Solving three-dimensional contact problems for foundation design in green building

Abstract

Design of foundations on an elastic base is carried out using the solution of three-dimensional problems of contact interaction. Improving the accuracy of engineering calculations is necessary to ensure economic efficiency and increase energy savings in green building. The problems of indentation of punches with a flat base bounded by doubly connected close to polygonal contact areas are researched in the present work. Small parameter method is used to obtain explicit analytical expressions for the contact pressure distribution and the punch displacement dependence in a simplified form, which is convenient for engineering practice. The found load-displacement dependence satisfies the known inequalities that are valid for an arbitrary contact domain. Also a numerical-analytical method is in consideration. It uses the simple layer potential expansion and successive approximations for the problems accounting roughness of the elastic half-space. Roughness coefficient is considered as a parameter of regularization of the integral equation for the smooth contact problem. The results of both methods coincide with sufficient accuracy.

Construction of mathematical and computer models for calculating contact characteristics of interaction between a rigid punch and an elastic half-space

“…The analytical solution was obtained using a variant of the perturbation method, based on the small-parameter expansion of the potential of a simple layer distributed over a doubly connected region. In this way, the problem of pressing a flat punch in the form of a non-circular ring is reduced to a sequence of problems for a punch in the form of a circular ring [9][10][11][12]21]. Special software for calculations and analysis of the results was developed in the publicly available C++ language (USA).…”

“…, . ρ θ ∈Ω (21) Since the integrand function in the integral (20) turns to infinity at the point (ρ 0 , θ 0 ), when finding the derivatives for the expansion of (20), it is necessary to first exclude this point from the region Ω. To this end, the point (ρ 0 , θ 0 ) is cut out of Ω by a circle of radius α.…”