scholarly journals Mathematical model of nonlinear deformation of three-layer shells

2020 ◽  
Vol 17 (3) ◽  
pp. 94-100
Author(s):  
V. V. Karpov ◽  
◽  
E. A. Kobelev ◽  
Keyword(s):  
Mathematical Model ◽  
Modulus Of Elasticity ◽  
Nonlinear Deformation ◽  
Single Layer ◽  
Geometrically Nonlinear ◽  
Elastic Shells ◽  
Arbitrary Type ◽  
Study Results ◽  
Thin Walled ◽  
The Given

The article presents the study results of geometrically nonlinear deformation of elastic shells of arbitrary type with consideration of transverse shifts. There is constructed a new mathematical model of nonlinear deformation of thin-walled elastic isotropic three-layer shells. Each layer of the shell is made of different materials, but with similar shear modules. The thickness of the layers can be different. Averaging of all three layers becomes possible, and deformation of a three-layer shell as a single-layer shell with the given characteristics of the modulus of elasticity and the Poisson's ratio can be considered.

scholarly journals Grapho-analytical studies of deformation in deformed thin-walled contours

2020 ◽  
Vol 23 (9) ◽  
pp. 7-11
Author(s):  
Bogdan Sheludchenko ◽  
Yaroslav Yarosh ◽  
Andrii Zabrodskyi ◽  
Andriy Kondratiuk ◽  
Victor Biletskiy ◽  
...  
Keyword(s):  
Elastic Shell ◽  
Operational Reliability ◽  
Analytical Models ◽  
Geometrical Parameters ◽  
Initial Shape ◽  
Operational Feature ◽  
Elastic Shells ◽  
Power Load ◽  
Thin Walled ◽  
The Given

Increasing the levels of operational reliability of technical means of modern production involves, in particular, the optimization of the deformation parameters of individual components of these tools. The main deformation-operational feature of such structures as elastic shells of the pneumatic periphery of mobile vehicles, and individual links of long-link cargo chains is a stochastic change of their shape in contact with the deformed environment. The basis for the optimization of the operational reliability of deformed thin-walled circuits of such structures under power load is to determine the ratios of their geometric parameters, in which the process of deformation under load does not transform their initial shape from “folded” (out-of-bounds) state to “foldless” state toroidal surfaces, which should be described using the Cassini family of ovals. Based on the established regularities of changing the configuration of the meridian of soft elastic shell and flat closed structures, which are deformed by external loads, three main conditions of using model typical contours of Cassini ovals as graph-analytical models of elastic shells of pneumatic mobile periphery chains. These conditions of graph-analytical modelling include: closedness and continuity of the curvature of the toroidal surface; generalization of the initial shape of the surfaces of toroidal contours; reduction of variable geometric shapes of contours to a single generalized equation. The results of the given grapho-analytical researches allow to define design structural and geometrical parameters of tires of engines of mobile means and separate links of cargo chains with the increased operational indicators of reliability of their work.

Validation of mathematical model of electrothermal calculation of DC catenary on the basis of scale model

2018 ◽  
Vol 77 (4) ◽  
pp. 222-229 ◽  
Author(s):  
A. V. Paranin ◽  
A. B. Batrashov
Keyword(s):  
Mathematical Model ◽  
Operating Conditions ◽  
Scale Model ◽  
Contact Network ◽  
Scaled Model ◽  
Cross Sectional ◽  
Current Collection ◽  
Topological Features ◽  
Study Results ◽  
Real Physical Process

The article compares the results of calculation of the finite element simulation of current and temperature distribution in the scale model of the DC catenary with the data of laboratory tests. Researches were carried on various versions of the structural design of catenary model, reflecting the topological features of the wire connection, characteristic of the DC contact network. The proportions of the cross-sectional area of the scaled model wires are comparable to each other with the corresponding values for real DC catenary. The article deals with the operating conditions of the catenary model in the modes of transit and current collection. When studying the operation of the scale catenary model in the transit mode, the effect of the structural elements on the current distribution and heating of the wires was obtained. Within the framework of the scale model, theoretical assumptions about the current overload of the supporting cable near the middle anchoring have been confirmed. In the current collection mode, the experimental dependences of the current in the transverse wires of the scale model are obtained from the coordinate of the current collection point. Using the model it was experimentally confirmed that in the section of the contact wire with local wear, not only the temperature rise occurs but also the current redistribution due to the smaller cross section. Thus, the current share in other longitudinal wires of the scale model increases and their temperature rises. Scale and mathematical models are constructed with allowance for laboratory clamps and supporting elements that participate in the removal of heat from the investigated wires. Obtained study results of the scale model allow to draw a conclusion about the adequacy of the mathematical model and its correspondence to the real physical process. These conclusions indicate the possibility of applying mathematical model for calculating real catenary, taking into account the uneven contact wear wire and the armature of the contact network.

scholarly journals Computer Modeling of Aerosol Emissions Spread in the Atmosphere

2019 ◽  
Vol 97 ◽  
pp. 05023 ◽  
Author(s):  
Daler Sharipov ◽  
Sharofiddin Aynakulov ◽  
Otabek Khafizov
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Atmospheric Boundary Layer ◽  
Computer Modeling ◽  
Numerical Experiments ◽  
Climatic Factors ◽  
Numerical Algorithms ◽  
Aerosol Emissions ◽  
The Given ◽  
And Diffusion

The paper deals with the development of mathematical model and numerical algorithms for solving the problem of transfer and diffusion of aerosol emissions in the atmospheric boundary layer. The model takes into account several significant parameters such as terrain relief, characteristics of underlying surface and weather-climatic factors. A series of numerical experiments were conducted based on the given model. The obtained results presented here show how these factors affect aerosol emissions spread in the atmosphere.

scholarly journals The possibilities of using group regression in the analysis of the diameter structure development in selection forests of Tara

2002 ◽  
pp. 79-89 ◽  
Author(s):  
Slobodanka Mitrovic ◽  
Stanisa Bankovic
Keyword(s):  
Mathematical Model ◽  
Future Development ◽  
Functional Dependence ◽  
Primary Objective ◽  
Structure Development ◽  
Study Results ◽  
The Future ◽  
Diameter Structure ◽  
Group Regression ◽  
Diameter Classes

Based on the presented study results, it can be concluded that the distribution of tree numbers per diameter degrees (diameter structure) in the four measurements of the compartments 51 and 75, did not change. It was also concluded that one functional dependence could be applied for both compartments N=e5,9?e?0,39*d The result of the above is that also in the following measurements, the diameter structure will remain unchanged, in cases of the same or similar selection cuttings both by the scope and by the distribution of felled trees per diameter classes The primary objective of this type of study is to predict, based on a mathematical model of diameter structure development, effect of the scope of selection cuttings and the number of recruitments on the diameter structure, and the simulation of growth, the distribution of trees per diameter classes in the following measurement or measurements, i.e. to foresee the future development of selection stands.

scholarly journals Mathematical Model to Optimize Production of Loading-Unloading Operations on the Vessel

2020 ◽  
pp. 29-30
Author(s):  
Ibraim Didmanidze ◽  
Givi Tsitskishvili
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Coming Out ◽  
Scientific Work ◽  
Equal Strength ◽  
Optimal Classification ◽  
A Priority ◽  
The Given

In scientific work it is shown, that our goal is to choose the desired option from variety of alternatives (in our case different options of loading-unloading operations on the vessel) or to take decision which is the best (optimal). Classification in this case is the grounds, as taking the choice is based on choosing certain class, which can be assigned to an alternative. Stratification and rating gives us wide option to make reasonable selection, or to take a kind of decision which will be optimal for the certain moment and occasion. These methods can be used with equal strength at all stages of the processes taking place in the area of current decision making management. This refers to the object of our study of course – solution of selecting optimal option to optimize loading-unloading operation on the vessel. It goes without saying that variety of alternatives doesn’t have any structure, thus abundance of each element was never structured randomly retrieved or no consideration has been proposed, and they are not a priority and in any order. Coming out of this it’s impossible to mention which alternative is better and which is less desirable. In order to solve the task of selecting a set of alternatives successfully, it is necessary, to make structure of the given abundance of alternatives in any form.

scholarly journals Time Coordination of Periodic Passenger Train Connections in Conditions of Single-Track Lines

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Filip Lorenz ◽  
Vit Janos ◽  
Dusan Teichmann ◽  
Michal Dorda
Keyword(s):  
Mathematical Model ◽  
Mathematical Programming ◽  
Real Data ◽  
Real Problem ◽  
Single Track ◽  
Railway Stations ◽  
Optimization Software ◽  
Proposed Model ◽  
The Individual ◽  
The Given

The article addresses creation of a mathematical model for a real problem regarding time coordination of periodic train connections operated on single-track lines. The individual train connections are dispatched with a predefined tact, and their arrivals at and departures to predefined railway stations (transfer nodes) need to be coordinated one another. In addition, because the train connections are operated on single-track lines, trains that pass each other in a predefined railway stations must be also coordinated. To optimize the process, mathematical programming methods are used. The presented article includes a mathematical model of the given task, and the proposed model is tested with real data. The calculation experiments were implemented using optimization software Xpress-IVE.

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