Maria Grazia D'Urso

On a generalized Love's problem

We present explicit expressions for computing the displacements induced in a homogeneous, linearly elastic half-space by uniform vertical pressure applied over an arbitrary polygonal region of the horizontal surface. By suitably applying Gauss theorem and recent results of potential theory we derive formulas which allow one to evaluate the displacements at an arbitrary point of the half-space solely as a function of the position vectors of the boundary of the loaded region assumed to be polygonal. Representative numerical examples referred to geodetically observed elastic displacements of the Earth surface due to water loads show the effectiveness and the flexibility of the proposed approach. Actually, it allows for a more realistic evaluation of displacements distribution and to achieve a considerable simplification in data handling since it is now possible to avoid tiling of complex regions by the simple load shapes, such as circles or rectangles, for which analytical solutions are currently available in the literature.

A NEW ALGORITHM FOR POINT-IN-POLYGON TEST

Abstract An original point-in-polygon test, based upon an electric analogy, is illustrated. It enhances an analogous procedure, previously developed by the first author [5], by almost halving the computer time required to numerically perform the test. The result is obtained by proving an addition formula for the inverse tangent function that corrects the one which can be usually found in mathematical handbooks. Further, the equivalence of the proposed method with the sum of angles method is shown.