EVALUATION OF THE STRESS-STRAIN STATE OF HALF-SPACE WITH CYLINDRICAL CAVITIES

A three-dimensional problem was solved in the theory of elasticity for an elastic uniform halfspace with cylindrical cavities parallel to each another and the half-space boundary. Stresses rapidly decaying to zero at big distances from the origin of coordinates are specified on the boundaries of cylindrical cavities and on the half-space boundary. The problem of solving such problems is topical. It is encountered in practice and solved using approximate methods. The approach used herein yields solutions of the stated problem with an a priori specified accuracy depending on the system order. In contrast to publications referred to in the paper, the focus, apart from another approach, was on analysing the stress state of half-space to study the mutual influence of cylindrical cavities and of the cavities with half-space boundary. The problem was solved using the generalised Fourier method for Lame equations in cylindrical coordinates linked to cylinders and Cartesian coordinates linked to half-space. For transition between basic solutions of Lame’s equations, special formulas were used for transition between local cylindrical systems of coordinates and between the Cartesian and cylindrical systems of coordinates. The truncation method was used to solve infinite systems of linear algebraic equations to which the problem was reduced. This yielded displacements and stresses in an elastic body. The numerical results were derived for the case of half-space and two cylinders under a load applied to the half-space boundary. Separate computations were performed for a load applied to the surface of the cylindrical cavity. In both cases the analysis of the stress-strain state indicates that space weakening due to cylindrical cavities or the half-space boundary gives rise to extremal stresses in these sites. The method can also be used for other boundary conditions.