Construction of full-strength holes for a mixed problem of plane elasticity theory with multy-connected domain

Author: Nana Odishelidze
Keywords: mixed problem, stress state, outer and inner boundaries
Annotation:

The paper addresses to the construction of full-strength holes of problem of plane elasticity theory for a multy- connected domain, which external boundary is rhombus boundary; the internal boundary is required two holes that are symmetric with respect to its diagonals. Absolutely rigid punches with rectilinear bases are applied to each segment of outer boundary of given body and they are under the action of the forces that applies to their middle points. There is no friction between the surface of given elastic body and punches. The unknown hole boundaries are free from external load. Tangential stresses are equal to zero along the entire boundary of the domain and the normal displacements on the linear parts of the boundary are constant. The shape of the holes´ contour and the stress state of the given body are determined, provided that the tangential normal stress arising at the holes´ contour takes a constant value. Such holes are called full-strength holes. Full-strength contours and stress state are found by means of method of complex analysis. The solution is written in quadratures. All calculations and construction of full -strength contours were carried out using the program Mathcad.