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 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 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.

Penetration of a Half Space by a Rectangular Cylinder

1979 ◽  
Vol 46 (3) ◽  
pp. 587-591 ◽  
Author(s):  
A. Cemal Eringen ◽  
F. Balta
Keyword(s):  
Half Space ◽  
Stress Singularity ◽  
Elastic Solid ◽  
Interatomic Interaction ◽  
Elastic Half Space ◽  
Rigid Block ◽  
Field Equations ◽  
Displacement Fields ◽  
Rectangular Cylinder ◽  
Stress And Displacement Fields

The stress and displacement fields are determined in an elastic half space loaded by a rectangular frictionless, rigid block normally at its surface. The semi-infinite solid is considered to be an elastic solid with nonlocal interatomic interaction. The field equations of the nonlocal elasticity and boundary conditions are employed to treat this contact problem. Interestingly the classical stress singularity at the edges of the block are not present in the nonlocal solutions. Consequently the critical applied load for the initiation of penetration of the rigid cylinder into the semi-infinite solid can be determined without recourse to any criterion foreign to the theory. The stress field obtained is valid even for penetrators of submicroscopic width.

Variational Approach in Elastic-Indentation Problems

2005 ◽  
Author(s):  
Roman V. Riznychuk
Keyword(s):  
Variational Method ◽  
Half Space ◽  
Contact Stress ◽  
Variational Approach ◽  
Stress Singularity ◽  
Elastic Half Space ◽  
Contact Spot ◽  
Rigid Punch ◽  
Elliptical Contact ◽  
Indentation Problem

The indentation problem of rigid punch with curvilinear base on elastic half-space is solved by variational method. The method is based on Betti theorem and on condition of absence of stress singularity at the edge of contact spot. Variation condition of absence of stress singularity at the edge of contact spot gives the equations connecting the displacement and the size and the shape of the contact spot and gives the expression for contact stress under curvilinear base of punch. The case of elliptical contact spot is considered.

The Load Transfer Problem in Shafts Coupled Through a Sleeve

1973 ◽  
Vol 40 (4) ◽  
pp. 997-1003 ◽  
Author(s):  
F. Erdogan ◽  
G. D. Gupta
Keyword(s):  
Stress Intensity ◽  
Load Transfer ◽  
Transfer Problem ◽  
Singular Integral Equations ◽  
Intensity Factors ◽  
Numerical Examples ◽  
Elastic Disk ◽  
Shrink Fit ◽  
Transfer Problems ◽  
Perfect Adhesion

The following load transfer problems are considered in this paper: torque transfer between an elastic shaft and a finite elastic disk or sleeve of different materials, torque transfer between two identical shafts coupled through a finite sleeve, and torque transfer between two dissimilar shafts coupled through a finite sleeve. In all cases it is assumed that the contact between the sleeve and the shafts is one of perfect adhesion accomplished through bonding or shrink-fit. The problems are shown to reduce to singular integral equations with generalized Cauchy kernels. Some numerical examples are worked out and the stress-intensity factors and distribution of contact stresses are given.

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