Application of the Methods of the Theory Similarity and Dimensional Analysis for Research the Local Stress-strain State in the Neighborhood of an Irregular Point of the Boundary

Abstract

In this paper, the methods of similarity theory and dimensional analysis analyzes the features of solving the problem of elasticity, caused by a form of boundary or “geometric factor” and the finite break of specified internally strains emerging in an irregular point of the boundary. Given the similarity criteria for the self-similar solution of the elasticity problem in a neighborhood of irregular points on a singular line of the elastic body of the border.Due to self-solve the elastic problem, stress, strain, displacement in a neighborhood of an irregular point of the boundary admit of the group similarity and functions possess the property of homogeneity, characterized by the fact that these functions can be represented in the form of power complexes. The properties of similarity and homogeneity must have an experimental solution, resulting in the model as the fringe pattern by photoelasticity. Therefore, sequence stripes in some neighborhood of irregular point of the boundary should have the property of similarity, homogeneity as well as stress and be represented in the form of power complexes, m ∼ Cλr, which is confirmed by research of experimental data.