Computing Stress-Strain State of a Workpiece During Drawing with Wall Thinning Through a Die with a Small Taper Angle

2019 ◽  
pp. 71-86
Author(s):  
P.M. Vinnik ◽  
E.Yu. Remshev ◽  
E.V. Zaterukha ◽  
D.S. Filin
Keyword(s):  
Strain State ◽  
Tool Path ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Taper Angle ◽  
Stress Strain State ◽  
Wall Thinning ◽  
Deformation Stages ◽  
Toroidal Coordinates ◽  
Final Operation

The paper considers computing the stress-strain state of a workpiece during drawing with wall thinning through a die with a small taper angle. A manufacturing process for a sleeve usually includes several drawing operations, whereas recommendations for the final drawing operation are a low extent of deformation and using dies with a small taper angle of (2°--4°). We present a diagram for drawing with wall thinning, delineating all deformation stages recorded on the chart showing force as a function of tool path. We computed the stress-strain state and deformation in the workpiece wall during the final operation of drawing through a die with a small taper angle α ≤ 4°. We provide equilibrium equations in toroidal coordinates and compute stress-strain state parameters and extents of deformation for the axisymmetric problem statement. No longer assuming a plane strain state, we compute the stress-strain state and extent of deformation in the workpiece wall during drawing with wall thinning through a die with a small taper angle α = 2°--4°. We show that at the stage when intermediate product walls are formed, for a small taper angle it is reasonable to consider the process of drawing with wall thinning to be monotone.

Determination and prediction of the stress-strain state of pipeline, taking into account soil changes during operation

2020 ◽  
Vol 10 (4) ◽  
pp. 372-378
Author(s):  
Aydar К. Gumerov ◽  
◽  
Rinat M. Karimov ◽  
Robert М. Askarov ◽  
Khiramagomed Sh. Shamilov ◽  
...  
Keyword(s):  
Strain State ◽  
Mathematical Framework ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Optimal Method ◽  
Initial Stress State ◽  
Soil Response ◽  
Stress Strain State ◽  
Support Reaction ◽  
Key Factor

The key factor determining the strength, reliability, service life and fail-safe operation of the main pipeline is its stress-strain state. The purpose of this article is to develop a mathematical framework and methodology for calculating the stress-strain state of a pipeline section laid in complex geotechnical conditions, taking into account all planned and altitude changes and impacts at various points of operation, as well as during repair and after its completion. The mathematical framework is based on differential equations reflecting the equilibrium state of the pipeline, taking into account the features of the sections (configuration, size, initial stress state, acting forces, temperature conditions, interaction with soil, supports, and pipe layers). The equilibrium equations are drawn up in a curvilinear coordinate system – the same one that is used for in-pipe diagnostics. According to the results of the solution, all stress components are determined at each point both along the length of the pipeline and along the circumference of any section. At the same time, transverse and longitudinal forces, bending moments, shearing forces, pipeline displacements relative to the ground and soil response to displacements are determined. As an example, a solution is given using the developed mathematical framework. During the course of calculation, the places where the lower form of the pipe does not touch the ground and the places where the support reaction becomes higher than a predetermined limit are determined. A comparative analysis was accomplished, and the optimal method for section repair has been selected.

scholarly journals PECULIARITIES OF MODELING OF STRESS-STRAIN STATE OF PIPELINES THROUGH WHICH GAS-LIQUID MIXTURES WITH AGGRESSIVE COMPONENTS ARE TRANSPORTED

2019 ◽  
pp. 128-135
Author(s):  
A. P. Oliinyk ◽  
B. S. Nezamay ◽  
L. I. Feshanych
Keyword(s):  
Internal Pressure ◽  
Cross Sections ◽  
Strain State ◽  
Smoothing Splines ◽  
Liquid Mixtures ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Stress Strain State ◽  
Current State ◽  
The Given

The task of estimating the stress-strain state of pipelines through which gas-liquid mixtures with aggressive components are transported is considered, the purpose, object and object of research are established. The analysis of the current state of scientific and technical researches on the given subject is carried out, the circle of unresolved problems is revealed. The combined effect on the pipelines through which gas-liquid mixtures with aggressive components are transported stress – strained state change  is estimated by two models - the model for determining the change of the stress-strain state of the pipeline by data on the surface points certain set displacement   taking into account the quasi-stationarity of the process. The device uses interpolation smoothing splines and methods of differential geometry, 6 components of strain and stress tensors are determined. In order to substantiate the method of estimation of annular stresses at the wear of the pipeline walls due to the action of the aggressive components of the transported mixtures, systems of equilibrium equations for pipeline sections and for quasi-rectilinear sections with altered cross-section configuration have been derived. Boundaryt conditions for equilibrium equations are established. Calculation formulas for estimation of annular stresses arising under the action of internal pressure for sections with shape defects caused by the action of aggressive components are established. The results of calculations that allow to quantify the change of the most significant ring stresses arising in the pipeline material under the action of internal pressure in the pipeline cross sections, which were exposed to the aggressive components, are presented. It is assumed that the deformed sections are little different from the shape of the circle.

scholarly journals STRESS-STRAIN STATE IN BOUNDARY LAYER OF THE CIRCULAR PLATES WITH VARIOUS THICKNESSES BASED ON THE REFINED THEORY

2020 ◽  
Vol 82 (1) ◽  
pp. 32-42
Author(s):  
Val.V. Firsanov ◽  
Q.H. Doan ◽  
N.D. Tran
Keyword(s):  
Boundary Layer ◽  
Stress State ◽  
Strain State ◽  
Three Dimensional ◽  
Refined Theory ◽  
Circular Plates ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Stress Strain State ◽  
Three Dimensional Elasticity

A variant of the refined theory on calculation of the stress-strain state of circular plates with symmetrically various thicknesses according to an arbitrary law in the radial direction was presented. Equations of the plate state were established by using the three-dimensional elasticity theory. The required displacements were approximately calculated according to upright direction to the middle plane by polynomials with two degrees higher than in the classical Kirchhoff - Love theory. The differential equation at equilibrium in displacements with various coefficients was obtained by using means of the Lagrange variational principle. The direct integration of the equilibrium equations in the three-dimensional elasticity theory was used to determine the transverse normal and shear stresses. Of an isotropic circular plate with changing in thickness by using the analyzing Fourier chain, the obtained differential equilibrium equations in displacements with variable coefficients containing supplement components and taking into account of the effect of thickness on the stress-strain state of the plate. Examples of calculating the stress state of a circular plate with a thickness varying according to linear and parabolic laws under the action of a uniformly distributed load were considered. The limited difference method was employed to solve the boundary value problem. Comparison results of the refined and classical theories were investigated. It is demonstrated that the study on the stress state in the zones of its distortion (compounds, local loading zones, etc.) should use a refined theory, since the additional corresponding stresses of the “boundary layer” type are of the same order with the values of the main (internal) stress state. This is important to increase the reliability of strength calculations of such elements of aircraft-rocket structures as the power housings of aircraft, their various transition zones and connections, as well as objects in various engineering industries.

scholarly journals Mathematical model of the stress-strain state of belt with the load of tubular belt conveyer

2019 ◽  
Vol 3 (122) ◽  
pp. 42-54
Author(s):  
Ruslan Vissarionovych Kyriia ◽  
Hryhorii Ivanovych Larionov ◽  
Mykola Hryhorovych Larionov
Keyword(s):  
Mathematical Model ◽  
Strain State ◽  
Order Differential Equation ◽  
Limit State ◽  
Conveyor Belt ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Stress Strain State ◽  
Bulk Load ◽  
Belt Conveyors

The article developed a mathematical model of the stress-strain state of a tubular conveyor belt filled with bulk load. In this case, the belt is considered as a thin elastic inextensible cylindrical shell, and the bulk load in the belt is in the limit state. A system of differential equilibrium equations for a tubular belt with a bulk load with respect to forces and bending moments in a belt was obtained, which, when simplified, was reduced to a fourth-order differential equation for belt deflections. Based on this mathematical model, analytical dependencies of the deflections of the tubular conveyor belt on the parameters of the conveyor, the radius and properties of the belt, as well as the properties of the bulk load are obtained and analyzed. As a result, the maximum allowable distance between the roller supports of the tubular conveyor is determined. It was found that the allowable distance between the roller bearings is directly proportional to the tension of the belt and inversely proportional to the square of the radius of the belt and the bulk weight of the load. The research results can be used in the design of tubular belt conveyors transporting bulk load.

scholarly journals Behavior of solution of the elasticity problem for a radial inhomogeneous cylinder with small thickness

2021 ◽  
Vol 6 (7 (114)) ◽  
Author(s):  
Natik Akhmedov ◽  
Sevda Akbarova
Keyword(s):  
Boundary Layer ◽  
Lateral Surface ◽  
Strain State ◽  
Theory Of Elasticity ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Small Thickness ◽  
Homogeneous Solutions ◽  
Stress Strain State ◽  
Inhomogeneous Cylinder

A non-axisymmetric problem of the theory of elasticity for a radial inhomogeneous cylinder of small thickness is studied. It is assumed that the elastic moduli are arbitrary positive piecewise continuous functions of a variable along the radius. Using the method of asymptotic integration of the equations of the theory of elasticity, based on three iterative processes, a qualitative analysis of the stress-strain state of a radial inhomogeneous cylinder is carried out. On the basis of the first iterative process of the method of asymptotic integration of the equations of the theory of elasticity, particular solutions of the equilibrium equations are constructed in the case when a smooth load is specified on the lateral surface of the cylinder. An algorithm for constructing partial solutions of the equilibrium equations for special types of loads, the lateral surface of which is loaded by forces polynomially dependent on the axial coordinate, is carried out. Homogeneous solutions are constructed, i.e., any solutions of the equilibrium equations that satisfy the condition of the absence of stresses on the lateral surfaces. It is shown that homogeneous solutions are composed of three types: penetrating solutions, solutions of the simple edge effect type, and boundary layer solutions. The nature of the stress-strain state is established. It is found that the penetrating solution and solutions having the character of the edge effect determine the internal stress-strain state of a radial inhomogeneous cylinder. Solutions that have the character of a boundary layer are localized at the ends of the cylinder and exponentially decrease with distance from the ends. These solutions are absent in applied shell theories. Based on the obtained asymptotic expansions of homogeneous solutions, it is possible to carry out estimates to determine the range of applicability of existing applied theories for cylindrical shells. Based on the constructed solutions, it is possible to propose a new refined applied theory.

scholarly journals Strength of thin-walled elastic building structures

2021 ◽  
Vol 274 ◽  
pp. 03019
Author(s):  
Lilya Kharasova
Keyword(s):  
Boundary Conditions ◽  
Strain State ◽  
Holomorphic Functions ◽  
Integral Representations ◽  
Nonlinear Operator Equation ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Stress Strain State ◽  
Generalized Displacements ◽  
Thin Walled

The existence theorem is proved within the framework of the shear model by S.P. Timoshenko. The stress-strain state of elastic inhomogeneous isotropic shallow thin-walled shell constructions is studied. The stress-strain state of shell constructions is described by a system of the five equilibrium equations and by the five static boundary conditions with respect to generalized displacements. The aim of the work is to find generalized displacements from a system of equilibrium equations that satisfy given static boundary conditions. The research is based on integral representations for generalized displacements containing arbitrary holomorphic functions. Holomorphic functions are found so that the generalized displacements should satisfy five static boundary conditions. The integral representations constructed this way allow to obtain a nonlinear operator equation. The solvability of the nonlinear equation is established with the use of contraction mappings principle.

scholarly journals PECULIARITIES OF MODELING OF STRESS-STRAIN STATE OF PIPELINES THROUGH WHICH GAS-LIQUID MIXTURES WITH AGGRESSIVE COMPONENTS ARE TRANSPORTED

2019 ◽  
pp. 128-135
Author(s):  
A. P. Oliinyk ◽  
B. S. Nezamay ◽  
L. I. Feshanych
Keyword(s):  
Internal Pressure ◽  
Cross Sections ◽  
Strain State ◽  
Smoothing Splines ◽  
Liquid Mixtures ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Stress Strain State ◽  
Current State ◽  
The Given

The task of estimating the stress-strain state of pipelines through which gas-liquid mixtures with aggressive components are transported is considered, the purpose, object and object of research are established. The analysis of the current state of scientific and technical researches on the given subject is carried out, the circle of unresolved problems is revealed. The combined effect on the pipelines through which gas-liquid mixtures with aggressive components are transported stress – strained state change  is estimated by two models - the model for determining the change of the stress-strain state of the pipeline by data on the surface points certain set displacement   taking into account the quasi-stationarity of the process. The device uses interpolation smoothing splines and methods of differential geometry, 6 components of strain and stress tensors are determined. In order to substantiate the method of estimation of annular stresses at the wear of the pipeline walls due to the action of the aggressive components of the transported mixtures, systems of equilibrium equations for pipeline sections and for quasi-rectilinear sections with altered cross-section configuration have been derived. Boundaryt conditions for equilibrium equations are established. Calculation formulas for estimation of annular stresses arising under the action of internal pressure for sections with shape defects caused by the action of aggressive components are established. The results of calculations that allow to quantify the change of the most significant ring stresses arising in the pipeline material under the action of internal pressure in the pipeline cross sections, which were exposed to the aggressive components, are presented. It is assumed that the deformed sections are little different from the shape of the circle.

КОНСТРУКТИВНО-ТЕХНОЛОГІЧНІ ОСОБЛИВОСТІ ХВОСТО-ВИХ БАЛОК СІТЧАСТОГО ТИПУ З ПОЛІМЕРНИХ КОМПО-ЗИЦІЙНИХ МАТЕРІАЛІВ ВЕРТОЛЬОТІВ ТРАНСПОРТНОЇ КАТЕГОРІЇ

2020 ◽  
pp. 15-30
Author(s):  
А. Г. Гребеников ◽  
И. В. Малков ◽  
В. А. Урбанович ◽  
Н. И. Москаленко ◽  
Д. С. Колодийчик
Keyword(s):  
Finite Element ◽  
Strain State ◽  
Layer Structure ◽  
Metal Structure ◽  
Element Model ◽  
Stress Strain ◽  
Element Analysis ◽  
Mesh Structure ◽  
Stress Strain State ◽  
Mesh Structures

The analysis of the design and technological features of the tail boom (ТB) of a helicopter made of polymer composite materials (PCM) is carried out.Three structural and technological concepts are distinguished - semi-monocoque (reinforced metal structure), monocoque (three-layer structure) and mesh-type structure. The high weight and economic efficiency of mesh structures is shown, which allows them to be used in aerospace engineering. The physicomechanical characteristics of the network structures are estimated and their uniqueness is shown. The use of mesh structures can reduce the weight of the product by a factor of two or more.The stress-strain state (SSS) of the proposed tail boom design is determined. The analysis of methods for calculating the characteristics of the total SSS of conical mesh shells is carried out. The design of the tail boom is presented, the design diagram of the tail boom of the transport category rotorcraft is developed. A finite element model was created using the Siemens NX 7.5 system. The calculation of the stress-strain state (SSS) of the HC of the helicopter was carried out on the basis of the developed structural scheme using the Advanced Simulation module of the Siemens NX 7.5 system. The main zones of probable fatigue failure of tail booms are determined. Finite Element Analysis (FEA) provides a theoretical basis for design decisions.Shown is the effect of the type of technological process selected for the production of the tail boom on the strength of the HB structure. The stability of the characteristics of the PCM tail boom largely depends on the extent to which its design is suitable for the use of mechanized and automated production processes.A method for the manufacture of a helicopter tail boom from PCM by the automated winding method is proposed. A variant of computer modeling of the tail boom of a mesh structure made of PCM is shown.The automated winding technology can be recommended for implementation in the design of the composite tail boom of the Mi-2 and Mi-8 helicopters.

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