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 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.

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.

Improving Methods of Assessment of a Stress State of Structures According to the Results of Coercive Measurements

2018 ◽  
Vol 284 ◽  
pp. 1332-1336
Author(s):  
N.L. Zaytsev
Keyword(s):  
Stress State ◽  
Strain State ◽  
Steel Structures ◽  
Stress Strain ◽  
Stress Strain State ◽  
Assessment Of Stress

At the present time the assessment of stress-strain state of steel structures uses the results of coercive measurements. However, the methods presented in various works are contradictory and not deprived of errors of a methodological nature, which may lead to erroneous conclusions. This article reveals the analysis of disadvantages of the known methods and proposes possible ways to eliminate these shortcomings.

scholarly journals Stress-strain state of a composite near rectangular inclusion

2018 ◽  
Vol 243 ◽  
pp. 00021
Author(s):  
Pavel Pisarev ◽  
Aleksandr Anoshkin ◽  
Vladislav Ashihmin
Keyword(s):  
Numerical Simulations ◽  
Numerical Experiments ◽  
Strain State ◽  
Maximum Stress ◽  
Three Dimensional ◽  
Thermoplastic Composite ◽  
Model Construction ◽  
Stress Strain ◽  
Stress Strain State ◽  
Rectangular Inclusion

In this research we developed a technique for calculating the stress-strain state of a model construction from a thermoplastic composite material with an embedded piezoactuator. Numerical simulations of the model construction stress-strain state with different arrangement of piezoactuators: upper and middle,-were performed. Numerical simulations were carried out in a three-dimensional setting taking into account the complete technological scheme of laying and anisotropy of the properties of reinforcing layers. The results of numerical experiments revealed the areas of maximum stress. Recommendations for the MFC’s embedding into composite materials were formulated.

scholarly journals The stress-strain state of the foundation of various forms using the Kelvin equation

2015 ◽  
Vol 4 ◽  
pp. 4-6
Author(s):  
Pilyagin A.V.
Keyword(s):  
Stress State ◽  
Strain State ◽  
Ground Surface ◽  
Deep Foundations ◽  
Natural Basis ◽  
Stress Strain ◽  
Concentrated Force ◽  
Kelvin Equation ◽  
Large Depth ◽  
Stress Strain State

The article discusses the stress-strain state of Foundation of various forms. It is noted that for foundations on natural basis is traditionally used for the solution of Boussinesq (1885) about the force applied to the ground surface, i.сe. without taking into account the fact that the depth of the foundations, and the solution obtained Mindlin (1950) takes into account the fact that the depth of foundations, but does not consider the development of tensile stresses above the level of application of the load. The analysis of the Kelvin equation for concentrated force applied at an infinitely large depth. The analysis of the stress state of grounds for the buried foundations using solution of Kelvin indicates the possibility of its use in the case of the use of deep foundations.

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