Distribution Of Tangential Stresses Research Articles

THE DETERMINATION OF THE OPTIMAL COMPOSITION OF AN ARBOLITE WALL PANEL USING MATHEMATICAL METHODS AND THE CALCULATION OF ITS STRESS STATE

In the article, the optimal composition of the arbolite mixture was determined using a preliminary mathematical method for the manufacture of wall panels. With the help of optimal compositions, wall panels were manufactured and its stress state under load was calculated. For the production of arbolite products, the advanced technology of pressed arbolite, manufactured by conveyor method, has been applied. Using the methods of mathematical planning of experiments, the optimal composition was determined – the ratio of rice husk and a multicomponent binder with high strength. A method for calculating the stress state of wall plates based on rice husk and its straw with an internal thermal insulation layer of class B1 arbolite has been developed. Formulas for determining the distribution of tangential stresses along the longitudinal axis of a wall panel along its thickness are obtained. Deviations of the wall plate under the action of an off-center longitudinal load are determined. An experimentally developed method for calculating wall plates has been tested and confirmed. Experimental data on the testing of wall panels based on rice husk and straw of natural size have shown sufficient reliability and adequacy. The water absorption of arbolite based on rice husk and multicomponent binder was 24%, and the thermal conductivity λ = 0.18-0.19 W/ (m·oC). The resulting arbolite has a frost resistance of 30-35 cycles.

Simplified Calculation of the Inertia Moment of the Cross Section of the Console under Loading

Introduction. Published studies on the rigidity of consoles under load focus on the issues of their deformation and destruction. Calculations of the inertia moment, fundamentally important characteristic of the strength of the rod, are described. However, the problem of significant time consumption for such calculations has not been solved. The presented study meets the lack. The objective of the work is to describe a new rapid method for analytical calculation of the shear stress distribution in the section of the console corresponding to the action of an external applied force. For the first time, tangential stresses are considered, and examples of calculating the inertia moment for two non-standard sections of the console are given in this context.Materials and Methods. To develop a new method, the console was presented as a pack of plates oriented parallel to the vector of external force. The source calculations were based on the scheme of a console beam with a dedicated plate. The deformation of the rod elements was modeled taking into account the effect of a uniform shear stress field in the plate section. To validate the simplified calculation of the inertia moment of the sections, schemes of a square, ellipse, triangle, hexagon, six-pointed star, and a figured cross were used. Analytical and mathematical research methods were applied, specifically, the Huygens–Steiner theorem.Results. A rapid valid method for calculating the inertia moment of the cross section of the console under loading has been developed. Its difference is the rejection of calculations for each section, taking into account the shape and other features. For any shape of the section, the beam is represented as a bundle of infinitely thin plates, their inertia moments are integrated, and a well-known solution for deflection of a thin plate is used. The method allows us to unambiguously show the distribution of tangential stresses at the end of the console, providing a given deflection, and tangential stresses are used for such solutions for the first time. Their profiles are obtained depending on the direction of the external applied force. Formulas for the inertia moments of complex sections — a six-pointed star and a figured cross — are derived for the first time. Each section is correlated with the stress distribution curve and its maximum value. This data is visualized in the form of diagrams. It is found that the inertia moment and the rigidity of the console do not change when the external applied force is rotated by 30° for a star-shaped section and by 45° for a square and a figured cross. In general, the tangent field depends on the geometry and on the orientation of the section relative to the external applied force.Discussion and Conclusion. The proposed simplified approach to calculating the inertia moment of the cross sections of the consoles makes it possible to uniquely determine the field of tangential stresses at the end, which provides the appropriate value of the external applied force for the given deflection. Engineers and mechanics can use the results of the presented work in the calculations and modeling of deformation of rod structural elements.

Detection method for contact stress distribution of tapered roller bearings

The axle box of high-speed train adopts double row tapered roller bearings as transmission parts, and the reliability of bearings directly affects the safety of train operation. Tapered roller bearings can withstand axial and radial loads, their service life being closely related to the distribution of contact stress. The test object is the axle box bearing of high-speed train. According to bearing’s structural characteristics, based on the digital speckle correlation method (DSCM) and machine vision, the contact stress distribution detection devices for rollers and complete sets of bearings are developed respectively and an effective detection method is proposed. The contact stress data of the bearing which has reached the service life and the new bearing under the condition of no lubrication and grease lubrication are collected and normalized. Through the geometric relationship, based on the measured data of the selected detection points, the normal and tangential contact stress distribution of the roller and raceway under different contact conditions is obtained by data fitting. The test can be used as an evaluation basis for the effectiveness of bearing modification and provide reference for bearing design.

Elastic-plastic response of tunnel in GZZ-based constitutive model

Investigating the stress redistribution characteristics after tunneling is critical for designing and constructing deeply buried tunnels. Three-dimensional stresses are more prominent in deep than in shallow tunnels, resulting in nonlinear strength. The generalized Zhang–Zhu (GZZ) criterion captures the nonlinear strength well. Therefore, this study established a 2D plane-strain numerical model using a GZZ-based constitutive model. The effects of the axial stress and rock properties on the stress redistribution and plastic zone are discussed. The initial axial stresses changed the axial stress distribution after excavation and had little effect on the radial and tangential stress distributions. The size of the plastic zone decreases with decreasing geological strength index and increasing rock mass mi . However, with increasing dilation coefficient, the stress distributions remained almost unchanged, whereas the radial deformation gradually increased.

Computational assessment of ratcheting in rail-wheel contact with solid contaminant

A numerical method for the fast evaluation of ratcheting in solid-contaminated contact between rollers was developed. The physical problem was simplified with a plane-strain half-infinite body, with a distribution of pressure and tangential stress on the contact surface obtained by considering the presence of evenly spaced solid contaminant particles between the contacting bodies. Such a distribution was obtained by an analytical method, which considered the material of the contacting bodies as linear elastic. The stresses under the contact surfaces were calculated using the Boussinesq-Cerruti model. Subsequently, the plastic strain accumulated in the roller after each application of the contact load was calculated by means of a non-linear kinematic-hardening constitutive law, also considering the effect of wear in removing material layers from the surface.First, the effects of the introduced approximations were evaluated. In particular, the error in calculating the plastic strain using contact load distributions from a theory based on linear elastic behavior was evaluated by comparison with the results of finite element models. Subsequently, the method was used to assess the experimental results of previously published studies on sand-contaminated contact between rail and wheel materials. Despite the approximations and indetermination of some model constants, the method was proven to be able to qualitatively explain many of the damage mechanisms related to the interaction of the contacting bodies with the contaminant particles.

КОНТАКТНАЯ ЗАДАЧА ДЛЯ НАКЛАДКИ, СЦЕПЛЕННОЙ С УПРУГОЙ ЧЕТВЕРТЬПЛОСКОСТЬЮ.

The paper considers the problem of contact between a pad attached to an elastic quarter-plane under the action of a horizontal force. The normal and shear stresses between the overlay and the quarter plane are determined. The problem is solved by B.N. Zhemochkin’s method by dividing the contact area into twenty sections. Results were obtained for changing the longitudinal force in the pad. It is shown that the presence of a quarter-plane edge introduces disturbances into the distribution of normal and tangential stresses in comparison with similar results for a half-plane. The results for the rigid overlay are shown separately. It is concluded that it is necessary to take into account bending moments when calculating linings.

Dynamic strength and full-field cracking behaviours of pre-cracked rocks under impact loads

The impact loads have a significant influence on the dynamic strength and cracking behaviours of pre-cracked rocks, which plays a key role in the stability and safety of rock engineering. In this study, impact tests were performed by using a split Hopkinson pressure bar (SHPB) in conjunction with the high-speed photography technique. The dynamic strength of pre-cracked rocks under different strain rates and flaw angles was analysed, and the full-field cracking behaviours were elucidated by the evolution of strain localization zones based on the digital image correlation (DIC) analysis. By means of discrete element method (DEM), the impact tests were numerically reproduced to study the strength enhancement and the cracking processes. The results illustrate that the increase in the strain rate and flaw angle would lead to the increasing dynamic strength, the change of tensile and shear crack number is consistent with the strength variation, implying that the microcracking processes has a significant influence on the rate dependency of dynamic strength. As for the cracking behaviours, the strain localization zones would form around the flaw, and the crack branching phenomenon could be witnessed in dynamic tests. Furthermore, the complexity of cracking patterns becomes larger with the increasing strain rate, while the samples with the large flaw angle are difficult to generate strain localization zones and macroscopic cracks. By using a DIC-based method to analyse the crack initiation mechanisms, three types of stress-induced cracks were identified, i.e., mode I, II, and mixed mode I/II cracks. Among these cracks, the mode II cracks are the dominate type of cracks. Based on the mathematical analysis of Griffith model, the combined action of the tangential stress distribution and sliding deformation might be the reason for the crack initiation, and the rate-dependent strength might be induced by the increase of the maximum tangential stress regarding external stress.

Coned disk spring with friction or restraint at its edges: Explicit solution and experimental study

The behavior of a coned disk spring can be significantly affected by friction or restraint, yet the existing theoretical solutions cannot fully capture these influences. The limitation is particularly problematic for analyzing the behavior of coned disk springs with bi-stability. This paper proposes an explicit solution that can predict the behavior of the coned disk spring under these boundary conditions. The solution considers detailed influences of friction and restraint at the edges of the coned disk spring on its moment equilibrium and location of the neutral fiber. The theoretical results are validated using existing literature, FE analysis, and a series of tests. The theoretical solution confirms that the friction force at the edge of the coned spring significantly affects the axial response of the spring but not its bending moment or distribution of tangential stress. The bending moment and overall behavior of the coned disk spring are, on the other hand, very sensitive to restraints in radial directions. The proposed explicit solution shows good accuracy for coned disk springs with restrained radial stretching and rotation. The solution is particularly useful for coned disk springs in multistable structures and metamaterials.

Distribution of tangential stresses and the value of the actual contact area along the length of the joints with tension, as a factor of their tightness

The aspects of the uneven distribution of tangential stresses and the actual contact area along the length of the joints with tension from the position of ensuring their tightness are considered. It is shown that the actual contact area is uneven and corresponds to the uneven distribution of tangential stresses. Keywords: tightness connection, tightness, contact zones, tangential stresses, actual contact area. kurnosov-ne@mail.ru

Analysis of the Magneto-Thermal Bidirectional Coupling Strength of Macro and Micro Integration for Self-Starting Permanent Magnet Hysteresis Synchronous Motors

High-speed permanent magnet synchronous motors (PMSMs) are usually started with the hybrid low-speed open-loop and high-speed closed-loop control mode. However, low-speed open-loop control produces large starting current, or even current overload, resulting in demagnetization and motor damage. Therefore, there is an urgent need to develop a high-speed permanent magnet synchronous motor with self-starting ability at low speed, that is, a permanent magnet hysteresis motor (PMHM). This paper takes the permanent magnet ring hysteresis column rotor structure as the research object. Firstly, the performance of this type of rotor is improved using the micro level of effective layer material AlNiCo, and the mechanical properties of AlNiCo are calculated. Secondly, based on the thick-walled cylinder theory, the analytical model for calculating the strength of the composite rotor considering the temperature effect is deduced, and the tangential and radial stress distribution for each part of the rotor under no-load and load conditions are obtained. Then, the electromagnetic losses and temperature field distribution of the rotor are obtained using the magneto-thermal bidirectional coupling finite element method. Finally, strength of the thermal rotor is analyzed by substituting the temperature rise curve function and AlNiCo parameters at the operating temperature. The comparison of the stress calculation results of the semi-analytical solution and the finite element method showed that the error between both of them is less than 5%, which verified that the semi-analytical solution can accurately analyze the thermal stress distribution of the rotor during high-speed rotation.

Analytical Modeling of Shrink-Fitted FGM Thick-Walled Cylinder

One off the most powerful assembly technique is the shrink-fitting process.It is found in many fields such us mechanics, petroleum, military industries as well as in nuclear power plants etc. This article developed an analytical formulation of shrink-fitted Functionally Graded Material axisymmetric thick-walled cylinder based on the linear plane elasticity theory. The stresses and displacement fields in the thick cylindrical shells are calculated using the laws of linear elasticity. The resulting displacements and stresses are analyzed, and particularly the residual contact pressure and her relationship with the interference values. The results show that the variation of the FGM material composition has a clear effect on the fit pressure in the intersection area of the two fitted cylinders. The value of this pressure affects the distribution of radial and tangential stresses in the FGM cylinder walls. Subsequently, we highlighted the influence of the interference value, on the residual contact pressure which increases with the increase of the interference value. The stresses are modeled for a case study using MATLAB software. keywords. shrink-fit, FGM, Interference, residual stress, Elasticity.

Cross-sectional performance prediction of metal tubes bending with tangential variable boosting based on parameters-weight-adaptive CNN

Metal bending tubes have been widely used in various fields owing to their excellent performance; however, bending defects significantly affect their quality. This study proposes a tangential variable boosting (TVB) scheme to reduce the severity of multiple defects generated during the rotary draw bending (RDB). The boosting pressure die is divided into several parts. Different process parameters were applied to the divided semi-parts based on the tangential stress distribution trend. To explore the effects of the TVB, a cross-sectional defect prediction method is proposed based on a parameter-weight-adaptive convolutional neural network (PWA-CNN). To validate the proposed prediction method, a dataset for training the prediction model was constructed using a series of numerical simulations of aluminum-alloy tubes. The prediction results of the PWA-CNN were then compared with those of the other CNNs and different weight assignment methods. The comparison results show that the PWA-CNN exhibits the best performance in predicting the tube cross-sectional distortion. Finally, the effects of the TVB on the forming quality of the bending tubes were obtained. A reasonable TVB is beneficial for reducing the wall-thinning and contour distortion ratios of the tubes and has a negligible effect on the short-axis variation rate.

Analytical Approach for Large Size Reinforced Square Hole With Rounded Corners in Orthotropic Circular Cylindrical Shells

Full field tangential stress distribution in a uniaxially loaded composite circular cylindrical shell with various laminate sequences with reinforced square hole with rounded corners is achieved and good agreement is obtained with finite element results. Available solution for stress distribution in an infinite plate with square hole under axial load is suitably modified with unknown coefficients in the power series of hole shape parameter, ε and curvature parameter, β (orthotropic plate solution + trigonometric terms as a function of πβ2 /2). The reinforcement thickness for a desired target SCF value (preferably 50% reduction) and region of reinforcement over the shell surface w.r.t hole centre for any combination of hole size, shell thickness and radius are arrived at by an empirical relation based on numerical analysis. Solution for shell with reinforced square hole with β ≤ 0.25 is arrived at by an iterative technique and further expressed and validated for large size reinforced holes for β ≤ 2.0.

COMPARATIVE ANALYSIS OF THE ANALYTICAL AND NUMERICAL METHODS FOR CALCULATING THE STRESS-STRAIN STATE OF THE NEAR-WELLBORE ZONE BASED ON THE ELASTIC MODEL TAKING INTO ACCOUNT THE MAIN STRUCTURAL ELEMENTS OF THE WELL

Link for citation: Popov S.N., Chernyshov S.E., Krivoshchekov S.N. Comparative analysis of the analytical and numerical methods for calculating the stress-strain state of the near-wellbore zone based on the elastic model taking into account the main structural elements of the well. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 5, рр.94-102. In Rus. The relevance of the research is caused by the scientific interest in calculating the near-wellbore zone stress-strain state to improve the development of oil and gas fields, to predict the casing stability and the safety of the cement stone. The main aim: based on a comparative analysis of the methods of analytical and numerical simulation of stress calculation near a vertical well using an elastic model, determine the distribution of radial and tangential stresses, compare the accuracy of their calculation by different methods and identify the advantages and disadvantages of each of them. Objects: near-wellbore zone of the terrigenous reservoir of the Achimov deposits of one of the fields of the Khanty-Mansiysk autonomous region. Methods: analytical and numerical finite element methods for stress-strain state calculating of the near-wellbore zone, taking into account the main structural elements of the well and using a linear elastic model. Results. The paper considers the analytical relationships used to calculate the radial and tangential stresses in the casing, cement stone and reservoir rock, as well as the equations used in numerical finite element modeling of stresses near a vertical well. The authors have developed a finite element scheme of the near-wellbore zone, including its main structural elements. The paper introduces the results of calculation of the main components of the stress tensor in the structural elements of the well depending on the radial coordinate for the bottom hole pressure of 20, 40 and 60 MPa. The authors carried out the comparative analysis of the stress calculations results by the methods used. It is shown that the largest discrepancy between the analytical and numerical methods was 2 % that corresponds to radial stresses for the calculation option with a bottom hole pressure of 20 MPa. On average, the discrepancies were: for radial stresses – 0,04 %, for tangential stresses – 0,72 %. It is concluded that when using the model of a linearly elastic medium and under boundary conditions in the form of fixing the model in the upper and lower parts along the normal to the surface, and also without taking into account the pressure distribution in the depression funnel of the model, it is sufficient to use the analytical method of calculation. If it is supposed to use combined boundary conditions, a poroelastic model, taking into account viscoplastic deformations, then it is most preferable to use the numerical simulation method.

Axisymmetric Thermoelastic Deformation of a Multilayer Foundation with Imperfect Thermal Contact of the Layers

An axisymmetric stationary problem of thermoelasticity for a multilayer foundation with imperfect thermal contact between the layers is solved by the method of compliance functions along with the Hankel transform. The recurrence relations are constructed for the auxiliary functions and the compliance functions of neighboring layers of the foundation. We analyze the influence of the coefficient of thermal resistance on the distribution of normal and tangential stresses and temperature at the points of the bottom boundary of the top layer for a two-layer foundation subjected to the action of thermal loads.

Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel

To study the stress distribution characteristics of surrounding rock and the spalling mechanism of deep hard rock tunnels with different arch heights, the complex variable function and angle-preserving transformation method in elasticity theory were applied to the analytic solution of tangential stress distribution of arch tunnels during stress adjustment. In addition, true triaxial tests were conducted on granite cube specimens (100 mm × 100 mm × 100 mm) containing holes with three arch heights (including the 25 mm semi-circular arch, 16.7 mm three-centered arch, 12.5 mm three-centered arch) to simulate the spalling process under different initial ground stresses. The stress distribution solution and experimental results show that the initial failure stress of arch holes is 0.39–0.48 times the uniaxial compressive strength (UCS) of the rock. The initial failure location occurs at the arch foot, where tangential stress maximizes. When the lateral pressure coefficient is in the range of 0.38–0.50, the tangential stress is 3.2–3.5 times the UCS. The rock debris of the hole wall are in thin flake shapes. Symmetrical V-shaped or curved failure zones occurred on hole sidewalls. The stress distribution resolution of the surrounding rock of tunnels with different arch heights shows that with the increasing burial depth, the bearing performance of the semi-circular arch tunnel is optimal. In addition, the maximum tangential stress increases as the height of the arch decreases or the lateral stress increases, making it easier for the initial failure to occur at the foot of the arch.

Numerical and experimental study of the viscosity and mechanical parameters effect on tow feeding quality during automated fiber placement

For automated fiber placement (AFP), it is crucial to research the contact characteristics between tow and roller during the tow feeding process. However, it has not been widely explored. In this paper, a theoretical model of contact characteristics for the tow feeding process is established by analyzing the distribution of normal stress, tangential stress, adhesion zone, and slip zone, respectively. The model proposed a numerical algorithm for calculating the contact characteristic. Then the contact characteristic of the tow feeding system can be acquired and validated by the experiment and finite element method. The model that provides theoretical support for AFP optimization. Furthermore, proper pressure (P = 0.6Mpa) and tension (T = 3 N) for towpreg feeding under experimental conditions were obtained.

Study on the global stress field of the rock mass under compression and shear considering three kinds of crack parameters

AbstractThe mechanical behavior of the cracked rock mass is controlled by the crack initiation and propagation under compression and shear. The key to predicting the wing crack initiation angle is to correctly describe the distribution of the stress field at the crack tip. First, the previous studies are reviewed, and their inadequacies are discussed in detail. Next, according to the experimental results, three kinds of crack parameters (i.e., geometry, strength, and deformation) are introduced, and a stress transfer model on the crack face under compression and shear considering crack parameters is proposed. Then, the relevant formulae of stress intensity factors (KI and KII) and non‐singular term (T‐stress) at the crack tip are obtained. Finally, the proposed model is verified by other researchers' test results, and the effects of three kinds of crack parameters and the rock property on the distribution of tangential stress at the crack tip are discussed.

MODEL OF PLASTIC DEFORMATION OF POLYMER MATERIAL

The article considers a model of plastic deformation of polymer material in the inter-roll space of the processing equipment under conditions of compression and shear, based on which it is established that the all-round pressure created in the polymer by the working bodies of the processing equipment causes only viscoelastic deformation, and therefore plastic compaction of the material in the process of its destruction does not occur. Numerical modeling of the plastic deformation of polymer waste between the rolls of the Relo profile made it possible to obtain the distribution of tangential stresses on the plane of the polymer material, based on which graphical dependences of the stress on the rate of deformation, which is determined by the circular speeds and radii of the rolls, are constructed.

The onset of unstable fracture and crack deflection of AA7085 in mixed mode I + II loading

The current study focuses on the planar mixed mode fracture of AA7085. A loading device based on the concept given by Richard et al. has been developed for inducing planar mode-mixity in compact tension and shear (CTS) specimens. The CTS specimens extracted from the AA 7085 plate were subjected to mixed mode quasi-static loading after pre-cracking the specimens by fatigue loading under mode-I conditions. The desired pre-cracking length was achieved after performing an extended finite element method (XFEM) based fatigue crack growth simulation. Different mode-mixity has been introduced in the specimens by changing the orientation of the loading device with respect to the loading axis of the machine. Experimentally observed crack deflection was compared with the angles predicted by different planar mixed mode fracture criteria, namely MTS, Richards, and strain energy density. Equivalent stress intensity factors proposed at the onset of unstable fracture have been determined using different criteria and compared with each other. A new equivalent stress intensity factor for mixed mode has been proposed from Shah's equation of fracture locus. It has been found that the equivalent stress intensity factor based on Shah's equation of fracture locus is suitable for the alloy being investigated. The fracture morphology of the fractured specimen was inspected in a field emission scanning electron microscope. Both inter-granular and dimpled ductile fracture was observed in the specimens irrespective of the mode-mixity. Extended finite element simulation was performed to determine tangential stress distribution at a distance around the crack tip.