Load Transfer From a Finite Cylindrical Fiber Into an Elastic Half-Space

1994 ◽  
Vol 61 (4) ◽  
pp. 971-975 ◽  
Author(s):  
Ven-Gen Lee ◽  
Toshio Mura
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Load Transfer ◽  
Transfer Problem ◽  
Numerical Procedure ◽  
Elastic Half Space ◽  
Equivalent Condition ◽  
Algebraic Equations ◽  
Equivalent Inclusion Method ◽  
Cylindrical Fiber

Based on the equivalent inclusion method, the load transfer problem of a finite cylindrical fiber embedded in an elastic half-space of different elastic properties is presented. The equivalent condition of inhomogeneity and inclusion problems simulates the fiber to an inclusion with chosen eigenstrains, and the problem is formulated to a set of integral equations with the unknown strength of eigenstrains. A numerical procedure is developed using a discretizing scheme by which the set of integral equations is reduced to a system of algebraic equations.

Load Diffusion and Absorption Problems From a Finite Fiber to Elastic Infinite Matrix

1994 ◽  
Vol 61 (3) ◽  
pp. 567-574 ◽  
Author(s):  
Ven-Gen Lee ◽  
Toshio Mura
Keyword(s):  
Integral Equations ◽  
Load Transfer ◽  
Approximate Solutions ◽  
Infinite Matrix ◽  
Algebraic Equations ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Transfer Behavior ◽  
Ring Elements ◽  
Inhomogeneity Problem

The load transfer behavior of a finite fiber perfectly bonded to an infinite matrix of distinct elastic moduli is investigated in this paper. The fiber is subjected to the uniformly distributed loading applied at infinity or on one cross-section of the fiber. The stress disturbance due to the existing fiber is simulated by the equivalent inclusion method, which formulates the inhomogeneity problem to a system of integral equations. By dividing the fiber into finite numbers of ring elements with uniform distributed eigenstrains, the integral equations can be further reduced to a system of algebraic equations with coefficients expressed in terms of the integrals of Lipschitz-Hankel type. Numerical results are presented for resultant axial force for various fiber length and material properties. The limiting cases of the infinite and semi-infinite fibers are also compared with the exact and approximate solutions.

A Reconsideration of Elastostatic Load Transfer Problems Involving a Half Space

1984 ◽  
Vol 8 (4) ◽  
pp. 219-226 ◽  
Author(s):  
P. Karasudhi ◽  
R.K.N.D. Rajapakse ◽  
K.K. Liyanage
Keyword(s):  
Half Space ◽  
Load Transfer ◽  
Transfer Problem ◽  
Stress Singularity ◽  
Elastic Half Space ◽  
Main Concern ◽  
Elastic Bar ◽  
Interacting Systems ◽  
Real Phenomenon ◽  
Transfer Problems

This paper is a reconsideration of elastostatic load transfer problem of a long cylindrical elastic bar partially embedded in an elastic half space. Each problem is considered as consisting of two interacting systems, an extended half space and a one-dimensional fictitious bar. A compatibility condition is imposed near the interface of the interacting systems. In order to incorporate the real phenomenon of stress singularities at the ends of the bar, without carrying our a complicated derivation of the stress singularity factor, the basic unknown force at both ends of the fictitious bar is set to zero. However, the effects of the stress singularity are found to be not significant, especially for long bars and when the main concern is only on the force-displacement relationship at the top end of the bar.

Load Transfer Problem for an Embedded Shaft in Torsion

1970 ◽  
Vol 37 (4) ◽  
pp. 959-964 ◽  
Author(s):  
L. M. Keer ◽  
N. J. Freeman
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Load Transfer ◽  
Transfer Problem ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Infinite Cylinder ◽  
Axially Symmetric ◽  
Homogeneous Cylinder

This paper deals with the axially symmetric torsion of a semi-infinite cylinder embedded into an elastic half space, where the cylinder is allowed to protrude by a finite amount. The problem is formulated to include the case of the protruding portion of the cylinder when it is a different material and partially bonded to the embedded portion. With the use of integral transforms and Dini series, the problem is reduced to the determination of the solution of an integral equation. Stress singularities of a fractional order are noted and computed at the juncture, when all members are perfectly bonded. A numerical solution of the integral equation is obtained for the case of a homogeneous cylinder. The bond stress on the cylinder—half space interface and the torque-twist (and consequently, strain energy) for the entire system are computed for different values of the elastic constants.

On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

THREE-DIMENSIONAL SURFACE CRACK ANALYSIS OF ELASTIC HALF-SPACE UNDER ROLLING CONTACT LOAD

2009 ◽  
Vol 06 (02) ◽  
pp. 317-332 ◽  
Author(s):  
MENG-CHENG CHEN ◽  
HUI-QIN YU
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Rolling Contact ◽  
Contact Load ◽  
Hypersingular Integral ◽  
Space Body ◽  
Planar Crack

In this work a three-dimensional planar crack on the surface of elastic half-space was analyzed under rolling contact load. The stresses interior to an elastic half-space body under rolling contact load and those produced by an infinitesimal displacement jump loop for the elastic half-space body were used to reduce the planar crack problem to the solution of a system of two-dimensional hypersingular integral equations with unknown displacement jump. The ideas of finite element discretization were employed to construct numerical solution schemes for solving the integral equations. An appropriate treatment of the associated hypersingular integral in the numerical solution to the integral equations was proposed in Hadamard's finite-part integral sense. The numerical results showed that the present procedure yields solutions with high accuracies. The stress intensity factors near the crack front edge under rolling contact load were indicated in graphical form with varying the crack shape, the radius of rolling contact zone and the friction coefficients, respectively. In addition, the influence of the lubricant infiltrating the crack surfaces on the crack propagation was also discussed in the paper.

scholarly journals Two Contact Problems for Annular Rigid Stamp on an Elastic Half Space

2018 ◽  
Vol 17 (6) ◽  
pp. 458-464
Author(s):  
S. V. Bosakov
Keyword(s):  
Functional Equation ◽  
Half Space ◽  
Bessel Functions ◽  
Infinite System ◽  
Annular Plate ◽  
Contact Problems ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Algebraic Equations ◽  
Linear Algebraic Equations

The paper presents solutions of two contact problems for the annular plate die on an elastic half-space under the action of axisymmetrically applied force and moment. Such problems usually arise in the calculation of rigid foundations with the sole of the annular shape in chimneys, cooling towers, water towers and other high-rise buildings on the wind load and the load from its own weight. Both problems are formulated in the form of triple integral equations, which are reduced to one integral equation by the method of substitution. In the case of the axisymmetric problem, the kernel of the integral equation depends on the product of three Bessel functions. Using the formula to represent two Bessel functions in the form of a double row on the works of hypergeometric functions Bessel function, the problem reduces to a functional equation that connects the movement of the stamp with the unknown coefficients of the distribution of contact stresses. The resulting functional equation is reduced to an infinite system of linear algebraic equations, which is solved by truncation. Under the action of a moment on the annular plate  die, the distribution of contact stresses is searched as a series by the products of the Legendre attached functions with a weight corresponding to the features in the contact stresses at the die edges. Using the spectral G. Ya. Popov ratio for the ring plate, the problem is again reduced to an infinite system of linear algebraic equations, which is also solved by the truncation method. Two examples of calculations for an annular plate die on an elastic half-space on the action of axisymmetrically applied force and moment are given. A comparison of the results of calculations on the proposed approach with the results for the round stamp and for the annular  stamp with the solutions of other authors is made.

The In-Plane Loading of a Rigid Disk Inclusion Embedded in an Elastic Half-Space

1991 ◽  
Vol 58 (2) ◽  
pp. 362-369 ◽  
Author(s):  
A. P. S. Selvadurai ◽  
B. M. Singh ◽  
M. C. Au
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Space Region ◽  
Rigid Disk ◽  
Lateral Translation

The paper examines the problem of the in-plane loading of a rigid disk inclusion which is embedded in bonded contact with an isotropic elastic half-space region. The governing coupled integral equations, derived via a Hankel transform technique, are evaluated numerically to generate results for the in-plane stiffness of the rigid disk inclusion and the rotation which accompanies the lateral translation.

The Singularity at the Apex of a Bonded Wedge-Shaped Stamp

1979 ◽  
Vol 46 (3) ◽  
pp. 577-580 ◽  
Author(s):  
K. S. Parihar ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Singular Integral ◽  
Green's Functions ◽  
Green’S Functions ◽  
Singular Integral Equations ◽  
Elastic Half Space

The problem of determining the singularity at the apex of a rigid wedge bonded to an elastic half space is formulated by considerations of Green’s functions for the loaded half space. The eigenvalue problem is reduced to finding the solution of a coupled pair of singular integral equations. A numerical solution for small wedge angles is given.

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