MATHEMATICAL MODEL OF THE STRESS-STRAIN STATE OF AN ELASTIC CYLINDRICAL BODY WITH A POROUS FILLER

Introduction. For the purposes of this article, geodeformation processes mean processes associated with deformations arising from the movement of species and blocks of the lithosphere at various depths, including surfaces. The objective is to reconstruct geodynamic stress fields, which cause modern shifts and deformations in the Lithosphere. A mathematical model and software for estimating the stress-strain state of the Earth Lithosphere are considered. Materials and Methods.For mathematical modeling of stresses, isostatically reduced data on abnormal gravitation field were used. The methods of continuum mechanics and methods of the theory of differential equations were used to design a model for estimating the stressstrain state of the Earth Lithosphere. For processing input, intermediate and outcoming data, the Fourier transform method of spectral analysis for constructing grid functions and spectral-temporal method were used. To model for the stress-strain state of the Lithosphere globally, stress calculation was corrected on the basis of sputnik-derived velocity data at the surface of the earth crust. The data on the rates of horizontal and vertical movements at the surface of the Earth crust were processed to obtain a distribution of velocities in the uniform grid embracing longitudes and latitudes. The processing procedure was carried out on the basis of the Kraiging method. The software was developed in Borland Delphi 7.0 programming environment. Results. Based on the data on the abnormal gravitation field in isostatic reduction and information on the distribution of velocities of horizontal motions on the surface of the Earth crust, a mathematical model of the stress-strain state of the Lithosphere was constructed. With the help of the obtained mathematical model and software complex, the stress-strain state of the Lithosphere was calculated at various depth using elastic and elastic-viscous models, and maps of equipotential distribution of shear elastic-viscous deformations in the lithosphere at the depth of 10 km were constructed. Discussion and Conclusion. The presented mathematical model and software allow restoring fields of both elastic and elastic-viscous deformations that is fundamental for quantification of elastic-viscous shear stresses deep in the Earth Lithosphere.

Download Full-text

A BEM-based mathematical model of the human cornea stress-strain state

10.1063/1.5135125 ◽

2019 ◽

Author(s):

N. A. Babailov ◽

A. E. Bogachev ◽

S. A. Korotkih ◽

O. A. Nefedova ◽

L. F. Spevak

Keyword(s):

Mathematical Model ◽

Strain State ◽

Human Cornea ◽

Stress Strain ◽

Stress Strain State

Download Full-text

Stress-strain state of ship hull structures restored using polymer coating

MORSKIE INTELLEKTUAL`NYE TEHNOLOGII ◽

10.37220/mit.2021.51.1.001 ◽

2021 ◽

pp. 12-17

Author(s):

С.И. Корягин ◽

О.В. Шарков ◽

Н.Л. Великанов

Keyword(s):

Mathematical Model ◽

Polymer Coating ◽

Strain State ◽

Metal Layer ◽

Adhesive Layer ◽

Metal Structure ◽

Polymer Coatings ◽

Calculation Algorithm ◽

Stress Strain ◽

Stress Strain State

Применение полимерных покрытий для ремонта корпусных конструкций выдвигает как актуальную задачу определения прочностных характеристик конструкций с покрытиями. Наличие отверстий, сквозной коррозии, являющихся концентраторами напряжений, делает эти места наиболее опасными, с точки зрения потери прочности, герметичности. Чаще всего разрушение происходит по адгезионному слою. Представлена математическая модель, учитывающая сосредоточенные усилия на концах адгезионного слоя композиционной конструкции типа «металл-покрытие». Проведены расчеты нормальных и касательных напряжений. Наибольшие значения напряжений в полимерном покрытии получены на кромке отверстия в слое металла. В результате анализа установлено, что увеличение перекрытия полимерным покрытием контура отверстия и удаленность от контура отверстия приводят к существенному уменьшению величин напряжений. Разработанная математическая модель и алгоритм вычислений позволяют расчетным путем определить напряженно-деформированное состояние металлической конструкции с отверстием и полимерным покрытием. The use of polymer coatings for the repair of hull structures puts forward as an urgent task to determine the strength characteristics of structures with coatings. The presence of holes, through corrosion, which are stress concentrators, makes these places the most dangerous, in terms of loss of strength, tightness. Most often, the destruction occurs along the adhesive layer. A mathematical model is presented that takes into account the concentrated forces at the ends of the adhesive layer of a composite structure of the "metal-coating" type. Calculations of normal and tangential stresses are performed. The highest stress values in the polymer coating are obtained at the edge of the hole in the metal layer. As a result of the analysis, it was found that an increase in the overlap of the polymer coating of the hole contour and the distance from the hole contour lead to a significant decrease in stress values. The developed mathematical model and calculation algorithm allow calculating the stress-strain state of a metal structure with a hole and a polymer coating.

Download Full-text

Mathematical model of the stress-strain state of a rod with an inhomogeneous layered structure

Bulletin of the National Engineering Academy of the Republic of Kazakhstan ◽

10.47533/2020.1606-146x.113 ◽

2021 ◽

Vol 82 (4) ◽

pp. 14-22

Author(s):

S. M. Akhmetov ◽

◽

M. T. Userbayev ◽

Zh. U. Iklasova ◽

A. B. Bolatova ◽

...

Keyword(s):

Mathematical Model ◽

Layered Structure ◽

Strain State ◽

Stress Strain ◽

Stress Strain State ◽

Current State ◽

Tension And Compression ◽

The Difference ◽

State Of Research ◽

Wooden Structures

The stress-strain state (SSS) of a rod with an inhomogeneous layered structure is considered. On the basis of a brief review and analysis of the current state of research of rod systems, the relevance of the study of the SSS of layered-heterogeneous wooden structures is substantiated, taking into account the presence of different resistance of layers to tension and compression. On this basis, the authors solve the problem of determining the SSS of layered-heterogeneous wooden rods in creep conditions, where factors such as humidity and temperature, as well as the difference in the resistance of wood layers to stretching and compression are taken into account. When solving the problem, the mechanical-sorption creep of wood is also taken into account.

Download Full-text

Visualization of the Stress-Strain State of Shell Structures Using Virtual and Augmented Reality Technologies

10.51130/graphicon-2020-2-3-13 ◽

2020 ◽

pp. paper13-1-paper13-12

Author(s):

Alexey Semenov ◽

Iurii Zgoda

Keyword(s):

Mathematical Model ◽

Thin Shell ◽

Strain State ◽

Interactive Visualization ◽

Analysis Data ◽

Shell Structures ◽

Stress Strain ◽

Heat Maps ◽

Visualization Module ◽

Stress Strain State

The paper describes a mathematical model of changes in the geometry of thin-shell structures for visualization of the analysis data on their stress-strain state (SSS). Based on this mathematical model, a visualization module for shell SSS visualization using VR and AR technologies was developed. The interactive visualization environment Unity 2019.3 and C# programming language were used. The interactive visualization module makes a 3D image of a shell structure and visualizes the SSS either through heat maps over the shell or through the changes in the shell geometry on the basis of the shell type, its geometric characteristics, and SSS analysis data (transferred to the visualization module by means of a JSON file). While working on the visualization module, the authors developed a system of components that makes it possible to visualize any 3D surface with coordinate axes (including numbers with a pitch determined automatically), visualize heat maps with a graduated scale, visualize a mesh over the graph to improve the perception of the surface deformations. The middle surface can also be deformed on the basis of SSS analysis data. This solution increases the efficiency of the work of specialists in civil engineering and architecture and can be used when training specialists in courses on thin-shell structures and procedural geometry.

Download Full-text

INVESTIGATION OF STRESS-STRAIN STATE OF CYLINDRICAL BODY OF MODIFIED HDPE

IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENIY KHIMIYA KHIMICHESKAYA TEKHNOLOGIYA ◽

10.6060/ivkkt.20196207.5845 ◽

2019 ◽

Vol 62 (7) ◽

pp. 118-122

Author(s):

Stepan V. Litvinov ◽

Lyubov I. Lesniak ◽

Serdar B. Yazyev ◽

Ivan M. Zotov

Keyword(s):

Ionizing Radiation ◽

Strain State ◽

Polymeric Materials ◽

Cylindrical Body ◽

Rheological Parameters ◽

Scientific School ◽

Mechanical Parameters ◽

Principal Stresses ◽

Stress Strain ◽

Stress Strain State

The change in the stress-strain state over time in structures and their elements from polymeric materials can be quite substantial. This is due to the pronounced rheology of the polymers. One of the most accurate laws of stress-strain bond is generalized nonlinear Maxwell-Gurevich equation, which takes into account three rheological parameters: the modulus of elasticity, the velocity modulus and the coefficient of initial relaxation viscosity. A significant influence on the physico-mechanical parameters of the polymer is also exerted by various factors: the presence of a temperature field and ionizing radiation, the presence of additives in the polymer and so on. The paper presents the results of mathematical modeling of a disc made of high-density polyethylene (HDPE) in an axisymmetric setting under the influence of mechanical axial pressure. This model is chosen because of the most frequent use of HDPE irradiated and with additives in medicine, including for the manufacture of orthopedic prostheses. Different compositions of HDPE are considered: under the influence of ionizing radiation, with additives of hydroxyapatite and with their combined effect. All physico-mechanical parameters of HDPE (dose of ionizing radiation and the fraction of hydroxyapatite injected) are described by mathematical expressions obtained in the scientific school of Professor B.M. Yazyev on the basis of an analysis of the corresponding polymer relaxation curves. The results of the solution of the problem have shown that the basic stresses (radial, circumferential and axial) vary in the course of time in different ways. The growth of the value of the primary basic stresses can be 2-2.5 times. If the analysis is carried out on the main stresses, then their value increases by approximately 1.5 times. Also, the change in the principal stresses is observed even when it is not observed for the basic stresses.

Download Full-text

Mathematical model of a micromechanical accelerometer with temperature influences, dynamic effects, and the thermoelastic stress-strain state taken into account

Gyroscopy and Navigation ◽

10.1134/s2075108710010086 ◽

2010 ◽

Vol 1 (1) ◽

pp. 52-61 ◽

Cited By ~ 3

Author(s):

M. A. Barulina ◽

V. E. Dzhashitov ◽

V. M. Pankratov ◽

M. A. Kalinin ◽

A. A. Papko

Keyword(s):

Mathematical Model ◽

Strain State ◽

Thermoelastic Stress ◽

Dynamic Effects ◽

Stress Strain ◽

Stress Strain State ◽

Micromechanical Accelerometer

Download Full-text

MATHEMATICAL MODEL OF THE SOIL STRESS-STRAIN STATE IN THE PROCESS OF ITS INTERACTION WITH THE WORKING BODIES OF THE DIGGING MACHINE

Forestry Engineering Journal ◽

10.34220/issn.2222-7962/2019.2/17 ◽

2019 ◽

Vol 9 (2) ◽

pp. 157-163

Author(s):

Ольга Дорняк ◽

Olga Dornyak ◽

Михаил Драпалюк ◽

Mikhail Drapalyuk ◽

Игорь Казаков ◽

...

Keyword(s):

Mathematical Model ◽

Strain State ◽

Stress Strain ◽

Stress Strain State ◽

Soil Stress ◽

Working Bodies

Download Full-text

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

System technologies ◽

10.34185/1562-9945-3-122-2019-06 ◽

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.

Download Full-text