Analysis of Spectra of External Impacts, Reactions to Them, and Limit States under Loading in Nonstationary Modes

Abstract—It has been noted that, as a rule, during operation of technical systems, the so-called nonstationary loading is implemented, when external loadings increase or decrease arbitrarily. In engineering calculations, of practical interest are the final relations between stresses and strains. It has been shown that simple cyclic loading problems can be solved using state equations in the final ratios, which are based on the small elastic strain theory. In this case, the existence of a uniform generalized strain diagram, which suggests the final relation between corresponding stress and strain components for both the initial and cyclic deformation stages is important for analysis of investigated nonstationary cyclic loading conditions. Basing on this fact, it has been established that, in the analysis of conditions of achieving limit states at all lifetime stages, the criteria and system of computational equations become too intricate because of a variety of factors to be taken into account. Among these factors are, first of all, external and internal natural, technogenic, and anthropogenous impacts, load from them, and reactions of objects to such impacts and loads. A set of criteria defining a limit state is presented in the form of a functional dependence characterizing, on the one hand, a set of force and deformation parameters of the state of a technical system and, on the other hand, a complex of criterion characteristics of constructional materials with allowance for their change during operation. The most important stage in determining conditions for achieving the limit state, which causes fracture, is finding the critical parts that bring risks of emergencies and catastrophes, in which local and main fractures are initiated. In this case, the transition of an operated object from the design area to the zones of initiation of failures, accidents, and disasters occurs when the damage, defectiveness, and risk parameters attain their critical values.