Determination of displacements of surface points of a half-space under the action of axisymmetric complex load
It is shown that when the sphere is flattened, the distribution of contact pressure is a function of complex shape. The knowledge and description of the contact pressure distribution function is of practical importance in solving the issues of elastic punching of materials and elastic recovery of an imprint during unloading. A methodology for determining the displacements of half-space points under the action of a load of complex shape, i.e. load, which can be represented by a combination of several equations to describe in adjacent areas. To this end, the authors propose the use of an axisymmetric load of the form , where . It is indicated that the method previously used by the authors is not suitable for determining the movement of half-space from a complex load. According to the proposed methodology, the displacement of point A ( is first determined (half-spaces from the annular load created by constant pressure on the annular platform with a width at a distance from the axis of symmetry for cases when and . Then the total displacement of point A( is determined (within the limits of the load of a simple form. Verification of the obtained analytical results by the proposed method with the previously obtained by the determination of the displacements of the points of half-space showed their perfect coincidence. This made it possible to recommend the use of the proposed methodology for determining displacements within and outside the range of action on a half-space of a load of complex shape. Expressions are presented for using the proposed technique for determining the displacements of half-space from a load described by two functions.