Contact Stresses Between an Elastic Cylinder and a Layered Elastic Solid

1974 ◽  
Vol 96 (2) ◽  
pp. 250-257 ◽  
Author(s):  
P. K. Gupta ◽  
J. A. Walowit
Keyword(s):  
Integral Equation ◽  
Layer Thickness ◽  
Contact Pressure ◽  
Contact Zone ◽  
Numerical Solutions ◽  
Elastic Solid ◽  
Elastic Cylinder ◽  
Elastic Solids ◽  
Actual Contact ◽  
Wide Range

The generalized plane strain problem of the contact of layered elastic solids is reduced to an integral equation using Green’s function approach. Approximate numerical solutions are obtained by replacing the integral equation by a matrix inversion when the trapezoidal rule is used to represent the integral. Results for determining the actual contact pressure at the center of the contact zone and size of contact zone for a wide range of layer thicknesses are presented for two most practical cases, (i) when the indenter is rigid, and (ii) when the indenter is elastic having a modulus of elasticity equal to that of the substrate of the indented body. When the layer is softer than the substrate it is found that the actual contact pressure distribution is very closely determined by a weighted sum of elliptic and parabolic functions. For a substrate softer than the layer the pressures substantially deviate from an elliptical or parabolic behavior, for the cases when the layer thickness is finite. The analysis checks with the Hertzian solution in the extreme cases when the layer thickness either tends to zero or approaches infinity.

Problems Involving a Receding Contact Between a Layer and a Half Space

1972 ◽  
Vol 39 (4) ◽  
pp. 1115-1120 ◽  
Author(s):  
L. M. Keer ◽  
J. Dundurs ◽  
K. C. Tsai
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Contact Pressure ◽  
Auxiliary Function ◽  
Unexpected Result ◽  
Wide Range ◽  
Receding Contact ◽  
Axisymmetric Problems ◽  
Uniformly Distributed Loads ◽  
Two Bodies

The work reconsiders the smooth receding contact between an elastic layer and a half space when the two bodies are pressed together. The analysis leads to a Fredholm integral equation of the second kind for an auxiliary function that is directly related to the contact pressure. An unexpected result is that the integral equation is homogeneous, and that finding the extent of contact can be viewed as an eigenvalue problem. The integral equation can be solved numerically to any required degree of accuracy, and the extent of contact and the contact pressure are computed for concentrated and uniformly distributed loads in both plane and axisymmetric problems. The present analysis confirms the results of Weitsman rather than Pu and Hussain over a wide range of mismatch in the elastic constants.

A Fast-Solving Semi-Analytical Solution Method for Contact Problems Involving Multi-Layered Inhomogeneously Elastic Solids

2012 ◽  
Author(s):  
Stewart Chidlow ◽  
Mircea Teodorescu
Keyword(s):  
Analytical Solution ◽  
Contact Pressure ◽  
Solution Method ◽  
Elastic Solid ◽  
Contact Problems ◽  
Accurate Estimation ◽  
Rigid Punch ◽  
Iterative Solver ◽  
Elastic Solids ◽  
Selection Of

This work is concerned with the derivation of an iterative solver which allows the accurate estimation of both the contact half-width and contact pressure when an inhomogeneouly elastic solid comprising a homogeneous coating and substrate joined by a graded layer is indented by a rigid punch. A selection of numerical results are then presented illustrating the accuracy of this model.

Line Inclusions in Anisotropic Elastic Solids

1989 ◽  
Vol 56 (3) ◽  
pp. 556-563 ◽  
Author(s):  
Qianqian Li ◽  
T. C. T. Ting
Keyword(s):  
Integral Equation ◽  
Numerical Solutions ◽  
Form Solution ◽  
Fredholm Integral Equations ◽  
Homogeneous Field ◽  
Elastic Solids ◽  
The Matrix ◽  
The Difference ◽  
Anisotropic Elastic ◽  
Line Inclusion

A line inclusion located at x2 = 0, |x1| < 1 in the anisotropic elastic medium of infinite extent under uniform loading at infinity is considered. Stroh’s formalism is used to find the displacement and stress fields. The inclusion can be rigid or elastic. Conditions on the loading under which the line inclusion does not disturb the homogeneous field are derived. For the rigid inclusion, a real form solution is obtained for the stress and displacement along x2 = 0. When the inclusion is elastic (and anisotropic), a pair of singular Fredholm integral equations of the second kind is derived for the difference in the stress on both surfaces of the inclusion. The pair can be decoupled and asymptotic solutions of the integral equation are obtained when λ, which represents the relative rigidity of the matrix to the inclusion, is small. For the general cases, the integral equation is solved by a numerical discretization. Excellent agreements between the asymptotic and numerical solutions are observed for small λ.

scholarly journals Numerical Simulation of a Slipper Model with Multi-Lands and Grooves for Hydraulic Piston Pumps and Motors in Mixed Lubrication

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 55
Author(s):  
Toshiharu Kazama
Keyword(s):  
Numerical Simulation ◽  
Contact Pressure ◽  
Power Loss ◽  
Numerical Solutions ◽  
Friction Torque ◽  
Mixed Lubrication ◽  
Operating Conditions ◽  
Axial Piston Pumps ◽  
Wide Range ◽  
Axial Piston

A theoretical model of a slipper with multi-lands and multi-grooves for swashplate type axial piston pumps and motors was established, including surface interactions. Further, a numerical simulation was conducted under an unsteady state and mixed lubrication conditions. Four model configurations were considered: A slipper with a single main land; a slipper with inner and main lands and a groove; a slipper with outer and main lands and a groove; and a slipper with inner, main, and outer lands with two grooves. Numerical solutions were obtained across a wide range of operating conditions in terms of center clearance, pad attitude, contact pressure, flow rate, friction torque, power loss, and stiffness. The motion and characteristics were differentiated into two groups: Slippers with a single-land and an annex inner-land; and slippers with an annex outer-land and a triple-land. The single-land and annex inner-land slippers exhibited smaller pad swing, whereas the triple-land and annex outer-land slippers reduced contact pressure and power loss.

СONTACT INTERACTION OF A SLOTTED CYLINDRICAL SHELL WITH A DEFORMABLE FILLER ALLOWING FOR DRY INHOMOGENEOUS FRICTION

2018 ◽  
pp. 128-136
Author(s):  
О. О. Бедзір ◽  
В. М. Шопа
Keyword(s):  
Integral Equation ◽  
Cylindrical Shell ◽  
Contact Pressure ◽  
Mixed Problem ◽  
Numerical Solutions ◽  
One Dimensional ◽  
Frictional Interaction

The statement of the mixed problem on frictional interaction in the system which consists of cylindrical slit shells, divided by a deformable filler, is realized. Using one-dimensional shell and filler models, the integral equation for finding the contact is constructed. On the basis of numerical solutions the effect of mechanical, geometric and tribologic parameters of contacting pairs on nature of distribution of contact pressure, rigidity and strength of the system is investigated.

On Some Unbonded Contact Problems in Plane Elasticity Theory

1976 ◽  
Vol 43 (2) ◽  
pp. 263-267 ◽  
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Integral Equation ◽  
Elasticity Theory ◽  
Contact Pressure ◽  
Chebyshev Polynomials ◽  
Contact Region ◽  
Contact Problems ◽  
Elastic Cylinder ◽  
Plane Elasticity ◽  
Elastic Strip ◽  
Plane Elasticity Theory

Paper considers plane, frictionless, unbonded contact problems. It is shown that the integral equation relating the unknown contact pressure to the specified displacement in the contact region may be solved approximately by using an expansion in terms of Chebyshev polynomials. Three examples are chosen, a beam resting on a half plane, a rigid cylinder pressed into an elastic strip, and an elastic cylinder pressed between rigid planes. Graphs of results are presented.

scholarly journals UV Nanoimprint Lithography: Geometrical Impact on Filling Properties of Nanoscale Patterns

Nanomaterials ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 822
Author(s):  
Christine Thanner ◽  
Martin Eibelhuber
Keyword(s):  
Layer Thickness ◽  
Process Parameters ◽  
Nanoimprint Lithography ◽  
Failure Modes ◽  
Production Method ◽  
Efficient Production ◽  
Comprehensive Overview ◽  
Replication Method ◽  
Wide Range ◽  
Pattern Size

Ultraviolet (UV) Nanoimprint Lithography (NIL) is a replication method that is well known for its capability to address a wide range of pattern sizes and shapes. It has proven to be an efficient production method for patterning resist layers with features ranging from a few hundred micrometers and down to the nanometer range. Best results can be achieved if the fundamental behavior of the imprint resist and the pattern filling are considered by the equipment and process parameters. In particular, the material properties and pattern size and shape play a crucial role. For capillary force-driven filling behavior it is important to understand the influencing parameters and respective failure modes in order to optimize the processes for reliable full wafer manufacturing. In this work, the nanoimprint results obtained for different pattern geometries are compared with respect to pattern quality and residual layer thickness: The comprehensive overview of the relevant process parameters is helpful for setting up NIL processes for different nanostructures with minimum layer thickness.

scholarly journals The Band-Gap Studies of Short-Period CdO/MgO Superlattices

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Ewa Przeździecka ◽  
P. Strąk ◽  
A. Wierzbicka ◽  
A. Adhikari ◽  
A. Lysak ◽  
...  
Keyword(s):  
Band Gap ◽  
Layer Thickness ◽  
Energy Gap ◽  
Band Gaps ◽  
Short Period ◽  
Wide Range ◽  
Salt Structure ◽  
Short Period Superlattices ◽  
Direct Band ◽  
Sublayer Thickness

AbstractTrends in the behavior of band gaps in short-period superlattices (SLs) composed of CdO and MgO layers were analyzed experimentally and theoretically for several thicknesses of CdO sublayers. The optical properties of the SLs were investigated by means of transmittance measurements at room temperature in the wavelength range 200–700 nm. The direct band gap of {CdO/MgO} SLs were tuned from 2.6 to 6 eV by varying the thickness of CdO from 1 to 12 monolayers while maintaining the same MgO layer thickness of 4 monolayers. Obtained values of direct and indirect band gaps are higher than those theoretically calculated by an ab initio method, but follow the same trend. X-ray measurements confirmed the presence of a rock salt structure in the SLs. Two oriented structures (111 and 100) grown on c- and r-oriented sapphire substrates were obtained. The measured lattice parameters increase with CdO layer thickness, and the experimental data are in agreement with the calculated results. This new kind of SL structure may be suitable for use in visible, UV and deep UV optoelectronics, especially because the energy gap can be precisely controlled over a wide range by modulating the sublayer thickness in the superlattices.

On the Coherent Length of Fluid Nozzles in Grinding

2009 ◽  
Vol 404 ◽  
pp. 61-67 ◽  
Author(s):  
Michael N. Morgan ◽  
V. Baines-Jones
Keyword(s):  
Contact Zone ◽  
Fluid Velocity ◽  
Measured Data ◽  
Nozzle Geometry ◽  
Nozzle Orifice ◽  
Fluid Supply ◽  
Wide Range ◽  
Adequate Coverage ◽  
Nozzle Flows ◽  
Insight Into

The delivery of grinding fluid to the contact zone is generally achieved via a nozzle. The nozzle geometry influences the fluid velocity and flow pattern on exit from the nozzle orifice. It is important to the efficiency of the process and to the performance of the operation that the fluid is delivered in a manner that ensures the desired jet velocity has adequate coverage of the contact zone. Often, assumptions about adequate coverage are based on visual inspections of the jet coherence. This paper provides new insight into the internal nozzle flows and the coherent length of a wide range of nozzle designs. The work presents a new analytical model to predict coherent length which is shown to correlate well with measured data from experiment. Recommendations are given to guide a user to optimal design of nozzles to ensure adequate fluid supply to the contact zone.

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