Monte Carlo method for determination and analysis damage to the power system

The purpose of the work, the results of which are presented within the framework of the article, was to develop algorithms for calculating the damage to a solid or a system of solids based on the Monte Carlo method and the analytical boundary element method. The analytical boundary element method was used to calculate and analyze the stress-strain state of a solid under the distributed surface load. Based on indicators of the stress state, the algorithms for numerically assessing the dangerous volume and integral damage using the Monte Carlo methods, have been developed. Based on the pattern of distribution of stress fields, the technique of determining the area for randomly generating integration nodes is described. General recommendations have been developed for determining the boundaries of a subdomain containing a dangerous volume. Based on the features of the Monte Carlo methods, a numerical assessment of the indicators of damage of continuous media for a different number of integration nodes was carried out. Methods and algorithms were used to calculate the dangerous volume and integral damage in the plane and spatial cases for the two most common laws of the distribution of surface forces in the contact mechanics of solids: in case of contact interaction of two non-conformal bodies (Hertz problem) and when a non deformable rigid stamp is pressed into elastic half-plane or half-space. The scientific novelty of the work is to combine analytical and numerical approaches for the quantitative assessment of damage indicators of the power system. As a result the quantitative indicators of the dangerous volume (in the flat case - the dangerous area) and the integral damage of the half-plane and half-space related to the value of the applied load are obtained.