Application of various uncertainty measures in the problem of critical force searching for orthotropic shell in conditions of the carrying capacity

The questions of measures calculation of events containing uncertain quantities of random, fuzzy and rough nature are considered. The algorithms of determination of measures of events, based on methods of statistical simulation, are proposed. The "chances" of realization an uncertain event - the simultaneous fulfillment of the conditions of the bearing capacity of a cylindrical orthotropic shell compressed by an axial force, which can be presented in a random, fuzzy or rough manner, are investigated. The stochastic uncertainty is given by the distribution density of the random variable. Fuzzy data are defined by the membership function, and rough data are defined by a deterministic upper and lower approximation. Each type of uncertainty is characterized by its own measures: the probability - for the description of the modality - "probably", the possibility - for the description of the modality is "fuzzy", trust - to describe the modality "rough". The paper proposes procedures for calculating the listed measures. Also numerical illustrations of the calculation of modalities as "probably", "fuzzy", "rough" for the analysis of the limit force of carrying capacity in the problem of optimal design of the compressed orthotropic cylindrical shell made of fiberglass in conditions of uncertainty of the problem of geometrical parameters, such as thickness and radius, and description of the corresponding degree of implementation of an uncertain event are shown. Uncertain event is to fulfill the limitations of general and local stability and durability. The results of the calculations are compared with the solution of the problem with deterministic data. The results show the "reaction" of the values of the critical force to the possible presence of uncertain factors in the problem and the degree of uncertainty. Thus, the bearing capacity of the shell decreases significantly more in the presence of factors of random and rough nature in comparison to the fuzzy data.