Infinite Elastic Research Articles

Discussion: “The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid” (Shelley, Joseph F., and Yu, Yi-Yuan, 1966, ASME J. Appl. Mech., 33, pp. 68–74)

Discussion: “The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid” (Shelley, Joseph F., and Yu, Yi-Yuan, 1966, ASME J. Appl. Mech., 33, pp. 68–74)

The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid

Presented in this paper is a solution in series form for the stresses in an infinite elastic solid which contains two rigid spherical inclusions of the same size. The stress field at infinity is assumed to be either hydrostatic tension or uniaxial tension in the direction of the common axis of the inclusions. The solution is based upon the Papkovich-Boussinesq displacement-function approach and makes use of the spherical dipolar harmonics developed by Sternberg and Sadowsky. The problem is closely related to, but turns out to be much more involved than, the corresponding problem of two spherical cavities solved by these authors.

Transient Compressional Waves in an Infinite Elastic Plate, Generated by a Time-Dependent Radial Body Force

Transient Compressional Waves in an Infinite Elastic Plate, Generated by a Time-Dependent Radial Body Force

Dynamic Displacements in an Infinite Elastic Space and Matched Asymptotic Expansions

Dynamic Displacements in an Infinite Elastic Space and Matched Asymptotic Expansions

Thermal Stress of an Infinite Elastic Region in Uniform Heat Flow and Containing Some Spherical Cavities : Part 2, Solution for the Case of Containing Two Spherical Cavities

In this paper, the same method of solution for the problem of determining the thermal stress as mentioned in the previous report is illustrated by the example for the problem containing two spherical cavities. The stress distribution along the periphery of cavities was numerically calculated, so as to clarify the exact influence upon the stresses caused by the presence of some cavities in a heated region.

Thermal Stress of an Infinite Elastic Region in Uniform Heat Flow and Containing Some Spherical Cavities : Part 1, Solution for the Case of Containing Three Spherical Cavities

A method of solution to determining the thermal stress of an infinite elastic region under the conditions of linear thermoelasticity and containing some spherical cavities is illustrated by two examples for the problems containing two and three spherical cavities. The fundamental equations governing the temperature distribution of a uniform heat flow in a solid are first derived and then the elastic stresses in the solid bodies under prescribed temperature distributions are determined to satisfy the boundary conditions on the peripheries of the cavities. The method consists of a general series form of stress function in spherical coordinates, and it can be developed for a variety of cavity numbers and sizes. In this paper, the illustration for three cavities is given, and the numerical results are reported.

Thermal Stress of an Infinite Elastic Region in Uniform Heat Flow and Containing Some Spherical Cavities : Part 1, Solution for the Case of Containing Three Spherical Cavities

A method of solution to determining the thermal stress of an infinite elastic region under the conditions of linear thermoelasticity and containing some spherical cavities is illustrated by two examples for the problems containing two and three spherical cavities. The fundamental equations governing the temperature distribution in a solid are first derived and then the elastic stresses in the solid bodies under prescribed temperature distributions are determined to satisfy the boundary conditions on the peripheries of the cavities. The method consists of a general series form of stress function in spherical coordinates, and it can be developed for a variety of cavity numbers and sizes. In this paper, the illustration for three cavities is given, and the numerical results are reported.

Thermal Stress of an Infinite Elastic Region in Uniform Heat Flow and Containing Some Spherical Cavities : Part 2, Solution for the Case of Containing Two Spherical Cavities

In this paper, the same method of solution for the problem of determining the thermal stress as described in the previous report is illustrated by the example for the problem containing two spherical cavities. The stress distribution along the periphery of cavities was numerically calculated, so as to clarify the exact influence as exerted upon the stresses by the presence of some cavities in a heated region.

Flexural Stress Waves in an Infinite Elastic Plate Due to a Suddenly Applied Concentrated Transverse Load

The problem solved is that of an infinite plate subjected to a suddenly applied concentrated transverse shear load. The solution is derived from a plate theory that incorporates, in addition to bending, the effect of shear force and rotatory inertia on the deflection. These added effects give the present theory true wave character along with greater accuracy in the waves predicted. Numerical evaluation of the solution brings out the effects of dispersion and distortion on the moment and shear-force response of the plate. A criterion is developed for judging the accuracy of this response. It is based on a comparison, employing the stationary phase method, of the present approximate and exact (three-dimensional) theories.

Discussion: “Thermal Stresses in Infinite Elastic Disks” (Sharma, Brahmadev, 1956, ASME J. Appl. Mech., 23, pp. 527–531)

Discussion: “Thermal Stresses in Infinite Elastic Disks” (Sharma, Brahmadev, 1956, ASME J. Appl. Mech., 23, pp. 527–531)

Thermal Stresses in Infinite Elastic Disks

Abstract A direct method of solving problems of thermal stress in a disk of finite thickness and infinite radius is discussed in this paper.

Forced Vibrations of a Body on an Infinite Elastic Solid

Abstract The paper considers the forced vibration of a rigid body resting on a homogeneous elastic medium of infinite surface area and constant depth which may be finite or infinite. Four modes of vibration for a body with a circular base are investigated; (a) vertical translation, (b) torsion, (c) horizontal translation, (d) rocking. For a semi-infinite medium the amplitude response can be obtained for any mass in terms of known constants of the system and two fundamental functions f1 and f2, which depend only on the exciting frequency and the properties of the medium. Close approximations to these functions have been evaluated for each mode. Experiments on an elastic model are described, the results of which are in good agreement with theoretical prediction. The behavior of a stratum of infinite area is more complex since functions f1 and f2 also depend on stratum depth. These functions have been evaluated for the torsional mode only, experimental results being given for the other modes.

On the Motion produced in an Infinite Elastic Solid by the Motion through the Space occupied by it of a body acting on it only by Attraction or Repulsion

The title of the present communication describes a pure problem of abstract mathematical dynamics, without indication of any idea of a physical application. For a merely mathematical journal it might be suitable, because the dynamical subject is certainly interesting both in itself and in its relation to waves and vibrations. My reason for occupying myself with it, and for offering it to the Royal Society of Edinburgh, is that it suggests a conceivable explanation of the greatest difficulty hitherto presented by the undulatory theory of light; the motion of ponderable bodies through infinite space occupied by an elastic solid.