Smooth Contact Between the Running Rayleigh Wave and a Rigid Strip

1995 ◽  
Vol 62 (2) ◽  
pp. 362-367 ◽  
Author(s):  
O. Y. Zharii ◽  
A. F. Ulitko
Keyword(s):  
Rayleigh Wave ◽  
Mixed Boundary ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mixed Boundary Value Problem ◽  
Trigonometric Functions ◽  
Frictionless Contact ◽  
Dual Series Equations ◽  
Analytic Expressions ◽  
Smooth Contact

A problem of frictionless contact between the running Rayleigh wave and a rigid strip is investigated. The corresponding mixed boundary value problem of elastodynamics is reduced to a system of dual series equations involving trigonometric functions. On the base of the closed-form solution obtained, explicit analytic expressions for distributions of normal displacements and stresses and of tangential velocities on the surface have been derived.

Adhesive Contact Between the Surface Wave and a Rigid Strip

1995 ◽  
Vol 62 (2) ◽  
pp. 368-372 ◽  
Author(s):  
O. Y. Zharii
Keyword(s):  
Integral Equation ◽  
Surface Wave ◽  
Stress Distribution ◽  
Contact Area ◽  
Mixed Boundary ◽  
Closed Form Solution ◽  
Adhesive Contact ◽  
Form Solution ◽  
Mixed Boundary Value Problem ◽  
Analysis Of Variation

A problem of adhesive contact between the running surface wave and a rigid strip is investigated. The mixed boundary-value problem of elastodynamics is reduced to a singular integral equation for a complex combination of stresses and an exact closed-form solution of it has been derived. Analysis of variation of contact area dimensions, stress distribution and rotor velocity on the frequency of excitation displayed significant differences between the results corresponding to conditions of adhesion and slipping in contact area. The origin of these differences is discussed.

Frictionless Contact of Layered Half-Planes, Part I: Analysis

1993 ◽  
Vol 60 (3) ◽  
pp. 633-639 ◽  
Author(s):  
M.-J. Pindera ◽  
M. S. Lane
Keyword(s):  
Integral Equation ◽  
Contact Stress ◽  
Stiffness Matrix ◽  
Fourier Transforms ◽  
Mixed Boundary ◽  
Contact Region ◽  
Closed Form Solution ◽  
Cauchy Type ◽  
Frictionless Contact ◽  
Local Stiffness

A method is presented for the solution of frictionless contact problems on multilayered half-planes consisting of an arbitrary number of isotropic, orthotropic, or monoclinic layers arranged in any sequence. A displacement formulation is employed and the resulting Navier equations that govern the distribution of displacements in the individual layers are solved using Fourier transforms. A local stiffness matrix in the transform domain is formulated for each layer which is then assembled into a global stiffness matrix for the entire multilayered half-plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary condition on the top surface of the medium subjected to the force of the indenter results in an integral equation for the unknown pressure in the contact region. The integral possesses a divergent kernel which is decomposed into Cauchy type and regular parts using the asymptotic properties of the local stiffness matrix and the ensuing relation between Fourier and finite Hilbert transform of the contact pressure. For homogeneous half-planes, the kernel consists only of the Cauchy-type singularity which results in a closed-form solution for the contact stress. For multilayered half-planes, the solution of the resulting singular integral equation is obtained using a collocation technique based on the properties of orthogonal polynomials. Part I of this paper outlines the analytical development of the technique. In Part II a number of numerical examples is presented addressing the effect of off-axis plies on contact stress distribution and load versus contact length in layered composite half-planes.

Some dual series equations with an application in the theory of elasticity

1982 ◽  
Vol 92 (3-4) ◽  
pp. 241-251 ◽  
Author(s):  
J. Tweed
Keyword(s):  
Closed Form ◽  
Trigonometric Series ◽  
Singular Integral ◽  
Crack Problem ◽  
Closed Form Solution ◽  
Singular Integral Equations ◽  
Theory Of Elasticity ◽  
Form Solution ◽  
Dual Series Equations ◽  
Carleman Type

SynopsisIn this paper the author investigates a system of simultaneous dual trigonometric series equations. A closed form solution is obtained by reducing the dual series to singular integral equations of Carleman type. The use of these equations is then illustrated by their application to a crack problem in the theory of elasticity.

scholarly journals New Poisson's Type Integral Formula for Thermoelastic Half-Space

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Victor Seremet ◽  
Guy Bonnet ◽  
Tatiana Speianu
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Mixed Boundary ◽  
Integral Formula ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Volume Dilatation ◽  
Type Integral

A new Green's function and a new Poisson's type integral formula for a boundary value problem (BVP) in thermoelasticity for a half-space with mixed boundary conditions are derived. The thermoelastic displacements are generated by a heat source, applied in the inner points of the half-space and by temperature, and prescribed on its boundary. All results are obtained in closed forms that are formulated in a special theorem. A closed form solution for a particular BVP of thermoelasticity for a half-space also is included. The main difficulties to obtain these results are in deriving of functions of influence of a unit concentrated force onto elastic volume dilatation and, also, in calculating of a volume integral of the product of function and Green's function in heat conduction. Using the proposed approach, it is possible to extend the obtained results not only for any canonical Cartesian domain, but also for any orthogonal one.

scholarly journals A PAIR OF PERFECTLY CONDUCTING DISKS IN AN EXTERNAL FIELD

2015 ◽  
Vol 20 (2) ◽  
pp. 273-288 ◽  
Author(s):  
Natalia Rylko
Keyword(s):  
Closed Form Solution ◽  
Elliptic Functions ◽  
Convergent Series ◽  
Fiber Composites ◽  
Form Solution ◽  
Local Fields ◽  
Trigonometric Functions ◽  
Method Of Images ◽  
Asymptotic Investigation ◽  
Asymptotic Formulae

A pair of non-overlapping perfectly conducting equal disks embedded in a two-dimensional background was investigated by the classic method of images, by Poincar´e series, by use of the bipolar coordinates and by the elliptic functions in the previous works. In particular, successive application of the inversions with respect to circles were applied to obtain the field in the form of a series. For closely placed disks, the previous methods yield slowly convergent series. In this paper, we study the local fields around closely placed disks by the elliptic functions. The problem of small gap is completely investigated since the obtained closed form solution admits a precise asymptotic investigation in terms of the trigonometric functions when the gap between the disks tends to zero. The exact and asymptotic formulae are extended to the case when a prescribed singularity is located in the gap. This extends applications of structural approximations to estimations of the local fields in densely packed fiber composites in various external fields.

Closed-Form Solution of the Frictional Sliding Contact Problem for an Orthotropic Elastic Half-Plane Indented by a Wedge-Shaped Punch

2014 ◽  
Vol 618 ◽  
pp. 203-225 ◽  
Author(s):  
Aysegul Kucuksucu ◽  
Mehmet A. Guler ◽  
Ahmet Avci
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Mixed Boundary ◽  
Closed Form Solution ◽  
Contact Problems ◽  
Form Solution ◽  
Orthotropic Materials ◽  
Principal Axes ◽  
The Coefficient Of Friction ◽  
Processing Techniques

In this paper, the frictional contact problem of a homogeneous orthotropic material in contact with a wedge-shaped punch is considered. Materials can behave anisotropically depending on the nature of the processing techniques; hence it is necessary to develop an efficient method to solve the contact problems for orthotropic materials. The aim of this work is to develop a solution method for the contact mechanics problems arising from a rigid wedge-shaped punch sliding over a homogeneous orthotropic half-plane. In the formulation of the plane contact problem, it is assumed that the principal axes of orthotropy are parallel and perpendicular to the contact. Four independent engineering constants , , , are replaced by a stiffness parameter, , a stiffness ratio, a shear parameter, , and an effective Poisson’s ratio, . The corresponding mixed boundary problem is reduced to a singular integral equation using Fourier transform and solved analytically. In the parametric analysis, the effects of the material orthotropy parameters and the coefficient of friction on the contact stress distributions are investigated.

Two dimensional mixed boundary-value problems in a wedge-shaped region

1968 ◽  
Vol 64 (2) ◽  
pp. 503-505 ◽  
Author(s):  
W. E. Williams
Keyword(s):  
Integral Equation ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Dual Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Mellin Transforms

In a recent paper Srivastav (2) considered the solution of certain two-dimensional mixed boundary-value problems in a wedge-shaped region. The problems were formulated as dual integral equations involving Mellin transforms and were reduced to the solution of a Fredholm integral equation of the second kind. In this paper it will be shown that a closed form solution to the problems treated in (2) may be obtained by elementary means.

scholarly journals Closed form solution to some mixed boundary value problems for a charged sphere

1987 ◽  
Vol 28 (3) ◽  
pp. 296-309 ◽  
Author(s):  
V. I. Fabrikant
Keyword(s):  
Closed Form ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Spherical Segment ◽  
Charged Sphere ◽  
Elementary Functions ◽  
Arbitrary Potential ◽  
Arbitrary Charge

AbstractA new method is described which allows an exact solution in a closed form to the following non-axisymmetric mixed boundary-value problem for a charged sphere: arbitrary potential values are given at the surface of a spherical segment while an arbitrary charge distribution is prescribed on the rest of the sphere. The method is founded on a new integral representation of the kernel of the governing integral equation. Several examples are considered. All the results are expressed in elementary functions. Some further applications of the method are discussed. No similar result seems to have been published previously.

scholarly journals An Axisymmetric Contact Problem of an Elastic Layer on a Rigid Circular Base

2020 ◽  
Vol 22 (1) ◽  
pp. 221-238
Author(s):  
B. Kebli ◽  
S. Berkane ◽  
F. Guerrache
Keyword(s):  
Elastic Layer ◽  
Mixed Boundary ◽  
Stress Singularity ◽  
Closed Form Solution ◽  
Integral Transforms ◽  
Form Solution ◽  
Rigid Base ◽  
Dual Integral Equations ◽  
Numerical Application ◽  
Stress Functions

AbstractAn analytical solution is presented to a doubly mixed boundary value problem of an elastic layer partially resting on a rigid smooth base. A circular rigid punch is applied to the upper surface of the medium where the contact is supposed to be smooth. The case of the layer with a cylindrical hole was considered by Toshiaki and all [5]. The studied problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer formula we get an infinite algebraic system of simultaneous equations for calculating the unknown function of the problem. The truncation method is used for getting the system coefficients. A closed form solution is given for the displacements, stresses and the stress singularity factors. The stresses and displacements are then obtained as Bessel function series. For the numerical application we give some conclusions on the effects of the radius of the punch with the rigid base and the layer thickness on the displacements, stresses, the load and the stress singularity factors are discussed.

Optimum Actuator-Disk Performance in Hover and Axial Flight by a Compact Momentum Theory with Swirl

2015 ◽  
Vol 60 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Ramin Modarres ◽  
David A. Peters
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Momentum Equation ◽  
Form Solution ◽  
Compact Form ◽  
Actuator Disk ◽  
Momentum Theory ◽  
Analytic Expressions ◽  
Induced Flow ◽  
Limiting Efficiency

A new compact form of momentum theory is introduced for actuator disks including swirl. The new form unifies both the axial and angular momentum balances into a single momentum equation, applicable over the entire range of thrust and power coefficients. While completely consistent with earlier momentum theories, such as that of Glauert with swirl, the compact form allows analytic expressions for the parameters of a Betz actuator disk and reveals additional insight into the limiting efficiency of rotors, propellers, and wind turbines. The compact form also allows a completely closed form for the truly optimum Glauert rotor. We will also present results from the Betz hypothesis as practically optimum. Closed-form results presented here include the practically optimum values of induced flow, inflow angle, thrust, induced power, and efficiency. Closed-form expressions are also given for practically optimum twist, chord distribution, and solidity in the presence of profile drag (along with the resulting overall efficiencies). This report also gives a closed-form solution for the truly optimum rotor in hover, based on the Glauert optimality criterion.

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