The paper presents a novel approach to evaluating the fatigue performance of asphalt pavements using fuzzy set theory to model the uncertainty in the elastic moduli of asphalt layers. The method integrates fuzzy numbers with an analytical multilayer elastic pavement model. By applying α-cut representation and defuzzification techniques, the model delivers fuzzy estimations of critical strain responses and associated fatigue lives under traffic loading. The proposed methodology captures uncertainty in material properties more realistically than conventional deterministic approaches. The effectiveness of this technique is demonstrated through the Asphalt Institute’s fatigue models for tensile and compressive strains. The results provide fuzzy bounds for fatigue life parameters and enable robust pavement design under material uncertainty. By incorporating fuzzy-modulus-based parameters into layered elastic half-space models, the proposed method significantly improves the predictive reliability of pavement performance.

Load-bearing elements of buildings and structures of the mining and metallurgical complex in recent decades need to develop new more effective design solutions due to the intensification of technological processes, an increase in temperature loads and aggressiveness of the environment. The main direction of increasing the efficiency of such elements is their design from economically alloyed steel, which allows to increase the resource of structures and prevent accidents with a significant increase in temperature. Due to the fact that alloyed steels have higher mechanical characteristics at elevated temperatures, the question arises of creating lightweight beam structures from such steels, reducing their material consumption while maintaining the stability and fatigue strength of beams, the most promising is the use of welded beams with a perforated wall and composite beams. The creation of the most effective cross-sectional shape of metal beams with a perforated wall and welded beams, as well as crane beams in transverse bending, considering strength, local stability, flat bending stability and fatigue strength is considered. It is shown that an effective shape of beams with a perforated wall is a box-shaped structure made of perforated channels. A calculation was carried out to select a rational design made of an assortment of hot-rolled channel profiles. It is shown that due to the use of the proposed sectional shape, significant savings in the weight of the structure can be achieved. Considering the three-dimensional stress-strain state, the fatigue strength of welded metal crane girders operating in severe conditions is estimated. The efficiency of using a hot-rolled I-beam as the upper chord of such welded beams is shown. The necessity of using a hot-rolled I-beam and to ensure the fatigue strength of the lower chord is demonstrated. The use of the previously proposed combined method for calculating the structures of industrial buildings and structures and the use of economically alloyed steels allows us to create new designs of critical elements that reduce their material consumption and increase their resource. Further research can be carried out for real object designs in order to reduce their cost and increase reliability during operation in the conditions of mining and metallurgical production.

Project reliability management of petroleum reservoirs

In modern structural mechanics, problems involving uncertainty in the initial data are becoming increasingly common. One of the effective methods for accounting for such uncertainty is the application of fuzzy set theory [14]. This paper presents a solution to a structural mechanics problem using the fuzzy set method to consider the uncertainty of input parameters. The studied object is a simply supported beam with an intermediate support, for which the position and gap size are defined fuzzily. Defuzzification was performed, resulting in the expected values of support reactions and displacements of the structure. An analysis of the influence of the specified fuzziness on the mechanical behavior of the system was carried out, allowing the assessment of the structure's sensitivity to variations in input parameters.

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.