elastic Wave ◽  
Frequency Domain ◽  
Boundary Element ◽  
Present Article ◽  
Maxwell Equations ◽  
Boundary Element Methods ◽  
Matrix Equations ◽  
Fast Multipole ◽  
Numerical Examples ◽  
Gmres Iteration

The solution of the elastodynamic equations using boundary element methods (BEMs) gives rise to fully-populated matrix equations. Earlier investigations on the Helmholtz and Maxwell equations have established that the Fast Multipole (FM) method reduces the complexity of a BEM solution to N log2 N per GMRES iteration. The present article addresses the extension of the FM-BEM strategy to 3D elastodynamics in the frequency domain. Efficiency and accuracy are demonstrated on numerical examples involving up to N = O(106) boundary nodal unknowns.

scholarly journals A simple weak form for contact problems with Coulomb friction

2011 ◽  
Vol 33 (4) ◽  
pp. 259-282
Author(s):  
Nguyen Huynh Tan Tai ◽  
Le Van Anh
Keyword(s):  
Contact Problem ◽  
Coulomb Friction ◽  
Virtual Work ◽  
Contact Problems ◽  
Initial Boundary ◽  
Weak Form ◽  
The Finite Element Method ◽  
Virtual Work Principle ◽  
Statics And Dynamics ◽  
Initial Boundary Value

This paper proposes a weak form for the contact problem with Coulomb friction, written as extension of the standard virtual work principle and involving both the displacements and the multipliers defined on the reference contact surface. The mixed relationship is shown to be equivalent to the strong form of the initial/boundary value contact problem, and it can be discretized by means of the finite element method in a simple way. Typical numerical examples are given to assess the efficiency of the formulation in statics and dynamics.

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