Different coverings with defects in static problems of seismology and nanomaterials

Abstract

A topological method for solving boundary problems is applied for studying the deformation mode of bodies with coverings. The case of simulation of a covering with different types of fragments of Kirchhoff plates arranged on a deformed multilayered substrate is analyzed. Fragments of plates contacting with the substrate without friction undergo vertical static loads and make contact with each other. Functional and pseudodifferential equations are constructed for this case. The case of two different-type fragments of plates in the form of half-planes contacting between each other along the coordinate plane is considered in detail. Different types of contact between the plates called defects, which violate the equality of movements and stresses at the joint, are investigated. These defects considerably supplement the conventional voids—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 continuity of the covering but do not correspond to the conjugation requirements for elastic bodies. It is shown that the topological method makes it possible to perform the standard investigation into the described types of defects, the number of which is sufficiently large.