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This paper presents a proposed mathematical model, describing the calculations involved in deducting the critical compression force for rectangular, parallelepiped paperboard packaging, and permitting the minimisation of the thickness of the package sidewall. A comparison is given between the obtained calculations regarding critical force and the experimentally-determined results. This has shown a sufficient level of accuracy both for the theoretical and the experimental results. This means that the proposed mathematical engineering calculations model can be applied to the design of rectangular, parallelepiped paperboard packaging.

When designing packaging in the shape of a rectangular parallelepiped from various paperboard materials, it is important to determine their resistance to vertical compression force, which should be less than the maximum compression force. This is especially relevant when the products packed in these boxes are stacked during transport or storage. The developed empirical models make it possible to more optimally/more accurately determine the critical vertical compressive force of these packages. The purpose of this work is to create an semi-empirical model of the maximum compressive force of a paperboard box (carton) based on the corrected formulas of the maximum compressive force of the McKee corrugated cardboard box (taking into account the height) of the box and allowing to optimize its parameters. The accuracy of the developed semi-empirical models is presented by comparing the results of theoretical and experimental studies. It should be noted that the determination of the maximum compression force of the box is a contact problem of the nonlinear theory of elasticity and plasticity for structures whose elements are made of an anisotropic material. On this basis, semi-empirical models of three and one parameters were developed, which also estimated the values of experimental studies previously performed by other authors. One mathematical model also estimates the height of the box, which is not determined by the McKee formula. For the experiments, we used cartons of different geometric parameters and made from different types of paperboards. During the experiment, the boxes were compressed with vertical force until the packages collapsed. The results of the compared theoretical and experimental studies show the suitability of the proposed

Abstract. Actuators with elements made from alloys with shape memory have been developed and explored. These actuators may be used in small compressors, in damping systems and in pneumo-vibrotransducers. Some experimental dependencies of mechanical and other physical characteristics of these actuators have been obtained. Equation systems describing the motion of the actuators have been studied. Some characteristics of vibrotransducers, properties and technical parameters of damper were analysed. Examples of technical soliutions are presented and concrete application areas for these actuators in technological processes are indicated.

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