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

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.

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 Mathematical Models and Evaluation Software for Stress-Strain State of the Earth’s Lithosphere

2019 ◽  
pp. 51-66
Author(s):  
Alexander O. Faddeev ◽  
Svetlana A. Pavlova ◽  
Tatiana M. Nevdakh
Keyword(s):  
Mathematical Model ◽  
Strain State ◽  
Uniform Grid ◽  
Shear Stresses ◽  
Stress Strain ◽  
Gravitation Field ◽  
Vertical Movements ◽  
Stress Strain State ◽  
The Earth ◽  
Viscous Shear

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.

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

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

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

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.

scholarly journals Mathematical modeling of stress-strain state of elements of joints of wooden structures on glued fiberglass washers

2021 ◽  
Vol 2131 (3) ◽  
pp. 032095
Author(s):  
M V Ariskin ◽  
D O Martyshkin ◽  
I V Vanin
Keyword(s):  
Mathematical Modeling ◽  
Bearing Capacity ◽  
Strain State ◽  
Single Component ◽  
Stress Strain ◽  
Design Models ◽  
Stress Strain State ◽  
Deformed State ◽  
Wooden Structures

Abstract Design models of single-component and three-component samples were developed on glued fiberglass washers in order to investigate the stress-strain state (SF) of the elements of joints of wooden structures. The picture and the nature of the actual stressed-deformed state of the wooden element with glued washers are obtained. Quite high bearing capacity of wooden structures connection is shown.

scholarly journals Consideration of the loading of the traffic lines in the design of automobile roads

2021 ◽  
Vol 274 ◽  
pp. 02009
Author(s):  
Denis Nikolenko ◽  
Maxim Nikolenko ◽  
Anastasiya Filippova
Keyword(s):  
Traffic Flow ◽  
Strain State ◽  
Dynamic Deformation ◽  
Uneven Distribution ◽  
Stress Strain ◽  
Stress Strain State ◽  
Freight Traffic ◽  
Design Solutions ◽  
The Difference ◽  
Strength And Durability

The article focuses on the importance of the strength and durability of highways due to the projected increase in freight traffic. It also describes the consequences of uneven distribution of loads in traffic lanes, depending on the prevailing traffic in each lane. The studies, that were carried out earlier by various scientists, were taken into account, thankfully to which results were obtained on the composition of the traffic flow, the difference in the loading of road pavements, as well as the stress-strain state of road structures. As a result, a model that reflects the dependence of the influence of the speed of movement of vehicles on the dynamic deformation of structures, was developed. Consequently, a number of design solutions were established to ensure the required strength of all structures.

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

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.

scholarly journals Influence of house bearing construction rigidi-ty of precast reinforced concrete on stress-strain state Continuous Flight Auger (CFA) piles foundations

2020 ◽  
pp. 48-57
Author(s):  
Viktor Nosenko ◽  
Oleg Krivenko
Keyword(s):  
Reinforced Concrete ◽  
Strain State ◽  
Residential Buildings ◽  
Precast Concrete ◽  
Relative Deformation ◽  
Construction Time ◽  
Stress Strain ◽  
Stress Strain State ◽  
Basement Floor ◽  
The Difference

At present, the tendency to build multi-storey residential buildings has become widespread in Ukraine. This is due to a number of reasons: significant increase in land prices in cities, dense urban development and the availability of appropriate equipment for the construction of such structures. One of the most common materials for multi-storey buildings is monolithic reinforced concrete. The main advantage of monolithic structures is the possibility of free spatial planning and the possibility of uniform redistribution of forces in the elements of the frame - the house works as one rigid entire structure. On the other hand, such structures require a long construction time and appropriate highly qualified control of monolithic works. Therefore, as an alternative, prefabricated reinforced concrete structures are used to accelerate the pace of construction. In this work, the influence of the rigidity of a precast reinforced concrete house on the stress-strain state of CFA piles foundation is investigated. The stress-strain state of a precast reinforced concrete building with two basement options is analyzed: precast and monolithic.                                                 The numerical modeling of the interaction of the system elements is used as a research method: soil base - foundation - aboveground structure. It was found that the replacement in a prefabricated house only one basement floor of precast concrete on a monolithic one affects the redistribution of forces, so the self-supporting wall is loaded 2.6 times, and the busiest wall, which rests on both sides of the floor slab, is unloaded to 2.1 times.  It was found that in the case of a basement made of precast reinforced concrete with a precast basement the difference efforts in pile heads (under the load-bearing walls) can differ 1.98 times, and in the case of a monolithic one 1.17 times. So it is mean, the monolithic foundation redistributed of efforts between the piles is more uniform. It is established that the monolithic reinforced concrete basement, in comparison with the prefabricated one, reduces the uneven settlement of the foundation by 2.4 times. When designing large-panel houses, it is advisable to provide a basement floor monolithic - this will allow to load the fundamental constructions more evenly, which in its reduction reduces the relative deformation of buildings and reduces their cost.

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