The paper presents a new refined-modified solution of the fundamental two-dimensional problem of the elasticity theory on the perpendicular application to the boundary of the half-plane of a concentrated-linear constant load. In contrast to the similar classical Fleman problem, which is a special case of a simple radial stress state, all three stress components, two normal and one tangent, as well as an additional geometric parameter characterizing the width of the site of the external local force’s actual distribution have been taken into consideration. In addition, on the basis of the classical interpretation of plane deformation, the known contradictions are eliminated that are associated with the uncertainty of the angular displacement at the boundary of the half-space and with the constancy of the second kinematic component in the pursuit of the infinity coordinates of an arbitrary point of the base material. In the course of the research, it is proved that there are cylindrical surfaces where equal tensile stresses act which trajectories have the shape of circles. In a simplified Fleman solution of such curves- isobars are Boussinesq circles with constant the principal compressive stresses. The derived analytical dependences are presented in a rectangular frame of reference, which allows to quantify the following with a high accuracy: 1) stresses in the depth of the base in horizontal and vertical sections; 2) contact pressure and draft of the soil elastic surface under the sole of a rigid long foundation when the base, within the generally accepted assumptions, is assumed to be linearly deformable, homogeneous, isotropic, solid, experiencing a one-time load. The results of the developed generalized physical and mathematical model can serve as a conceptual basis used in solving special fundamental and applied problems of mechanics directly related to the refined calculation of the bearing capacity of various parts and structures, widely used in modern engineering and construction such as bearings, cylindrical rollers, gears, foundations strip foundations, pavements in their steel compaction rolls, etc.

Âîñòî÷íî-Êàçàõñòàíñêèé ãîñóäàðñòâåííûé òåõíè÷åñêèé óíèâåðñèòåò (Ðåñïóáëèêà Êàçàõñòàí, 070014, ã. Óñòü-Êàìåíîãîðñê, óë. Ñåðèêáàåâà, 19) ÐÅÇÞÌÅ Ââåäåíèå. Ïðèâåäåííûå â ñòàòüå äàííûå ñâèäåòåëüñòâóþò î òîì, ÷òî ïðîáëåìà ïîâûøåíèÿ ïîaeàðíîé áåçîïàñíîñòè àâòîòðàíñïîðòíûõ ñðåäñòâ î÷åíü àêòóàëüíà. Öåëüþ ñòàòüè ÿâëÿåòñÿ ðàçðàáîòêà íàó÷íî îáîñíîâàííîãî ìåòîäà èññëåäîâàíèÿ ìåäíîãî ïðîâîäíèêà, èìåþùåãî ïðèçíàêè ëîêàëüíîé òîêîâîé ïåðåãðóçêè, äëÿ óñòàíîâëåíèÿ ïðè÷èíû åãî ïîâðåaeäåíèÿ â õîäå ïîaeàðíî-òåõíè÷åñêîé ýêñïåðòèçû. Ìàòåðèàëû è ìåòîäèêà. Èññëåäîâàíèÿ ïðîâîäèëèñü ñ èñïîëüçîâàíèåì ðàñòðîâîãî ýëåêòðîííîãî ìèêðîñêîïà JSM-6390LV ñ ïðèñòàâêîé äëÿ ýíåðãîäèñïåðñèîííîãî ìèêðîàíàëèçà. Ïîâåðõíîñòè ðàçðóøåíèÿ ìåäíîãî ïðîâîäíèêà ïîäâåðãàëèñü àíàëèçó áåç ïðåäâàðèòåëüíîé ïðîáîïîäãîòîâêè. Òåîðåòè÷åñêèå îñíîâû (òåîðèÿ è ðàñ÷åòû). Ðàçðàáîòàíà óòî÷íåííàÿ ìîäåëü ïðåäåëüíîãî íàïðÿaeåííî-äåôîðìèðîâàííîãî ñîñòîÿíèÿ íåóïðóãîãî ÷èñòîãî èçãèáà ìåäíîãî ñòåðaeíÿ, èìåþùåãî êðóãëîå ïîïåðå÷íîå ñå÷åíèå. Ðåøåíèå äîâåäåíî äî ïðîñòûõ ðàñ÷åòíûõ ôîðìóë, ïîçâîëÿþùèõ îöåíèâàòü íåñóùóþ ñïîñîáíîñòü èçãèáàåìûõ îäèíî÷íûõ ìåäíûõ ïðîâîäíèêîâ. Íà êîíêðåòíîì ïðèìåðå ïîêàçàíà ïðèìåíèìîñòü ðàçðàáîòàííîé ìàòåìàòè÷åñêîé ìîäåëè äëÿ ïðîâåäåíèÿ ïîaeàðíî-òåõíè÷åñêîé ýêñïåðòèçû. Ðåçóëüòàòû è îáñóaeäåíèå. Ïðèâåäåíû ïðèìåðû ïîaeàðîâ òðàíñïîðòíûõ ñðåäñòâ, âîçíèêíîâåíèå êîòîðûõ îáóñëîâëåíî êðèòè÷åñêèì èçãèáîì aeãóòà ïðîâîäîâ. Ýêñïåðèìåíòàëüíûìè äàííûìè ïîäòâåðaeäåíî, ÷òî îïëàâëåíèå ìåäíîãî ïðîâîäíèêà ïîä äåéñòâèåì òîêîâîé ïåðåãðóçêè ïðîèñõîäèò íà ó÷àñòêå êðèòè÷åñêîãî èçãèáà. Îáîñíîâàíà íåîáõîäèìîñòü óòî÷íåíèÿ ôîðìóëèðîâêè òåðìèíà "ëîêàëüíàÿ òîêîâàÿ ïåðåãðóçêà". Çàêëþ÷åíèå. Ïðåäëîaeåí ìåòîä îïðåäåëåíèÿ êðèòè÷åñêîãî èçãèáà ìåäíîãî ïðîâîäíèêà, ïðè êîòîðîì ìîaeåò ïðîèçîéòè åãî îïëàâëåíèå ïîä äåéñòâèåì ýëåêòðè÷åñêîãî òîêà. Ïðèâåäåííûå â ñòàòüå äàííûå ìîãóò áûòü èñïîëüçîâàíû ñïåöèàëèñòàìè ïðè ýêñïåðòíîì èññëåäîâàíèè ìåäíûõ ïðîâîäíèêîâ, èçûìàåìûõ ñ ìåñò ïîaeàðîâ, óñòàíîâëåíèè ìåõàíèçìà èõ ïîâðåaeäåíèÿ è â êîíå÷íîì ñ÷åòå ïðè÷èíû ïîaeàðà àâòîìîáèëÿ. Êëþ÷åâûå ñëîâà: ïîaeàð; ìåäíûé ïðîâîäíèê; êîðîòêîå çàìûêàíèå; ñâåðõòîê; ìåäü; ðàñòðîâàÿ ýëåêòðîííàÿ ìèêðîñêîïèÿ; íàïðÿaeåííî-äåôîðìèðîâàííîå ñîñòîÿíèå; èçãèá; äèàãíîñòè÷åñêèé ïðèçíàê; ïîaeàðíî-òåõíè-÷åñêàÿ ýêñïåðòèçà.

The paper considers a physically linear mathematical model of an isotropic circular plate-membrane with a non-deformable central disk, concentrated load and zero bending stiffness with the account for finite displacements. On this basis, the extreme problem of determining the rational geometric parameters of an elastic element from the condition of the target sensitivity function maximum with the equation of constraint in the form of the Huber- Hencky-Mises strength energy hypothesis is solved. The analytical study of the influence of the Poisson’s ratio on the basic optimal dimensionless characteristic of the membrane, which is the ratio of radii, in comparison with the known calculation by the formulas of the classical linear theory of transverse bending of rigid plates is presented. The results of the work can be used in the process of design of high-precision capacitive, inductive and strain gauges of membrane type, widely used in mechanical engineering, aviation, instrument engineering and construction when designing pressure tanks with controlled overpressure of gas or liquid.

A grinding process using a free impact breakage mechanism is used in industries. In order to make calculations, predict grinding results, and evaluate mills functioning, it is necessary to assess the parameters of the grinding process and interrelations between the process parameters, mills parameters and materials properties, i.e. it is necessary to use an adequate mechanical-mathematical model of the process. However it is difficult to model due to some phenomena occurring in this process. Nowadays, various researchers have established the basis for the structure of the grinding process, but the application of the existing hypotheses and methods to evaluate the grinding process is quite difficult. This paper solves the problem of a spherical shape particle impacting an absolutely rigid half-space. It proposes a refined mechanical and mathematical model describing the process of destruction of the particle using the free direct impact breakage mechanism on an absolutely rigid, stationary, and flat surface. By using the Hertz-Staerman's classical analytical dependencies on the force contact interaction of the spherical bodies and the technical theory of the longitudinal waves’ propagation in the elastic continuous medium, we obtained a new refined solution of the applied dynamic problem related to a direct impact of a ball simulating a particle of a feeding material (an absolutely rigid surface simulating the working body of the mill) taking into account local physically linear deformations, the time parameter and radial particle size. The improved theoretical model of the spherical particle destruction was brought to applicable analytical calculations, tested and illustrated by a numerical example. It made it possible to describe the fracture of the material particles, predict the result and calculate the grinding process depending on its parameters providing the required quality of grinding by regulating and selecting characteristics, designing and selecting the grinding equipment, and modeling the grinding process using the free impact breakage mechanism.