Parameters Of Stress-strain State Research Articles

Stress reindexation in coal seams when mining works cross zones of rupturing dislocations

A description of the stress state of the coal seam contained tectonic disturbance with closed edges is presented. The area of the disturbance is shown in the form of an elliptical inclusion and rupturing dislocation with displaced edges. Stress state is defined as a superposition of two solutions on the reference pressure of the coal seam and zone of rupturing dislocation. Changes in the stress-strain state parameters leads to reindexation of the axes with preserving their spatial orientation. This leads to changes in geomechanical state of the coal seams and properties of coal and adjoining rocks when approaching and passing through tectonic disturbances.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ РАСПРОСТРАНЕНИЯ ВИБРАЦИЙ В ТОНКОСТЕННЫХ КАРКАСИРОВАННЫХ КОНСТРУКЦИЯХ. 1. ОСНОВНЫЕ СООТНОШЕНИЯ И АНАЛИТИЧЕСКИЕ РЕШЕНИЯ ХАРАКТЕРНЫХ ЗАДАЧ

The design features of the of thin-walled aerospace, shipbuilding, etc. structures in the form of a load-bearing frame sheathed with thin-walled panels, walls, bulkheads, etc. are discussed. Variants of constructive coupling of the specified thin-walled panels with supporting elements of the load-bearing frame and methods for their mathematical description in the classical mechanics of a deformable solid body are considered. It is proposed, without distorting the physical picture of the dynamic behavior of thin-walled panels, to present them in the form of multisupport thin bars resting on rigid elements of the load-bearing frame along part of their front surface. By the example of a plane dynamic problem of the mechanics of a bar with a fixed section of finite length on one of the front surfaces, it is shown that in the study of deformation processes, taking into account the compliance of the fixed section, it is necessary to introduce the concept of transformation of the stress-strain state parameters and the mathematical models used to describe them. Such a transformation takes place when crossing the border from an unfixed section to a fixed one (from a fixed to an unfixed one). Within the framework of the classical Kirchhoff–Love model, it is impossible to take into account the compliance of the fixed section of the bar, and when using the simplest refined shear model of S.P. Timoshenko, such accounting is possible when fixing the length only on one of the front surfaces. In particular, previously discovered and not described in the scientific literature phenomenon of the vibrations transmission through the support joints, regardless of their design, is carried out due to the transformation of the stress-strain state of the dynamically loaded section of the bar into longitudinal-shear vibration modes of the bar in the clamped area, followed by their retransformation into bending vibrations of the adjacent span. Within the framework of S.P. Timoshenko model, the main resolving equations are constructed, and the kinematic and force conditions for conjugation of fixed and non-fixed sections of the bar are formulated. On the basis of the developed mathematical model, exact analytical solutions of typical problems are constructed, confirming the transmission of vibration through the clamped sections of the bar due to the deformability of the marked sections. A significant increase of transverse shear stresses level in the clamped section of the bar in the vicinity of the junction of the unfixed section with the fixed one is revealed.

Analysis of stress fields at the crack tip and fracture resistance parameters under conditions of gradient plasticity

This paper presents a numerical analysis based on previously obtained experimental data on crack growth for P2M and 34X steels, aluminum 7050 and titanium alloy Ti-6Al-4V compact samples (CTS) with a one-sided lateral incision, within the framework of the conventional theory of strain gradient plasticity (CMSG), based on the Taylor dislocation model. In this study, the initial points of the curved crack trajectory were considered for two classical states: plane strain and plane stress with normal separation and pure shear. The constitutional equations of material behavior for CMSGP theories were introduced into the finite element computational complex and new fields of stress-strain state parameters for the conditions of strain gradient plasticity were obtained. The results of FE calculations show a significant increase in the magnitude of the true stress fields at the crack tip, taking into account the plastic deformation gradients and the internal characteristic length of the material. The numerical results also show that the singularity in the crack tip region is different for the model of gradient plasticity of deformations and depends on the mode I/II. An important conclusion regarding the numerical results regarding the parameters of the material's fracture resistance is that the new plastic stress intensity coefficients for gradient plasticity differ for plane strain and plane stress, and also show significant sensitivity to the plastic properties of the material and to the scale parameter of the intrinsic material length, which is attractive from the point of view of practical application and further fundamental research.

Corrosion Fatigue Damages of Rebars under Loading in Time.

Nowadays, a relatively small number of studies concern the study of corrosion processes in reinforced concrete structures under load. Additionally, rather little research has been carried out concerning changes in the stress–strain state parameters of structures under the simultaneous action of aggressive environment and load. This issue requires additional experimental and theoretical investigation. Determination of mechanical properties, fatigue characteristics and susceptibility to corrosion cracking was performed on samples of reinforcing St3GPF steel. The chemical composition of steel was determined by structural analysis. The spectral method for the determination of alloying elements and impurities in steels is based on the excitation of iron atoms and admixtures by electric discharge, decomposition of radiation into a spectrum, followed by its registration on photoplate with the use of electrograph. Experimental tests of samples in an aggressive environment under the action of statically applied tensile force showed that corrosion damage has little effect on the strength characteristics. At the same time, the decrease in area reduction and the decrease in strain were recorded. Additionally, the action of cyclic loads in an aggressive environment leads to a significant reduction in the fatigue limit to values from 20 to 24% of the yield strength of the original samples, which is 2–3 times lower than the fatigue limit of undamaged samples.

Parametric investigations of strength of a composite panel after impact damage

Results of parametrical investigations of residual strength and buckling of damaged composite panels of civil aircrafts were considered. The investigations were performed on the base of the semi-empirical method developed by the author. The algorithm allows users to carry out the analysis of parameters of stress-strain state and to assess a general buckling behavior of composite panels in the automatic mode. The calculations were performed by using the special parametrical finite element models of composite panels that are typical for current civil aircrafts. The special models of panels consisted of composite laminated skin and different types of stiffeners have zones with reduced stiffness characteristics. The relationship between level of reducing mechanical characteristics of “damaged” zones and residual strength and buckling margins of the panels was determined.

Stress-Strain State of Elastic Plate with a Crack

The paper considers an infinite plate with a crack in the form of a narrow hole with a certain curvature at the tip of the crack. The stress-strain state parameters of this plate under uniaxial load are studied, such as the stress-concentration factor, crack-driving force, and elastic strain energy. Determined are the elastic energy consumption during the crack propagation, general laws of the mechanical state of the cracked plate, and curvature at the tip of the crack. It is shown that, in fact, the Griffith crack has no stress singularity at the end. The stress-strain state of the plate with an elliptical shaped crack is similar to that with a uniform plastic deformation zone.

Experimental assessment of solar radiation effect on the stress-strain state of a span with an orthotropic slab

The article is devoted to the experimental assessment of the solar radiation effect on the stress-strain state of a span with an orthotropic slab. Preliminary, comprehensive instrumental measurements of the road surface temperature distribution and the span elements were carried out at different times of the year. A detailed picture of the temperature distribution over the cross-section height was determined at different air temperatures and the Sun positions. To assess the solar radiation effect, instrumental measurements of deflections and deformations of the span‘s main beams under the influence of solar radiation were carried out and the nature of the change in the stress-strain state of the span during the day was determined. The measurements were carried out using the deflection meters and strain gauges mounted on the main beams that experience uneven heating throughout the day. Using the developed and previously tested finite element model, the calculated values of the span bearing elements‘ stress-strain state parameters for each case of exposure to solar radiation have been determined, taking into account the experimentally obtained temperatures. Comparison of the calculation results obtained on the basis of field measurements and calculation in the program of the finite element method has been carried out. The most unfavorable cases of the solar radiation effect on the main beams‘ displacement have been revealed.

Influencing of land transport load on structure of backfill arched Road Bridge

In this paper, for the objective assessment of stress-strain state parameters of backfill arched road bridge, the research work is carried out, where the model of reinforced concrete, corrugated structure is exposed to modern land transport load. In the course of numerical studies, stresses and deformations in sections of structure and the soil are determined. These studies allow revealing the mechanism of operation of corrugated reinforced concrete structures in the body of an embankment of highways when passing modern transport loads along with them.

Comparative Study of Superelastic Ti–Zr–Nb and Commercial VT6 Alloy Billets by QForm Simulation

A comparative simulation of hot radial shear rolling (RSR) of billets made of a superelastic Ti–Zr–Nb and a commercial VT6 alloy was performed using the QForm finite element modeling program. Rolling in 48 modes with a variable feed angle and elongation ratio at 4 levels and initial rolling temperature at 3 levels was investigated for each alloy. The Ti–Zr–Nb alloy rheology during hot deformation was determined experimentally by hot upset forging and imported into the QForm program. The presence of maxima on the flow curves at the initial stage of deformation, which are absent in the VT6 alloy, is revealed. Simulation results are presented in the form of fields of the stiffness coefficient, strain rate intensity, cumulative strain degree in the maximum reduction section depending on the rolling mode. General regularities of the Ti–Zr–Nb and VT6 behavior in RSR are similar. The gradient of the fields studied decreases, and the roll pressure and torque increase with an increase in the feed angle and elongation ratio. The initial rolling temperature does not significantly affect the deformation pattern, but it significantly affects the roll pressure and torque. At the same time, the experimental alloy demonstrated the greater tendency to localize deforming forces in the near-contact zone and to increase the gradient of stress-strain state parameters over the billet section. The study of the tightening shape and depth of rolled billet ends showed that the Ti–Zr–Nb alloy has a 3.5–9.6% greater tightening depth. It is shown that experimental alloy rolling requires 1.6–2.4 times higher roll pressure and torque as compared to the commercial alloy.

Study of stress-strain state of cold-drawn hexagonal steel rods

The results of the stress-strain state during drawing of hexagonal steel rods are presented. The effect of the drawing die angle and the degree of reduction on the distribution of the stress-strain state parameters and the elastic aftereffect of the deformed metal is studied.

К анализу чувствительности нестационарных откликов конечно-элементных моделей балочных конструкций

This paper discusses optimal design of structures in terms of various quality criteria with limitations for the parameters of dynamic stress-strain state (steady, unsteady, spectral). Efficiency of the methods based on the compliance with indirect optimality criteria, in particular, on the Kuhn-Tucker conditions, considerably depends on fast and accurate calculations of derivatives for the parameters of state in terms of design parameters, which is achieved by obtaining the analytical expressions. Introduction of these expressions to the optimization of FEM-based models is only possible if structural design parameters and the parameters of stiffness matrix and element masses are linked explicitly. The purpose of this work is to finalize and verify the methods for obtaining analytical derivatives of design parameters as functions of vibration frequencies, forced harmonic vibration frequencies and natural vibration frequencies of finite-element model with subsequent transition to completely analytical (not subtractive) differentiation of unsteady and spectral responses of design parameters. For an FE model of beam with a large number (one hundred) of finite elements, this study obtained and verified, for various boundary conditions and loading scenarios, the distributions of sensitivity coefficients for steady dynamic parameters in terms of design parameters, i.e. cross-sections of elements.

Comparative study of superelastic Ti–Zr–Nb and commercial VT6 alloy billets by QForm simulation

A comparative simulation of hot radial shear rolling (RSR) of billets made of a superelastic Ti–Zr–Nb and a commercial VT6 alloy was performed using the QForm finite element modeling program. Rolling in 48 modes with a variable feed angle and elongation ratio at 4 levels and initial rolling temperature at 3 levels was investigated for each alloy. The Ti–Zr–Nb alloy rheology during hot deformation was determined experimentally by hot upset forging and imported into the QForm program. The presence of maxima on the flow curves at the initial stage of deformation, which are absent in the VT6 alloy, is revealed. Simulation results are presented in the form of fields of the stiffness coefficient, strain rate intensity, cumulative strain degree in the maximum reduction section depending on the rolling mode. General regularities of the Ti–Zr–Nb and VT6 behavior in RSR are similar. The gradient of the fields studied decreases, and the roll pressure and torque increase with an increase in the feed angle and elongation ratio. The initial rolling temperature does not significantly affect the deformation pattern, but it significantly affects the roll pressure and torque. At the same time, the experimental alloy demonstrated the greater tendency to localize deforming forces in the near-contact zone and to increase the gradient of stress-strain state parameters over the billet section. The study of the tightening shape and depth of rolled billet ends showed that the Ti–Zr–Nb alloy has a 3.5–9.6 % greater tightening depth. It is shown that experimental alloy rolling requires 1.6–2.4 times higher roll pressure and torque as compared to the commercial alloy.

DEPENDENCE OF STRAIN-DEFORMED STATE OF FOUNDATIONS AND BASES DURING THEIR RESTORATION ON THE BASIS OF GROUT-INJECTED PILE TECHNOLOGY

Purpose. To obtain the dependences of the stress-strain state (SSS) of foundations and bases during their restoration on the basis of grout-injected piles for further analysis of the influence of the location of reinforcement elements. Methodology. To determine the SSS parameters and to obtain its dependencies in the foundations and bases during their restoration based on grout-injected piles, a case without reinforcement (option 0) and three options for its reinforcement (Option 1, Option 2 and Option 3) were selected. Reinforcement was carried out with 4 m long soil-cement piles with a diameter of 0.5 m, created on the basis of grout-injected pile technology. Corresponding finite element models have been developed for four options. Their numerical analysis was carried out using a professional licensed SCAD complex. Findings. Contours and isofields of displacements in the models are obtained. The error between analytical calculation and numerical analysis is 3%, which indicates the adequacy of the developed model. The constructed dependences of the stress-strain state of foundations and bases during their restoration based on grout-injected piles indicate that the option that minimizes the level of displacements is Option 1. Analysis of vertical displacements proves that they decrease 2.05 times at the center point of the foundation (option 1), 1.87 times (option 2) and 1.59 times (option 3). Analytical patterns of the stress state show a steady drop in horizontal stresses by 2.77 times (option 1), 1.80 times (option 2) and 1.09 times (option 3) and a steady increase in vertical stresses by 6.20 times (option 1), 4.06 times (option 2) and 1.38 times (option 3). Originality. It lays in obtaining the dependencies of restoring the structures of foundations and bases based on grout-injected piles based on the numerical analysis of the stress-strain state of the “foundation-base” system. Practical value. It consists of the substantiation of the change in the stress-strain state with a variation in the location of the restoration elements created on the basis of grout-injected piles technology.

GENERAL FUNDAMENTALS OF REINFORCED CONCRETE ELEMENTS AND STRUCTURES DEFORMATION MECHANICS

This article presents a critical development analysis of the general deformation theory and models of reinforced concrete elements and structures resistance to force effects. Their relationship with the defining provisions of the mechanics of reinforced concrete elements and structures deformation is estimated. The main disadvantages of the considered models are established. General provisions of the mechanics of reinforced concrete elements and structures deformation are proposed to be developed on the basis of a universal deformation-force model. It is noted that the latter is devoid of most of the shortcomings characteristic to other models. The main advantage of the deformation-force model is indicated, associated with the expansion of the well-known system of static, geometric and physical relationships to the level of statically definable. It becomes especially noticeable when calculating reinforced concrete elements and structures for deflections and crack resistance. One of the main features of the deformation-force model is emphasized, which makes it possible to quite simply «embed» or integrate the technical theory of reinforcement to concrete adhesion into the general theory of reinforced concrete deformation. Through the averaged design section and average deformations of materials in the block between adjacent cracks, all parameters of the normal cracks formation and opening in the deformation-force model are directly related to the parameters of reinforcement to concrete adhesion.The effectiveness of using the deformation-force model of reinforced concrete to force effects resistance was evaluated by a statistical comparison of theoretical calculations with the reinforced concrete elements experimental studies results tested by different authors. Similar comparisons were made for the methods of the current standards. It was confirmed that the priority in the accuracy of assessing the reinforced concrete elements stress-strain state parameters belongs to the calculation method, which is based on the deformation-force model of reinforced concrete resistance.

Finite element modelling reinforced concrete beam in transverse bending zone

The article presents methods and results of studying the stress-strain state of a reinforced concrete beam in its area of transverse bending, using the finite element models. The advantage of the finite element modelling method is relative simplicity of mechanical and physical interpretation of the finite element models. Herein, we present a description of finite element model and the method for numerical investigation during its loading and evaluation of the stress-strain state. Testing of the finite element models were performed using different lengths of shear span, taking into account the inelastic properties of concrete. During the models’ tests, the process of cracks formation and development was studied while taking into account the bond of reinforcement to concrete, which changes in line with the adopted law. We also evaluated the parameters of stress-strain state of the beam blocks separated by cracks and the stressed state of concrete at the tip of an inclined crack, depending on the loading level. Based on the results of numerical experiment, we obtained distribution patterns of principal stresses for the concrete and those of shear stresses along the reinforcement and concrete contact surface, depending on the level of loading, the degree of bond failure and the length of shear span.

Improvement of the Device for Continuous Pressing of Non-Ferrous Metals and Alloys and Computer Simulation of the Deformation Process in This Device

A new design of the device for continuous pressing is proposed, which combines the principles of the ECAP and Linex processes. To assess the possibility of the process and the efficiency of metal processing, computer modeling was performed. It is found that the greatest load is received by the mobile segments that ensure the movement of metal through the matrix. The distribution of stress-strain state parameters in the longitudinal section of the workpiece is extremely uneven, which is due to the transverse action of the pulling force. In the first two channels, due to a backpressure the compressive stresses occur. In the output channel, the metal experiences tensile stresses.

The civil structures bearing capacity assessment for 150 m high reinforced concrete ventilation pipe based on the field and numerical surveys

In the paper the results of the building structures bearing capacity assessment are presented for a reinforced concrete ventilation pipe with a height of 150 m under seismic effects and tornado loads, taking into account the results of full-scale dynamic and instrumental building structures surveys, based on the linear and nonlinear spatial design models numerical studies.
 This goal was achieved by solving the following tasks:
 
 the vibrodynamic surveys execution;
 the concrete structures strength determination by an ultrasonic method;
 development of linear and nonlinear spatial design models of the pipe;
 the calculations of class F3 tornado effects and intensities 6 (MDE) and 7 (above MDE) seismic impacts.
 
 Based on the results of vibrodynamic surveys, the actual dynamic parameters of the ventilation pipe structures were determined (vibration modes, prevailing periods and frequencies during principal modes vibrations). Based on the results of structures instrumental studies by ultrasonic method, the actual characteristics of concrete structures strength are determined. The obtained field data were used in the development of the facility spatial design models.
 To determine the bearing capacity of structures, the models calculations were performed using the LIRA CAD software package, which is a computer system for structural analysis and design.
 The calculations were performed for the class F3 tornado loads, as well as the intensities 6 and 7 seismic effects determined by the spectral method. Additionally, the bearing capacity of facility reinforced concrete structures was assessed under extreme loads (intensity 7 seismic impacts and class F3 tornado) taking into account the concrete and reinforcement plastic properties. The structures non-linear static analysis (Pushover analysis) applied in the standards of Ukraine, the European Union, the USA and other countries for the assessment of the operating structures seismic resistance was used.
 Based on the results of the research, the reinforced concrete ventilation pipe structures stress-strain state parameters under the considered seismic and tornado loads were obtained and the recommendations were prepared to reduce the possible consequences of an intensity 7 earthquake and a class F3 tornado.

The civil structures bearing capacity assessment for 150 m high reinforced concrete ventilation pipe based on the field and numerical surveys

In the paper the results of the building structures bearing capacity assessment are presented for a reinforced concrete ventilation pipe with a height of 150 m under seismic effects and tornado loads, taking into account the results of full-scale dynamic and instrumental building structures surveys, based on the linear and nonlinear spatial design models numerical studies.
 This goal was achieved by solving the following tasks:
 
 the vibrodynamic surveys execution;
 the concrete structures strength determination by an ultrasonic method;
 development of linear and nonlinear spatial design models of the pipe;
 the calculations of class F3 tornado effects and intensities 6 (MDE) and 7 (above MDE) seismic impacts.
 
 Based on the results of vibrodynamic surveys, the actual dynamic parameters of the ventilation pipe structures were determined (vibration modes, prevailing periods and frequencies during principal modes vibrations). Based on the results of structures instrumental studies by ultrasonic method, the actual characteristics of concrete structures strength are determined. The obtained field data were used in the development of the facility spatial design models.
 To determine the bearing capacity of structures, the models calculations were performed using the LIRA CAD software package, which is a computer system for structural analysis and design.
 The calculations were performed for the class F3 tornado loads, as well as the intensities 6 and 7 seismic effects determined by the spectral method. Additionally, the bearing capacity of facility reinforced concrete structures was assessed under extreme loads (intensity 7 seismic impacts and class F3 tornado) taking into account the concrete and reinforcement plastic properties. The structures non-linear static analysis (Pushover analysis) applied in the standards of Ukraine, the European Union, the USA and other countries for the assessment of the operating structures seismic resistance was used.
 Based on the results of the research, the reinforced concrete ventilation pipe structures stress-strain state parameters under the considered seismic and tornado loads were obtained and the recommendations were prepared to reduce the possible consequences of an intensity 7 earthquake and a class F3 tornado.

Model for Layer-by-Layer Analysis of the Stress-Strain State of Three-Layer Irregular Shells of Revolution of Double Curvature

Based on the layer-by-layer analysis approach, the construction of a model of two types of finite elements (FE) of natural curvature (two-dimensional FE of the momentary bearing layers and three-dimensional FE of the filler) is considered for refined investigation of the stress-strain state (SSS) in layers of three-layer generally irregular shells of revolution of double curvature. The presented model-building algorithm allows one to avoid errors due to the discontinuity of generalized displacements on the docking surfaces of the FE of the bearing layers and the aggregate, to analyze the SSS for all three coordinates to which the shell is assigned, and to obtain a solution in an updated statement for various shell shapes and boundary conditions of the layers, as well as violations of their continuity. At the same time, the aggregate layer can be modeled in thickness by the required number of finite elements, which allows one to take into account the change in geometric characteristics, physical and mechanical properties, and SSS parameters not only in the meridional and circumferential coordinates, but also in the thickness of the shell and aggregate layer. The proposed approach significantly expands the range of problems solved in the refined formulation and allows us to carry out the calculation with a high degree of accuracy and detail. As an example, the calculation of the SSS of a three-layer animated casing with cut-outs is given. The influence of the size of the cut-outs on the stress – strain state in the layers of the three-layer shell of rotation of double curvature is studied.

Напряженно-деформированное состояние трубопровода под воздействием комбинированной нагрузки

Theoretical and experimental study of the stress-strain state of a pipeline under the influence of two types of loads was carried out: 1) bending force in vertical plane; 2) combined action of bending force in vertical plane and internal pressure. The experiments were performed on a pipe sample: steel grade Ст3, outside diameter 114 mm, wall thickness 4.5 mm, length 0.94 m. Hoop and longitudinal strains were measured in different areas of the pipe sample wall under the bending force in the vertical plane. To determine other parameters of the pipe stress-strain state the theories of thick-walled and thin-walled cylindrical shell, the Hooke’s law, the Zhuravsky–Vlasov formula for calculating the greatest shear stress in a circular tube, the principle of superposition were used. The distributions of the stress-strain state parameters (hoop, longitudinal, radial strains; hoop, longitudinal, shear stresses; von Mises stress) of the pipe sample wall around the perimeter of different pipe cross sections are found. It is revealed that hoop and shear stresses have a significant effect in the considered cases of loading. The values of hoop and shear stresses should be taken into account when calculating von Mises stress and assessing strength of the main pipeline according to the maximum-distortion-energy theory.