GEOMETRIC DISCONTINUITIES IN ELASTOSTATICS
LEHIGH UNIV BETHLEHEM PA DEPT OF APPLIED MECHANICS
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Three-dimensional elastostatic problems for an infinite solid with geometric discontinuities are formulated and solved with the aid of potential functions. In the problem of a linearly varying pressure specified over a plane region bounded by an ellipse, use is made of the gravitational potential at an exterior point of a homogeneous elliptical disk. The problem of prescribing displacements on the surfaces of discontinuity is governed by the Newtonian potential of a simple layer distributed over a disk in the shape of the region of discontinuity. The mass density of the disk is proportional to the prescribed normal displacement. For an elliptically shaped region, the application of the symmetrical form of ellipsoidal coordinate leads to an integral equation of the Abel type for the potential function. It is shown that if the displacements normal to the elliptical plane are given by a polynomial in the variables x2 and y2, then the corresponding normal stress acting over the ellipse is also a polynomial. The results given in this report are useful in the prediction of the stability behavior of elastic solids containing geometric discontinuities.