Justification of Using Delta-Functions in the Theory of Shells Featuring Irregularities

Abstract

The delta-functions are used in calculation of the building structures to determine irregularity places, but the delta-function proper is a limiting function featuring no geometrical interpretation. In order to justify correctness of its application, it is necessary to carry out the limiting transition based on the method of variation limiting transformations. Consideration is given to the shallow shells supported by the narrow ribs or featuring jogs of the middle surface. The places of discrete variation of shell thickness or its curvature will be set by means of singular columnar functions. The limiting transition from such functions to delta-functions is used to obtain correlations for the rib shells and the shells featuring the middle surface. This is the way to justify a possibility of using delta-functions in the theory of shells featuring irregularities. At that, the equilibrium equations get simplified and, at the same time, the calculation accuracy gets lost.