Potential Energy Of Deformation Research Articles

Electron energy relaxation mechanism in n-type InxGa1-xAs1-yBiy alloys under electric and magnetic fields

We investigate the power loss per electron mechanism of hot electrons generated under electric and magnetic fields in n-type InxGa1-xAs1-yBiy epitaxial layers. Acoustic phonons are generated under various electric fields to determine the hot-electron energy relaxation mechanisms at low temperatures. The hot electron temperatures are determined by theoretical calculation of the amplitude of the magnetoresistance oscillation. The power loss per degenerate electron is analytically modeled with possible scattering mechanisms. The modeling of the experimental results reveals that power dissipation occurs by employing deformation potential energy scattering for all the samples. The deformation potential energy increases by ∼ 2.14 eV/Bi% when Bi atoms are introduced into ternary InGaAs alloy and the increase in the deformation potential energy is found to be independent of the electron density, which indicates that power dissipation occurs in the equipartition regime.

On some methods of determining proper frequencies torsional oscillations in metal-working machines

Forced torsional vibrations that occur in machine tool drives are one of the pressing problems of modern machine tool industry. The reasons for these fluctuations may be imbalances of rotating masses, structural imperfections of bearing units, operating or technological process features (for metal-cutting machines – eccentric clamping of the workpiece, processing of non-round workpieces, etc.). In this work, using the example of a real metal-cutting machine, the task of dynamic analysis of the drive of the main movement of the machine with determination of the natural frequencies of torsional vibrations is realized. The real object is replaced by a dynamic model (DM). When constructing the DM, the inertial and rigidity characteristics are determined from the conditions: – the kinetic energy of the object is equivalent to the kinetic energy of the DM (from this condition the axial moments of inertia of the concentrated masses of the row model are obtained); – the potential energy of elastic deformations of the object is equivalent to the potential energy of deformation of the DM (from this condition the rigidity coefficients of the DM are obtained). The natural frequencies of the row DM were determined in three ways: 1) by solving the frequency equation (exact method) in combination with the method of reducing the number of masses of A.P. Cherevkov; 2) partial systems method (fundamental frequency only); 3) method of residuals (Tolle). The following conclusions were made: 1) the main (smaller) frequency can be found by any of the methods considered (since the results of the three methods coincided); 2) when simplifying the DM using the method of partial systems, the criterion for the possibility of further simplifications over the specified frequency range should be taken into account; the transition from a three-mass DM to a two-mass one if the criterion in this calculation was not met led to an error in determining the value of the fundamental frequency of about 10%; 3) dynamic calculations of machines using DM and methods for determining natural frequencies make it possible, based on known frequencies of disturbing forces, to identify possible near-resonant operating modes and avoid them in advance by making changes to the design of the machine at the design stage

STUDY OF THE INFLUENCE OF THE GEOMETRIC FORM OF PIGS ON THE EFFICIENCY OF CLEANING PIPELINES

The effect of the geometric shape of the pigs on their passage and pipeline cleaning efficiency was investigated by numerical modeling and experimentally. For this, a 3D geometric model was built and experimental samples with a convex front and a concave back part were made from silicone compound. The properties of the pigs material are described by the Mooney-Rivlin deformation potential energy model. The simulation results are visualized by constructing three-dimensional colored fields of equivalent Mises stresses on the contours of the pigs for different values of the friction coefficient between its side surface and the inner wall of the pipeline. It was found that making the rear part of the pigs concave leads to a significant increase in the contact forces between the pigs and the inner wall of the pipe, which has a significant impact on its passage and the efficiency of cleaning the internal cavity of the pipeline. Moreover, with an increase in the coefficient of friction, the equivalent stresses near the rear end of the pigs increase, and therefore the contact forces increase and the flow through the pigs decreases.

Carrier mobility in doped Sb<sub>2</sub>Se<sub>3</sub> based on deformation potential theory

Antimony selenide (Sb<sub>2</sub>Se<sub>3</sub>) is an element-rich, cost-effective, and non-toxic material used as an absorber layer in solar cells. The performance of solar cells is significantly influenced by the transport characteristics of charge carriers. However, these characteristics in Sb<sub>2</sub>Se<sub>3</sub> have not been well understood. In this work, through density functional theory and deformation potential theory, we investigate the hole transport properties of pure Sb<sub>2</sub>Se<sub>3</sub> and As-, Bi-doped Sb<sub>2</sub>Se<sub>3</sub>. The incorporation of as element and Bi element does not introduce additional impurity levels within the band gap. However, the band gaps are reduced in both As-Sb<sub>2</sub>Se3 and Bi-Sb<sub>2</sub>Se<sub>3</sub> due to the band shifts of energy levels. This phenomenon is primarily attributed to the interactions between the unoccupied 4p and 6p states of the doping atoms and the unoccupied 4p states of Se atoms, as well as the unoccupied 5p states of Sb atoms. In this study, we calculate and analyze three key parameters affecting mobility: effective mass, deformation potential, and elastic constants. The results indicate that effective mass has the greatest influence on mobility, with Bi-Sb<sub>2</sub>Se<sub>3</sub> exhibiting the highest average mobility. The average effective mass is highest in As-Sb<sub>2</sub>Se<sub>3</sub> and lowest in Bi-Sb<sub>2</sub>Se<sub>3</sub>. The elastic constants of the As- and Bi-doped Sb<sub>2</sub>Se<sub>3</sub> structures show minimal differences compared with that of the intrinsic Sb<sub>2</sub>Se<sub>3</sub> structure. By comparing the intrinsic, As-doped, and Bi-doped Sb<sub>2</sub>Se<sub>3</sub>, it is evident that doping has a minor influence on deformation potential energy along various directions. The study reveals that the hole mobility in Sb<sub>2</sub>Se<sub>3</sub> displays significant anisotropy, with higher mobilities observed in the <i>x</i>-direction and the <i>y</i>-direction than in the <i>z</i>-direction. This discrepancy is attributed to stronger covalent bonding primarily in the <i>x</i>- and <i>y</i>-direction, while in the <i>z</i>-direction weaker van der Waals forces is dominant. The directions with enhanced charge carrier transport capability contribute to efficient transfer and collection of photo-generated charge carriers. Therefore, our research theoretically underscores the significance of controlling the growth of antimony selenide along specific directions.

Deformation as a process to transform shape and volume of protective structures of the development mine workings during coal-rock mass off-loading

Purpose is to assess deformation characteristics of protective structures while coal-rock mass off-loading to ensure wall rock stability as well as operating conditions of the development mine workings in coal mines. Methods. In a laboratory environment, uniaxial compression of protective structures has been applied on the models to identify the influence by deformation processes on the changes in their rigidness resulting from the shape and volume transformation. Findings. Under the deformation of rigid structures in the context of a safe strain resource, potential energy of their changes in shape is 4.1-6.5 times higher than the one of changes in volume. Beyond the safe deformation resource when critical level of the specific potential strain energy has been exceeded, strength of protective structures is not sufficient to restrict wall rock movement limiting their use. If relative volume variation in the rigid protective structures is δV > 0.06-0.082 then they lose their stability. Under such conditions, structural rigidity decreases by 14-22%. If pliable wooden protective structures are used then relative 0.62 ≤ δV ≤ 0.72 volume change doubles their rigidity. In the circumstances, the potential shape change energy is 2.1 times higher than the volume change energy; the abovementioned favours temporary compaction of wooden components of the compressive structure while improving its resistivity. Originality. Regularities of changes in the specific potential deformation energy of protective structures depending upon their shape and volume variation in terms of uniaxial compression have been identified. Practical implications. To ensure stability of wall rocks and maintain operating conditions of the development mine wor-kings, it is reasonable to apply pliable wooden protective structures which will help restrict roof and floor movements after their compaction. Insufficient residual strength of rigid protective structures, resulting if they lose their stability, provokes rock failure within the working areas of coal mines.

RITZ METHOD IN THE DISCRETE APPROXIMATION OF DISPLACEMENTS FOR SLAB CALCULATION

Introduction: The FEM reduces the problem of structural analysis for various building structures to the formation and solution of a system of linear algebraic equations. For this purpose, there are techniques available for obtaining FE stiffness and flexibility matrices where the main structural deformation characteristics are taken into account. However, the FEM can also be considered as a special case of the Ritz method in the discrete approximation of the required functions. In the functional of full potential deformation energy with regard to the considered structure, all adopted stress-strain state characteristics are taken into account. Since it is difficult or impossible to find continuous approximation functions both in the classic version of the Ritz method and in the Bubnov–Galerkin method for some types of edge restraint in such building structures as beams, slabs, or shells, it is possible to use the Ritz method in the discrete approximation of the required functions (by analogy with the FEM). This paper presents a method of such calculations using slab calculations as an example. It is shown that, due to introducing some notations (operators), the process of finding the coefficients of the system of linear algebraic equations creates no difficulties and is easily programmable. The proposed method is not an alternative to the FEM, which is the most effective numerical method for the calculation of complex three-dimensional building structures. Purpose of the study: We aimed to create a method for calculating slabs by the Ritz method in the discrete approximation of the deflection function for edge restraint cases when it is difficult or impossible to find continuous approximation functions in the classic version of the Ritz method and the Bubnov–Galerkin method. Methods: Based on the application of the Ritz variational method in the discrete approximation of displacements for slab calculation, all the basic relations for rectangular finite elements with 12 degrees of freedom are obtained, and an algorithm for forming the coefficients of the system of linear algebraic equations is developed. Results: For the first time, the solution by the Ritz method in the discrete approximation of slab displacements is obtained for the case when two edges of the slab are rigidly restrained and other two edges are free. In this case, the correct solution of the above problem is possible only with the use of the proposed method and FEM. For the test problem, we performed a comparison of the results of the calculation using the proposed method with the results using the classic Ritz method, which showed their very close agreement. The accuracy of the obtained results was assessed.

Evolution from gas outburst to coal outburst: An analysis from the perspective of asynchronous transfer difference of gas mass and coal deformation

Considering that coal and gas outburst is a highly complex nonlinear process, the synchronous energy criterion based on the gas expansion energy and the coal deformation potential energy is often adopted to evaluate the hazard. However, the synchronous energy criterion without considering the transfer difference of gas mass and coal deformation has defects in describing the evolution characteristics of coal-rock gas dynamic disasters. Hence, it is necessary to investigate the asynchronous characteristics of the gas expansion energy and the coal deformation potential energy. In this study, the deformation characteristics of coal injected with He and CH4 were measured respectively with the aid of a self-developed device for observing the asynchronous characteristics of effective stress and adsorption-induced deformation. Besides, the differentiated propagation characteristics of gas pressure and adsorption-induced deformation were obtained, and the asynchronous propagation starting point and propagation rate difference between them were analyzed and determined. Furthermore, based on the calculation formula of gas expansion energy and coal deformation potential energy, the values and propagation differences of the two types of energy at different times were revealed. Finally, the typical outburst phenomena were explained using the energy asynchronous theory. The following research findings were yielded. The adsorption-induced expansion process lasts longer than the gas pressure reduction process, which is the reason for asynchronous propagation of gas expansion energy and coal deformation potential energy. The coal deformation potential energy can be further divided into mechanical compression strain energy and desorption shrinkage strain energy. In the initial stage of outburst, the main sources of energy are free gas expansion energy and mechanical compression strain energy. As time progresses, the effect of desorption gas expansion energy and desorption shrinkage strain energy gradually strengthens. From the perspective of energy asynchrony, outburst occurrence at a low gas concentration in deep regions and delayed outburst in cross-cut coal uncovering can be explained as the result of dynamic load instability in surrounding stopes brought about by lagging superimposed deformation disturbances after gas desorption, or the result of self-induced lagging shrinkage deformation formed under special boundary conditions. The findings of this study are helpful to guide the design and connection of the prevention and control methods of deep coal-rock gas dynamic disasters.

Determining the deformation properties of crushed rock under compressive compression conditions

The object of this study is the process that forms fill materials from crushed rock under load for managing the condition of side rocks in a coal-bearing massif with preparatory workings. Deformation properties of crushed rock under laboratory conditions were evaluated on the basis of a study of compressive compression of the fill material. It was registered that there is a quadratic functional dependence between the change in the bulk density of crushed rock of different granulometric composition and the specific potential energy of deformation. It was experimentally established that the specific potential energy of deformation reaches the limit values at the maximum compression of crushed rock when the fill material consists of parts of different sizes. For experimental samples with different thickness of the rock layer h0 (m), there was a linear relationship between their longitudinal deformation Dh (m) and the external load F (kN), which determined the behavior of the deforming body at critical levels. Under such conditions, with a relative change in the volume of the fill material dV=0.36, that is, with the same relative deformation at any values of the parameter h0 (m) and the compaction coefficient of the crushed rock kcon=1.57, the maximum stiffness of the rock supports was ensured. With a limited amount of external static load on the experimental samples, in the process of their deformation when the parameter h0 was reduced by 2 times before their compression, the compaction coefficient of the crushed rock increased from kcon=1.33 to kcon=1.57. At the same time, the specific potential energy of deformation increased by 40 %, which made it possible to ensure the maximum rigidity of the fill material at the minimum value of the longitudinal deformation Dh (m) of the experimental samples

Cross-section geometry optimization of flexural thread using energy criterion

Purpose: The aim of this work is to develop a method to determine the best geometrical parameters of the flexural thread cross-section providing the lowest potential energy of deformation, thereby meeting the requirements for the minimum weight based on strength and rigidity limitations on the designed element.Methodology/approach: The problem of calculating the best parameters is reduced to nonlinear mathematical programming using the energy criterion. The latter provides to gain the minimum potential energy of deformation of the designed element.Research findings: The proposed methodology allows evaluating the results obtained. The numerical experiment determines the optimum cross-section geometry of flexural thread. The spread in values between proposed methodology and finite element method are insignificant.Practical implications: The proposed method provides the solution of inverse problems in a geometrically nonlinear formulation, including a search for optimum geometrical parameters of elements that combine the operation of beams and flexural thread. The proposed method can be used at the design stage of large-span shells of buildings.

Изгиб секторальной пластины: использование систем компьютерной алгебры

Purpose: To investigate the stress-strain state of a thin homogeneous isotropic plate in the form of a sector by numerical-analytical method. To consider the possibility of using computer algebra systems (CAS) to calculate sectoral plates operating under bending due to a transverse load. To demonstrate the effectiveness of applying one of these CASs through the example of the Maple system for calculations using the Ritz method — performing analytical transformations when calculating the integral that determines the total potential energy functional, forming and solving the main resolving system of linear algebraic equations with respect to unknown numerical coefficients in the formula approximating the deflection of the plate, visualization of the obtained solution. Methods: A direct method is used to solve the variational problem of minimizing the functional of the total potential energy of deformation of a thin homogeneous isotropic plate in the form of a sector — the Ritz method. The solution is constructed in the form of a series in terms of basis functions. As basis functions, polynomial functions are chosen that exactly satisfy all boundary conditions. Results: An approximate numerical-analytical solution has been obtained for the problem of bending a sectoral plate in the form of a quarter of a circle, clamped along the contour and loaded with a uniformly distributed load. The effectiveness of using the Maple analytical computing system for solving the problem of bending a sectoral plate by the variational Ritz method is demonstrated. It is shown that the resulting solution quickly converges both for deflection and for bending moments and stresses. Practical significance: The algorithm proposed in the article for solving the problems of bending sectoral plates can be recommended for practical use in determining the stress-strain state of such plates.

Numerical Simulation Study on Influence of a Structural Parameter of D Bolt, an Energy-Absorbing Rock Bolt, on its Stress Distribution

A D bolt, an energy-absorbing rock bolt, is a smooth steel bar with a number of anchors along its length. The anchors, which can be spaced evenly or unevenly along its length, are firmly fixed within a borehole using either cement grout or resin, while the smooth sections of the bolt between the anchors may freely deform in response to rock dilation. A series of numerical simulations have been conducted using the finite difference method to investigate the effects of D bolt on the displacement increase of rock mass around a roadway in comparison with normal fully encapsulated rebar. As a result, the displacement of 49 mm at the top of roadway roof in the D bolts supported model is much larger than 30.08 mm in the fully encapsulated rebar bolts supported model so that the former is capable of absorbing potential deformation energy of rock mass around a roadway to tolerate the large deformation of rock. Plans of spacing arrangement of D bolt’s anchor have a significant effect on stress redistribution of the bolt. The numerical simulation result shows that for the D bolt with its whole length of 2.4 m, the length of its exposed section of 0.1 m, and the 4 anchors with the length of 0.1 m, the maximum tensile stress of 3.25 GPa generated in the D bolt with the ratio of the spacing between anchors (RSA) of 30 : 40 : 50 : 70 is lower about 1.13–1.31 times than the other D bolts with different ratio of spacing, and the changing range of stress is also the smallest, where the ratio of 30 : 40 : 50 : 70 indicates a ratio of lengths of deformable sections which is determined by turns from the innermost section of rock mass around roadway to the outermost section of roadway space. This study demonstrates that it is reasonable to employ the RSA of D bolt which makes it bring out its energy-absorbing capability to the full.

Evaluation of the effectiveness of secondary support of haulage drifts based on a comparative analysis of the deformation characteristics of protective structures

The object of this study is the processes of managing the state of lateral rocks in the coal rock array with preparatory workings. The influence of deformation characteristics of the protective structures of the preparatory workings on the stability of lateral rocks in the coal rock array has been established. The stable state of the above-the-drift pillars of coal is provided within the deformation resource, which corresponds to the critical level of the specific potential energy of the deformation. The limits of the deformation resource are the range of change in the relative deformation of coal pillars 0.1≤λ≤0.25. When the critical level of the specific potential energy of deformation is passed, at λ˃0.25, there is a relative change in the volume of pillars δλ˃0,1, as a result of which their durability decreases and the state changes. Under such conditions, the residual strength of coal pillars is not enough to limit the movement of lateral rocks, which provokes their collapse. For protective structures made of crushed rock, within the established deformation resource of 0.4≤λ≤0.7, with an increase in static load and cross-sectional area, the specific potential energy of deformation decreases, simultaneously with the relative change in the volume of the embedded material. This is due to the compaction of the crushed rock and an increase in its strength. Regularities of change in the specific potential energy of deformation of protective structures have been established, which, under conditions of uniaxial compression, make it possible to assess, within the deformation resource, their stability. To ensure the stability of lateral rocks in the coal rock array and to preserve the operational condition of the preparatory workings, it is advisable to use protective structures made of crushed rock. This method will limit the movement of the roof and sole in the produced space and avoid collapses.

Applying conditional optimization to determine the allowable loads on flexurally rigid threads

Objective. Development of a methodology for determining the allowable loads on existing structural elements, the design model of which is a flexural-rigid thread, based on the requirements of strength and rigidity due to the changed operating conditions of structures.Method. This study is based on mathematical modeling of the problem of conditional optimization. The objective function is the total potential energy of deformation of a thread with some flexural rigidity. In this case, restrictions are imposed on strength, rigidity, and the condition of continuity of deformations. At the same time, to achieve this goal, the provisions of the strength of materials, as well as the apparatus of integral and differential calculation of functions of one or more variables, were used.Result. An assessment of the adequacy of the results obtained using the developed methodology was carried out. A numerical experiment was performed to determine the value of the allowable uniformly distributed load and the corresponding distribution of stresses and strains along the length of a thread of finite stiffness with given physical and geometric parameters. It has been established that the discrepancies in the values of the results obtained using the proposed modeling technology and the commercial computer-aided design and calculation system LIRA 10.8, implemented on the generally recognized finite element method, are no more than 5%.Conclusion. The developed technique allows setting and solving problems of determining the ultimate loads on flexural-rigid threads, based on the allowable stresses and strains, in contrast to existing commercial computer simulation systems that solve exclusively direct problems of determining the stress-strain state of various types of structures. It can be used at the stage of inspection of large-span coatings in the reconstruction of public buildings and engineering structures.

ОБҐРУНТУВАННЯ ЗАХОДІВ ЩОДО БЕЗПЕЧНОЇ РОЗРОБКИ КРУТИХ ВУГІЛЬНИХ ПЛАСТІВ

Purpose. Justification of measures regarding the safe development of steep coal seams to ensure the safe efficiency of coal mining and increase the safety of miners in deep coal mines. Methodology. In order to achieve the goal, laboratory studies of the deformation properties of protective constructions were carried out on the models subjected to uniaxial compression, and field studies of the stability of preparatory mining products with various methods of protection. Results. It was found that for coal cinders within the limits of the established deformation resource (0,10,25)) at the same time as their stiffness increases, the potential energy of deformation reaches a critical level, on which the short-term stability of protective constructions is realized. At the same time, there is a relative change in volume in the range of 0,05V0,1. With the increase in static use and the transition of the critical level of deformations, when 0,25 і V0,1, the loss of cylinder stability remains. For protective constructions made of crushed rock when they are uniaxially compressed, the change in the behavior of the deformed body is separated from the compaction of the primary material. Within the limits of the deformation resource (0,40,7), a relative change in the volume of crushed rock of 0,2V0,35 has been recorded. According to the number of sizes of such protective constructions, when the work of compression increases, the value of V decreases. At the same time, the bearing capacity of protective constructions increases. Scientific novelty. The deformation resource of protective constructions of preparatory mine workings determines the effectiveness of the protection method used. Within the limits of the deformation resource, a stable state of protective constructions is ensured, which operates under conditions of single-height compression until the critical level of the specific potential energy of deformations is reached. Practical significance. To ensure the stability of the pits in the coal-bearing massif and the operational condition of the prepared products in the mining areas, it is advisable to use partial or full laying of crushed rock or wooden chock with sleepers in the mined space.

ЗІСТАВЛЕННЯ ДЕФОРМАЦІЙНИХ ВЛАСТИВОСТЕЙ ОХОРОННИХ СПОРУД ПІДГОТОВЧИХ ГІРНИЧИХ ВИРОБОК

Purpose. Investigate and compare the deformation properties of protective structures in the form of coal pillars and structures made of crushed rock for a justified choice of the protection method, which can make it possible to ensure the stability of side rocks in the coal massif and preparatory works in the mining areas in the coal mine. Methodology. To achieve the goal, laboratory studies were performed on experimental samples subjected to uniaxial compression. For pillars, their thickness was changed, whereas for structures made of crushed rock the thickness of the rock layer was changed at a constant cross-sectional area. Results. As a result of the conducted research, the deformation properties of protective structures that were subjected to uniaxial compression have been determined. A 15% reduction in their stiffness was recorded for pillars, when their thickness h0 was two times changed, and for the external static load, which varied according to a linear dependence. Within the limits of the safe deformation resource, when the relative deformation is in the range of values 0.18≤λ≤0.23, the stability of the pillars and their bearing capacity is ensured. At the same time, the relative change in their volume should not exceed 7-9%. It has been established that exceeding the limit level of the specific potential energy of deformation by an average of 12-14% causes the destruction of coal pillars. For protective structures made of crushed rock with a relative volume change of 0.35≤δV≤0.28, the value of the compaction coefficient of the original material decreases from kcons = 1.5 to kcons = 1.42 with a simultaneous increase in the work of compression and an increase of more than 20% in the specific potential energy of deformation, thanks to which the rigidity of the embedded material and the bearing capacity of protective structures made of crushed rock are ensured. Scientific novelty. The regularities of formation of deformation properties of protective structures under conditions of uniaxial compression, taking into account the change in the specific potential energy of deformation and the relative change in their volume, have been established. Practical significance. In order to ensure the stability of side rocks in the coal massif and preparatory workings at excavation sites in the coal mine, the feasibility of using partial or complete paving of the produced space from crushed rock, which limits the movement of side rocks in the produced space, has been substantiated.

ДОСЛІДЖЕННЯ ПРОЦЕСІВ ДЕФОРМУВАННЯ ОХОРОННИХ СПОРУД ПІДГОТОВЧИХ ГІРНИЧИХ ВИРОБОК

Purpose. Research of deformation processes of protective structures of preparatory mine workings to ensure the stability of side rocks in the coal massif and preparatory workings in excavation areas in a coal mine. Methodology. To simulate the behavior of security structures under static load in laboratory conditions, experimental samples have been tested under conditions of uniaxial compression. Results. Rigid security structures (coal targets, BZBT bollards, cement blocks and cast strip) and flexible security structures (wooden bonfires and rolling bonfires made of wooden sleepers) have been considered. It has been established that under conditions of uniaxial compression of flexible security structures under the action of a static load, when the ratio of the potential energy of the change in shape Uф to the change in volume Uо is Uф/U0 ≤2.12, compaction of wooden structures (without loss of stability) and an increase in their bearing capacity, which makes it possible to limit the convergence of lateral rocks. For rigid protective structures, when Uф/U0 ≤4.1-6.5, there is a loss of stability of the supporting structures, a decrease in their bearing capacity, which eventually leads to the collapse of side rocks. The assessment of security structures in terms of stability, rigidity and bearing capacity should be based on the properties of the material of the supporting structures. Scientific novelty. Under the conditions of uniaxial compression, the functional dependence of the change in the specific potential energy of deformation of protective structures of preparatory mine workings on the coefficient of their transverse deformation has been established. Practical significance. To ensure the stability of side rocks in the coal massif during its unloading, it is advisable to use flexible protective structures.

STUDY OF THE BEHAVIOUR FOR THE WORK EQUIPMENT OF A FORKLIFT DURING THE WORKING PROCESS USING FINITE ELEMENT ANALYSIS

Industrial manipulators and robots play a very important role in the current process of advanced industrialization. The use of industrial robots has led to increased labor productivity, human replacement in hazardous work situations, increased product quality, rapid recovery of investment. Supple automation, the highest level of programmable automation, is organized into computer-driven production cells and serviced by one or more industrial robots. The transformation of production systems from the human-machine system to the human-robot-machine system has replaced the human in the process of performing dangerous or uncomfortable works. The diversity of definitions given to industrial robots and the lack of consensus on the notion of "industrial robot" is a premise for opening new horizons in trying to bring the machine closer to human perfection. The present paper aims to conduct a study of the behavior for the work equipment of a forklift during the work process. The tool used to conduct the study was finite element analysis using specialized Solid Edge software. A 3D model of the forklift's work equipment was introduced in Solid Edge and a dynamic analysis was performed, which led to the equipment's eigenmodes and eigenfrequencies. The displacement of the nodes of the structure in the first 10 eigenmodes of vibration and the potential deformation energy accumulated by the system were chosen for visualization, suggestive results and especially important for the specialists in the domain of construction equipments.

PARAMETERS RATIONALIZATION OF THE THIN-WALLED ANCHORED RETAINING WALLS

One of the priority areas of theoretical research in the field of building structures is to reduce their own weight at a given resource - rationalization. There is a certain number of building structures in which the form and nature of the external load are interdependent. The most striking representative are the structures that perceive lateral pressure from bulk material - retaining walls. From the above review of modern scientific research aimed at finding rational parameters of retaining walls, it follows that the authors, as a rule, describe the cantilever retaining wall by a finite number of parameters and the reduction of its own weight or cost of the structure was taken as the target function. In this case, the load on the structure does not change. The idea underlying this work is that the structure of the retaining wall and the soil backfill, which holds it, is considered as a single system. In this system, the configuration of the structure determines the nature and magnitude of lateral pressure distribution. The sequence of actions to solve the problem of searching for a rational configuration of the structure leads to the division of the curved foam wall into a finite number of linear sections. The anchor support is represented in the form of an additional concentrated force applied at the anchor fixing point. In the work the dependences between the attributes of the stress-strain state of the structure and the system of angles of inclination of the sections are constructed. The configuration of the anchor and retaining wall, which will minimize the potential deformation energy of the system, is found within the framework of the BEA method. Using the numerical output data, the validity of the proposed method is demonstrated. The realization of calculations is reduced to the search for the extremum of the objective function of n variables where the potential deformation energy acts as a functionb and the combination of angles of inclination of the system's breakdown sections as variables. The solution of the problem is implemented by the conjugate gradient method. as a result of calculations, an image of the structure is obtained that minimizes the introduced criterion. Keywords: retaining walls, deformation energy, curved surfaces, rationalization.

Оцінка міцності та надійності автотранспортних засобів

At present, the issue of ensuring the strength and reliability of wheeled vehicles, the creation of which requires compliance with all modern requirements, has not been fully resolved. In this regard, improving the methodology for assessing the strength and reliability of vehicles is an urgent task, the solution of which involves finding answers to the following questions: the choice of a rational version of the bearing system and economically sound profiles; selection of materials with appropriate physical and mechanical characteristics, etc. The choice of a rational variant of the load-bearing system of frame structures of vehicles requires a comparative assessment of possible options at all stages of design work. The load-bearing structures of vehicles are statically uncertain. Therefore, the process of assessing the strength and reliability of vehicles with different types of design schemes is a complex task, which today does not have a single methodological solution. In order to solve this problem, the model of the stress-strain state of the spatially loaded frame structure of the HESSTON S 125 solid fertilizer spreader is considered by a modified method of minimum potential deformation energy of structural structures using the Heaviside function. The frame is a welded load-bearing structure consisting of three longitudinal spars connected by a front beam and crossbars. Carrying out the correct and rational analysis of the stress-strain state of such a bearing system is possible only with the use of a modified method of minimum potential deformation energy. As a result of modeling, recommendations were obtained for the rational design of components and components of wheeled vehicles with increased reliability while reducing material consumption. Ultimately, this leads to an increase in their strength and reliability while reducing material consumption.

Решение задачи устойчивости оболочечных конструкций с применением тригонометрического и полиномиальных базисов

The application of Legendre polynomials as approximating functions to study the stability of shell structures is investigated. The shells in question are square in plan, made of steel and have an articulated fixed support. As a mathematical model for studying the stress-strain state of shells, the functional of the total potential energy of deformation is used, taking into account transverse shifts (Timoshenko-Reisner model). The stability of three structures of different geometries for different sets of approximating functions has been investigated. The results obtained are compared with similar results obtained using the trigonometric basis. The convergence of the bases for the considered structures is analyzed.