Peculiarities of hidden defects in different thin-shell coverings

Abstract

A topological method for solving boundary problems is applied to investigate the deformation mode of covered bodies. The case of covering modeling by various fragments of Kirchhoff plates arranged on a deformed multilayered substrate is analyzed. Fragments of plates in contact with the substrate are subjected to horizontal static loads and contact between each other. Functional and pseudodifferential equations are constructed for this case. The case of contacting of two different fragments of the plate in the form of half-planes contacting between each other along the coordinate axis is constructed in detail. Types of contact between the plates called defects, which violate the equality of motions and stresses at the joint, are investigated. These defects considerably complement the generally accepted cavities—cracks in plates, and precede the destruction of the latter. Some of such defects turn out to be visually hidden since they do not violate the covering integrity but do not satisfy the conjugation requirements of elastic bodies. It is shown that the topological method enables one similarly to investigate the described types of defects, the number of which is rather large.