Load Transfer Problem for an Embedded Shaft in Torsion

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.

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Stresses in a Thin Piezoelectric Element Bonded to a Half-Space

Applied Mechanics Reviews ◽

10.1115/1.3101836 ◽

1997 ◽

Vol 50 (11S) ◽

pp. S204-S209 ◽

Cited By ~ 13

Author(s):

Wolfgang E. Seemann

Keyword(s):

Integral Equation ◽

Shear Stress ◽

Half Space ◽

Piezoelectric Element ◽

Elastic Half Space ◽

Bonding Layer ◽

Rigid Substrate ◽

Stress Concentrations ◽

Piezoceramic Element

In this paper, a thin piezoceramic element is considered which is bonded to an elastic or a rigid half-space. Such a model may be an approximation of the interaction between piezoceramic elements and elastic structures like beams and plates. For an elastic half-space, the determination of the shear stress in the bonding layer leads to a singular integral equation. A half-space which is very stiff may be modeled as a rigid substrate. For this case, displacement functions are introduced. Hamilton’s principle for electromechanical systems allows the use of Lagrange multipliers to incorporate the condition of a stress free upper surface of the piezoceramic element. The stresses in the bonding layer and in the piezoceramic element are estimated by this method and compared with Finite Element results. Though the singularity near the ends of the piezoceramic element cannot be modeled by both methods, stress concentrations can clearly be seen for the shear stress as well as for the normal stress. As infinite stresses due to the singularity do not occur in reality, the results allow an estimation of the bonding stresses except in the near vicinity of the edges. The knowledge of these stresses is important to prevent failure due to delamination.

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A Reconsideration of Elastostatic Load Transfer Problems Involving a Half Space

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1984-0033 ◽

1984 ◽

Vol 8 (4) ◽

pp. 219-226 ◽

Cited By ~ 3

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.

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

Journal of Applied Mechanics ◽

10.1115/1.2901588 ◽

1994 ◽

Vol 61 (4) ◽

pp. 971-975 ◽

Cited By ~ 5

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.

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Mixed boundary-value problems for an elastic half-space

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100042390 ◽

1967 ◽

Vol 63 (4) ◽

pp. 1379-1386 ◽

Cited By ~ 27

Author(s):

L. M. Keer

Keyword(s):

Half Space ◽

Mixed Boundary ◽

Auxiliary Problem ◽

Integral Transforms ◽

Elastic Half Space ◽

Axially Symmetric ◽

Space Problem ◽

State Of Stress ◽

Unit Radius ◽

Toroidal Coordinates

In this paper the mixed problem for an isotropic, elastic half-space is considered. Boundary conditions are prescribed interior and exterior to a circular region of unit radius, and the state of stress is assumed to be axially symmetric. Several authors have treated this problem. Mossakovskii(1) considered a punch adhering to and indenting an elastic half-space. Has solution was obtained by introducing certain operators that transformed the half-space problem into a problem in plane potential theory. The method of linear relationship was used to solve this auxiliary problem and inverse operators returned the plane to the half-space. The general case of a circular, rigid punch adhering to a half-space was treated by Ufliand (2,3) and a solution was obtained through the use of toroidal coordinates and the Mehler-Fok integral transforms.

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Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space: Plane-Strain Case

Journal of Applied Mechanics ◽

10.1115/1.3176076 ◽

1989 ◽

Vol 56 (2) ◽

pp. 251-262 ◽

Cited By ~ 11

Author(s):

T. W. Shield ◽

D. B. Bogy

Keyword(s):

Plane Strain ◽

Half Space ◽

Contact Region ◽

Integral Transforms ◽

Elastic Half Space ◽

Geometrical Parameters ◽

Restricted Range ◽

Complete Contact ◽

The One ◽

Layered Half Space

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.

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