だ円形領域内に等分布荷重を受ける半無限体表面の変位について

概要

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In this paper, taking the case of a uniform load distributed over an elliptical area of the plane boundary, displacements of a point on the surface of the body are considered. Displacements of any point (x, y, 0) are given by the equations [numerical formula] where λ and μ are Lame's constants, r is a distance of a point (x, y, 0) from the point (ξ, η, 0), and the double integrations are taken over the elliptical area subjected to pressure. The horizontal components u, v are easily solved, but the normal component w can only be represented approximately. The case of a uniform load distributed over the area of a circle of radius a has already been obtained, whose results coincide with the special case of this problem, e=0 (e : eccentricity of the ellipse). As numerical examples, displacements of points on the axes of the ellipse are calculated, and plotted in figures. From these results, we conclude that for a point within the ellipse horizontal components u, v are proportional to x, y respectively, directing inwards, taking maximum values on the circumference, on the contrary, the vertical component w is maximum at the center, and decreases outwards.
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