SOME APPLICATIONS OF THE FRACTAL PARAMETRIC-HOMOGENEOUS FUNCTIONS

The purpose of this paper is to present some recent results concerning applications of so-called parametric-homogeneous (ph) functions to some problems of solid mechanics. The ph-functions have often fractal graphs and can be nowhere differentiable. An example of ph-function is the Weierstrass-Mandelbrot one. We introduce some ways of construction of the ph-function of both arbitrary degree and fractal dimension. We consider the discrete Hertz problem of contact between a punch, whose shape is described by a positive ph-function, and a deformable half-space. General expressions for changes of all functions, giving the solutions of the contact problems for a fractal punch, are derived exactly, without solving the field equations.