Date of Award

Spring 1970

Document Type

Dissertation

Degree Name

Doctor of Engineering Science in Mechanical Engineering

Department

Mechanical Engineering

First Advisor

Su Ling Cheng

Second Advisor

Arnold Allentuch

Third Advisor

Harry Herman

Fourth Advisor

Benedict C. Sun

Abstract

The redistribution of dynamic stresses caused by the presence of an elliptical discontinuity in an infinite isotropic homogeneous elastic solid is examined. The solutions are obtained for the special cases of the rigid immovable inclusion and the vacuous cavity inclusion, and numerical results are presented.

The solutions to the wave equations in elliptical coordinates are expressed in series of the elliptical geometry eigenfunctions. Application of the boundary conditions, vanishing displacements for the rigid immovable inclusion and vanishing stresses for the cavity inclusion, yields in each case two infinite sets of linear algebraic equations for the expansion coefficients of the series solutions.

The incident shear or compressional waves are generated by a line source of excitation whose location with respect to the inclusion may vary. Parametric studies are carried out to determine the influence of ellipse eccentricity, source location and frequency as well as Poisson's ratio with regard to the stresses on the discontinuity boundary.

It is found that the source location does not greatly affect the stress intensity over the range studied. Increasing the ellipse eccentricity causes pronounced increases in the stresses for certain propagation directions of the incident waves. Also the stresses are dependent upon the frequency and are in general maximized at frequencies where the wave length greatly exceeds the dimensions of the discontinuity. Poisson's ratio does not appear to be a critical parameter in the determination of stress intensities.

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