scholarly journals Неупругое растяжение медного однопроволочного проводника при неограниченных местных деформациях и положительной температуре

2021 ◽  
Vol 91 (6) ◽  
pp. 946
Author(s):  
А.И. Недобитков ◽  
Б.М. Абдеев
Keyword(s):  
Mathematical Model ◽  
Electron Microscope ◽  
Nonlinear Problem ◽  
Strain State ◽  
Mechanical Forces ◽  
Neck Formation ◽  
Stress Strain ◽  
Single Wire ◽  
Copper Conductor ◽  
The Mathematical Model

Results of experimental and desktop studies of the single-wire copper conductor deformation under the overcurrent action are given in the article. The conductor was studied using the JSM-6390L reflection electron microscope. A mathematical model of the stress-strain state of the copper bar in tension and under a temperature below 700 °С has been developed on the basis of the classical nonlinear problem of the structural mechanics. The mechanical forces in a single-wire copper conductor, which cause neck formation during overcurrent flow, have been determined. The mathematical model has been simplified to simple analytical dependences providing their use in forensic fire and technical investigations.

scholarly journals VALIDATION OF THE MATHEMATICAL MODEL OF FRAME CONSTRUCTION STRESS-STRAIN STATE

2015 ◽  
pp. 107-111
Author(s):  
V. V. Piven ◽  
G. E. Bityukov
Keyword(s):  
Mathematical Model ◽  
Strain State ◽  
Block Diagram ◽  
Stress Strain ◽  
Rheological Models ◽  
Stress Strain State ◽  
Spatial Beam ◽  
Frame Construction ◽  
Construction Optimization ◽  
The Mathematical Model

The problem of optimization of the stress-strain state of spatial beam structures with incorporation on elasto-visco-plastic base was reviewed. The rheological models of bases were analyzed. A block diagram of the mathemati-cal model of the construction optimization was developed. The objective function for optimization was defined.

scholarly journals OPTIMIZATION OF THE FLOOR STRUCTURE OF AN INDUSTRIAL BUILDING

2020 ◽  
pp. 26-32
Author(s):  
A. Yur'ev ◽  
L. Panchenko ◽  
I. Seryh ◽  
E. Chernysheva
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Strain State ◽  
Theoretical Calculations ◽  
Elastic Base ◽  
Industrial Building ◽  
Stress Strain ◽  
Stress Strain State ◽  
The Mathematical Model ◽  
Simplified Form

When determining the design of the floor, choosing materials and technology of its device, it is advisable to apply a systematic approach that takes into account its stress-strain state. The physical model of the floor of an industrial building in a simplified form is represented as a two-layer slab on an elastic base. The physical model of the floor of an industrial building in a simplified form is represented as a two-layer slab on an elastic base. The deformation of the ground base is inherent in the stress-strain state of the structure, which is manifested through geometric and mechanical characteristics, boundary conditions., glass fiber concrete is proposed as a coating material. It provides the compressive strength inherent in concrete and a proper crack resistance. The mathematical model is based on the S. Germain equation and the Winkler dependence. When solving the optimization problem in a linear elastic formulation, the criterion of the minimum potential energy of deformation is used, which leads to a minimum of material consumption. Its effectiveness is confirmed by comparing the results on a variational basis with the analysis of the regression equation. The modulus of longitudinal elasticity and the thickness of the layer are accepted as variable parameters. The calculation procedure uses a finite-difference analog of the mathematical model. A two-factor experiment is conducted to complete the study, the results of which are in good agreement with the theoretical calculations performed.

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 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 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.

Establishment of Flow Stress Model of EW75 Alloy

2013 ◽  
Vol 423-426 ◽  
pp. 241-246
Author(s):  
Ming Long Ma ◽  
Kui Zhang
Keyword(s):  
Mathematical Model ◽  
Flow Stress ◽  
Magnesium Alloy ◽  
Strain Rate ◽  
Strain Rate Range ◽  
Strain Rates ◽  
Stress Strain ◽  
Deformation Degree ◽  
Maximum Deformation ◽  
The Mathematical Model

The behavior evolvement of Mg-7.22Gd-4.84Y-1.26Nd-0.58Zr (EW75) magnesium alloy during the hot deformation process was discussed. The flow stress behavior of magnesium alloy over the strain rate range 0.002s-1to 2s-1and the temperature range 623K to 773K had been researched on Gleeble-1500D hot simulator under the maximum deformation degree 60%. A mathematical model was established to predict the stress-strain curves of this alloy during deformation. The experimental results showed that the stress-strain curves were obviously affected by the strain rates and deformation temperatures. The mathematical model could predict the stress-strain curves when the strain rates were under 0.2-1, but there was significant error in some of stress-strain curves when the strain-rate was 2-1by the reason of deformation temperature rising.

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