The analysis of statistical data showed that a large amount of plant waste is generated annually in oil and fat production plants, which must be processed and reused. The paper analyzes the problems of reusing sunflower oil production waste, which is characterized by a relatively high energy value: 1 ton of plant waste is equivalent to 0.625 tons of conventional fuel. According to the mathematical estimation, the actual total amount of impurities is 7.29%, in which major impurities constitute 25.7%. Studies have shown a high probability of oil – containing impurities – 37.25%. Therefore, it is recommended to process such impurities into fuel briquettes and technical oil to increase the profitability of sunflower oil production. For example, at the annual load of technological equipment of the Melitopol Oil Extraction Plant, in 250 days, at a daily processing capacity of 550 t˙day-1, an annual profit of 560,000 EUR is obtainable from the sunflower grain impurities processed into fuel and technical oil.

The problem of axial stretching of a plate with a double-periodic system of round holes arranged in a checkerboard pattern is considered. The specified problem is reduced to elasticity second problem for one period of plate, which was solved by the finite element method. As a result, the reduced elastic characteristics of the equivalent homogeneous orthotropic plate are found. The analysis of their behavior depending on dimensionless geometrical parameters is carried out. The area of variation of the geometric parameters was divided into two subareas. The behavior of the equivalent elastic characteristics in these areas is significantly different. It turned out that the double-periodic perforated plate shows significantly anisotropic behavior. The limit values of the Poisson's ratios can reach unity and, on the other hand, may be less than the original value. Dependences of the stress concentration coefficient on dimensionless geometrical parameters are obtained too. Performed comparative analysis of the obtained results with the results known from the literature, confirmed their adequacy.

A preliminary analysis of the available publications devoted to the study of crack resistance of reinforced concrete structures showed the absence of established general patterns of influence of important geometric parameters inherent in reinforced concrete elements on the distribution of the characteristics of fracture mechanics along the crack front. Based on the analysis, the purpose of the study was formulated: to establish these regularities for a concrete slab reinforced with a system of longitudinal steel rods. When conducting the research, a linear and elastic model of concrete was used, and the stress intensity factor was considered as a characteristic of the fracture mechanics. A surface crack of constant depth located in the cross-section of the slab was postulated. It was assumed that its faces completely cover the cross-section of reinforcing rods. The crack depth, the depth of reinforcing rods, their diameter, and the distance between adjacent rods were chosen as dimensionless geometric parameters relative to the thickness of the slab. The slab was loaded with two types of loads applied to its ends: constant tensile stresses (pure tension) and linearly variable axial stresses (pure bending). The problem of determining the stress intensity coefficient depending on geometric parameters was reduced to the boundary problem of elasticity theory. The CalculiX finite element analysis package was used to solve it and obtain the stress-strain state of the slab. More than four hundred finite element models were constructed for various combinations of parameters. Based on the known displacements of the crack face points, the values of the stress intensity factor along the crack front were calculated using the relation obtained in the study. It is established that its values significantly depend on the diameter of the reinforcement, and therefore, when conducting practical calculations, it is not recommended to replace the action of reinforcement on concrete with concentrated force. Polynomial approximations with a relative error of 10% are obtained for extreme values of the stress intensity factor. The materials of the study can be useful in the design of reinforced concrete structures, and when studying or teaching a course in fracture mechanics

In the present work the stress-strain state of a reinforced concrete slab with a transverse edge crack of constant depth is considered. There is investigated the effect of reinforcement upon the distribution of the fracture mechanics along the crack front. The uniformly or linearly distributed stresses at the slab ends are described as an external load. These loads correspond to pure tension and pure bending of the slab, respectively. For a case when the depth of the crack is less than the depth of the reinforcement rod, an analytical approach for an assessment of the crack state is proposed. As a characteristic of the crack state, the stress intensity factor (SIF) is used. Using the finite-element CalculiX package, the numerical results have been obtained, and adequacy of the analytical solution justified. The calculations have been performed for a wide range of variations in the geometrical parameters of the slab and the crack. For this purpose, a principle of replacing the external load with the pressure on the crack faces, well known in linear fracture mechanics, is generalized for the case of heterogeneous elastic bodies. The results of calculations show that the variation of the SIF value along the crack front is insignificant (up to 5% for practically realizable parameter values). On this basis it is concluded that the crack depth most likely is constant in the early stages of its fatigue development. For shallow cracks the SIF value will decrease near the reinforcing rod. It is interesting to note that for deep cracks the presence of reinforcement can lead to local increasing, not decreasing, of the SIF values. Considering this fact, the results presented in the paper may be useful in the design of reinforced concrete structures. It is especially important to take it into account in an individual design, in particular, in designing agricultural buildings where non-standard reinforced concrete structures are used.

The wide application of elements with periodic configuration in dynamically loaded structures stimulates a study of the propagation phenomenon of harmonic waves in mechanical systems of a periodic structure. The absolute majority of investigations of the wave propagation phenomenon in periodic structures concern one-dimensional and quasi-one-dimensional systems. Therefore, it is of certain interest to study the regularities in the distribution of the "transparency windows" of a mechanical system of a periodic structure with continuously changing parameters, which can be obtained by passing through the limit from the corresponding system with the threshold-type irregularities. Besides, the non-homogeneity in these systems is of a discrete, i.e. threshold type. The article presents the research results of propagation of harmonic waves along unfixed beams of a periodic structure. In addition two beam configurations are considered: with a constant cross section in individual segments and a continuous change in the cross section along the beam axis. The solution of the two problems has been made on the basis of the Floquet theory. As a result of the solution of this problem, frequency bands of the waves for both types of beams were found, and a comparative analysis of their propagation was carried out.