Two-dimensional Statement Research Articles

Longitudinal wave propagation in an extended cylindrical body with external Coulomb friction

The propagation of elastic longitudinal waves in an extended cylindrical body located inside an unstrained body and interacting according to the Coulomb law is considered in the article. The problem is studied in a two-dimensional statement; therefore, the friction force (i.e., the interaction conditions) is included in the system of equations as a boundary condition. The Coulomb friction force arises due to the deformation of a cylindrical body. The reliability of numerical calculations is substantiated by solving test cases and comparing the calculations with experimental results. The numerical results obtained are presented in the form of graphs and analyzed. It is shown that the parameters (stresses and strains) of waves propagating in an elastic cylindrical body with external Coulomb dry friction decay with distance. The mechanism for reducing the stress-strain state and wave parameters is explained by the consumption of elastic energy to overcome the friction force that occurs on the contact surface. The results of the two-dimensional problem are also compared with the results of a similar problem in the one-dimensional theory, where the friction force enters directly into the equations of motion. The deviations of the results of the one-dimensional theory are up to 8-15% depending on the accepted values of the friction coefficient, i.e. the violation of the plane section hypothesis taken in one-dimensional calculations amounts to 15%. With a decrease in the radius of a cylindrical body, these deviations are reduced.

A reduced kinetic scheme for methyl methacrylate gas-phase combustion

Gas-phase combustion of methylmethacrylate (MMA) monomer is an essential stage of solid polymethylmethacrylate (PMMA) combustion, which is of interest in many applications. A skeletal kinetic scheme for MMA combustion in air is proposed including 44 irreversible elementary reactions for 29 species. The mechanism is derived from the reduced kinetic scheme for MMA oxidation comprised of 263 reactions for 66 components. In this work, the mechanism predictive capabilities are demonstrated by solving the self-ignition problem, as well as the premixed flame propagation problem for MMA-air mixtures. It is shown that the skeletal mechanism overpredicts the ignition delay times due to significant simplification of the MMA decomposition stage reaction pathways. The flame propagation speed is predicted reasonably for lean and nearly-stoichiometric mixtures, but overpredicted for fuel-rich mixtures. Also, a diffusion flame representing the cup burner of liquid MMA is simulated in two-dimensional statement of the problem, the results are shown to agree well with the measurements and numerical simulations performed earlier on the basis of a detailed kinetic scheme. The skeletal mechanism can be used in the numerical simulations of gas-phase combustion of MMA, including the problems of flame propagation over the solid PMMA polymer.

DETERMINATION OF KINEMATIC CHARACTERISTICS OF METAL PLASTIC FLOW UNDER CONDITIONS OF AXIAL SYMMETRY OF THE DEFORMATION PROCESS

With axisymmetric deformation, the deformable body and the load have a common axis of symmetry. Such deformation occurs in numerous technological operations. About 70% of parts obtained by cold extrusion are deformed under conditions of axial symmetry. The plane problem of the theory of plasticity is reduced to a solution in the framework of a two-dimensional statement, when the motion of points in the section of a workpiece is analyzed. Each point can move only in the section plane, and its velocity can be decomposed into two mutually perpendicular directions along the coordinate axes. For plane deformation, it is assumed that the velocity in the direction of the third coordinate axis is equal to zero. The presence of axial symmetry allows us to confine ourselves to studying the behavior of points located on the plane of the meridional section of the workpiece. In this case, each point can move only in the section plane and its velocity can be decomposed into two orthogonal directions: along the axis and along the radius. The component of the velocity vector in the circumferential direction is equal to zero, so only four of the six independent components of the strain rate tensor remain. In this regard, axisymmetric problems of the theory of plasticity are of considerable interest from the point of view of solving applied problems. The article discusses the possibility of using mixed Euler and Lagrange coordinates to determine the components of the strain rate tensor in plastic deformation processes characterized by the axisymmetric nature of metal plastic flow. The vector field of displacements at each point in space reflects the transformation of the initial (non-deformed) configuration into the current one, and therefore determines the configuration of the deformed body in space in a certain frame of reference. The deformation process is first considered in a single Cartesian coordinate system, and then in a cylindrical coordinate system, the use of which is more appropriate for axisymmetric deformation. It is assumed that the functions of the Euler coordinates from the Lagrange coordinates are obtained by approximating the experimental data.

Statement spectrum with two dimensional eigenvalues for intelligent software fault localization

The existing Software Fault Localization Frameworks (SFLF) based on program spectrum for estimation of statement suspiciousness have the problems that the feature type of the spectrum is single and the efficiency and precision of fault localization need to be improved. To solve these problems, a framework 2DSFLF proposed in this paper and used to evaluate the effectiveness of software fault localization techniques (SFL) in two-dimensional eigenvalues takes both dynamic and static features into account to construct the two-dimensional eigenvalues statement spectrum (2DSS). Firstly the statement dependency and test case coverage are extracted by the feature extraction of 2DSFLF. Subsequently these extracted features can be used to construct the statement spectrum and data flow spectrum which can be combined into the optimized spectrum 2DSS. Finally an estimator which takes Radial Basis Function (RBF) neural network and ridge regression as fault localization model is trained by 2DSS to predict the suspiciousness of statements to be faulty. Experiments on Siemens Suit show that 2DSFLF improves the efficiency and precision of software fault localization compared with existing techniques like BPNN, PPDG, Tarantula and so fourth.

Mathematical Modeling of Human Activity on Forested Areas from Point Objects of Railway Infrastructure in a Two-Dimensional Statement

Human activity causes a large quantity of wildfires in areas close to the location of different industrial or transport infrastructure. All the infrastructure facilities of JSC Russian Railways may be classified into linear, point and area sources of human activity. This work purpose is to suggest an approach for predicting, assessing, and monitoring the human activity on forested areas based on a deterministic mathematical model. Partial differential equations have been solved using the finite difference method. The program realization is executed in the RAD Studio software. Expressions like the heat conduction equation are used to describe the propagation of human activity around railway facilities. Different railway objects have produced different distribution of the virtual (possible) number of forest fires (VNF) caused by the different level of human activity. Different sizes of the railway facilities have also showed that a highest VNF is predicted for large one. The proposed mathematical model is applicable to predict wildfires due to human activity. This paper discusses the possibility of predicting forest fire dangers near point infrastructure facilities of JSC Russian Railways. The results obtained are part of a large project aimed to develop methods for predicting, assessing, and monitoring forest fire danger near infrastructure facilities of Russian Railways.

Simulation of continuous spin detonation in an annular combustion chamber in two-dimensional statement

Simulation of continuous spin detonation in an annular combustion chamber in two-dimensional statement

INTERFERENCE OF CLOSABLE CRACKS AND NARROW SLITS IN AN ELASTIC PLATE UNDER BENDING

The problem of bending of an infinite plate containing an array of trough closable cracks and narrow slits is considered in a two-dimensional statement. A crack is treated as a mathematical cut, the edges of which are able to contact along the line on the plate outside. A slit is referred to as a cut with contact stress-free surfaces and the negative jump of normal displacement can occur on this cut. The crack closure caused by bending deformation was studied based on the classical hypothesis of direct normal and previously developed model of the contact of edges along the line. A new boundary problem for a couple of biharmonic equations of plane stress and plate bending with interconnected boundary conditions in the form of inequalities on the cuts is formulated. The method of singular integral equations was applied in order to develop approximate analytical and numerical solutions to the problem. The forces and moments intensity factors near the peaks of defects and contact reaction on the closed edges of the cracks are calculated. A detailed analysis was carried out for parallel rectilinear crack and slit, depending on their relative location. Presented results demonstrate qualitative differences in the stress concentration near the defects of different nature.

Assessment of WWER-1000 Core Baffle Form Alteration during Operation

The paper illustrates the results of the computer assessment of the form alteration in WWER-1000 core baffle obtained via the solution to the coupled thermoelastoplastic task considering the strains of irradiation growth and creep. In the modeling of the contact conditions, the temperature redistribution is considered due to the incompliance of the coolant flow in the contact zone between the core baffle and in-vessel core barrel with the design conditions. The modern approaches to the modeling of strains of the irradiation growth and irradiation creep in austenite steels are used in the space-limited environment under neutron exposure and elevated temperature. The finite element analysis involves the mixed scheme of the finite element method, which allows determination of the stress-strain state with high accuracy. The calculations are performed in the two-dimensional statement for the cross-section of the core baffle with the maximum damaging dose and irradiation temperature under the condition of the generalized plane strain. The results of the calculations are presented for full-scale reactor operation and scheduled shutdown to recharge the fuel cluster at the end of core life. The data on the distribution and value of the gap between the core baffle and barrel, as well as the spacer grids of the edge fuel assemblies and reactor core baffle edges, have been obtained from the median values of the dose dependence on swelling at different temperatures in Kh18N10T austenite steel.

Dynamic stability and vibrations of thin-walled structures considering heredity properties of the material

Dynamic stability and vibrations of thin-walled structures, taking into account the heredity properties of the material are considered in the paper. Mathematical models were constructed in a two-dimensional statement, using the Karman theory of plane plate strains and A.A. Ilyushin aerodynamic theory. When realizing the physico-mechanical properties of the material of the object, the systems of integro-differential equations (IDE) in partial derivatives with the corresponding initial and boundary conditions are taken as mathematical models of the problems under consideration. The obtained nonlinear partial IDEs using the Bubnov-Galerkin method under considered boundary conditions are reduced to solving systems of nonlinear ordinary IDEs with constant or variable coefficients with respect to the time function. The integration of equations obtained using the polynomial approximation of the deflections was carried out by a numerical method based on the use of quadrature formulas. Based on this method, an algorithm for the numerical solution of the problem was developed suitable for all viscoelastic and elastic elements of thin-walled structures of plate type.

Numerical modeling in a two-dimensional statement of the process of dropship of electrode at welding

Numerical modeling in a two-dimensional statement of the process of dropship of electrode at welding

Development of the model to determine the fuel temperature field in a two-dimensional problem statement

Water-cooled water-moderated reactors (VVER) are widely used at Russian nuclear power plants. The VVER reactor core is formed by fuel assemblies consisting of fuel rods. The fuel in fuel rods is uranium dioxide. The safety of the reactor operation is ensured through stringent requirements for the maximum nuclear fuel temperature. Calculation of temperature fields within the reactor core requires associated problems to be solved to determine the internal energy release in fuel based on neutronic characteristics. Dedicated software for such calculations is not available to a broad range of users. At the present time, there are numerical thermophysical modeling packages available for training or noncommercial applications which are used extensively, including Elcut, Flow Vision, Ansys Fluent, and Comsol Multiphysics. Verification of the obtained results is becoming an important issue in building models using these calculation packages. An analytical solution was obtained as part of the study for the fuel temperature field determination. A program was developed in MathCAD based on this solution. A model was developed in Comsol Multiphysics to determine the fuel temperature field with constant thermophysical properties in a two-dimensional problem statement. The numerical model was verified using the analytical solution. The influence of the number of the grid nodes on the solution accuracy was established. The analytical solution can be used to determine the fuel temperature field at any radial coordinate of the reactor. The temperature field determination model developed in MathCAD can be used to verify numerical models of the fuel temperature field determination developed in dedicated packages.

Modeling and simulation of textile composite plates under a punching load

The work suggests a mathematical model of deforming textile composite materials (TCMs) based on aramid fibres under the punching load. This model takes account of peculiarities of deformation characteristics of the considered class of composites: the possibility of deforming without failure at finite deformations, a considerable difference between diagrams of deforming under tension and under compression, a dependence of the diagrams on a loading rate, the presence of pseudoplastic properties of materials caused by pulling threads from the fabric etc. Viscoelastic features of aramid fibres are taken into account as well. In addition, the model considers the damage and breakage of fibres in textile composites in their punching. A problem statement is formulated for dynamic deforming of textile composites. To solve the problem in its two-dimensional statement we applied the band adaptive grid method. The problem on punching a textile composite shield by a hard striker was solved numerically, and the computed results were compared with experimental data on punching the aramid textile composite plates.

Разработка модели по определению температурного поля твэла в двумерной постановке задачи

Разработка модели по определению температурного поля твэла в двумерной постановке задачи

Investigation of the interaction of two parallel shifted cracks in plate bending adjusted for their closure

The problem of interaction of two parallel shifted cracks in plate bending is considered. The cracks closure has been investigated in the classical two-dimensional statement, using the model of smooth contact along a line. The influence of the relative position of cracks and of the contact of their edges on the forces and moment intensity factors has been studied by the singular integral equations method.

Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shells

Relevance. To determine the stress-strain state (SSS) of thin-walled shells due to the complexity of obtaining numerical results, the theory of thin shells was developed with the introduction of the direct normal hypothesis to reduce the three-dimensional SSS to the two-dimensional one. With the modern development of digital technology and numerical methods of calculation, in particular the finite element method (FEM), it became possible to obtain numerical results without the use of the direct normal hypothesis, namely on the basis of the theory of elasticity in three-dimensional formulation even for thin shells. Aims. The aim of this work is to compare the efficiency of algorithms for the use of finite element stiffness matrices obtained on the basis of the theory of thin shells with the hypothesis of a straight normal and on the basis of the relations of the three-dimensional theory of elasticity. Methods. The results of comparative analysis of finite element calculations of thin shells using a two-dimensional sampling element in the form of a quadrangular fragment of the middle surface and a three-dimensional element in the form of an eight-node six-face are presented. The components of the displacement vector and their first derivatives were chosen as the nodal variable parameters. The functions of the form for both types of discretization elements were represented by products of Hermite polynomials of the third degree. Results. On the example of calculation of the cylindrical shell clamped at the ends it is shown that the two-dimensional statement in calculations of thin shells is adequate and allows to receive acceptable results at optimum costs of machine time.

Laminar free convection heat transfer and separated flow structure in a vertical channel with isothermal walls and two adiabatic opposing fins

Results of numerical study of laminar free convection and heat transfer in a vertical plane-parallel channel with two thin adiabatic fins on its walls are presented. The channel has the open inlet and outlet, and its surfaces are maintained at the same temperature. The channel height is unchanged with elongation parameter A = L/w = 10, and the fins are located in the middle of the channel toward each other. Fin height l/w = 0 ÷ 0.4 and Rayleigh number Ra = 102 ÷ 105 are varied in calculations. The effect of these parameters on the flow structure, temperature field, local and integral heat transfer, and gas flow caused by gravitational forces are analyzed in detail. Numerical analysis is based on solving the full Navier–Stokes and energy equations in twodimensional statement and Boussinesq approximation. To determine the dynamic and thermal parameters at the inlet and outlet, the calculation is carried out with two large volumes attached to the inlet and outlet. The features of the flow and heat transfer at separated flow around the channel fins are studied in detail in this work.

Effect of the Indenting Electrode Impact on the Stress-Strain State of an AMg6 Alloy on Electrodynamic Treatment

The calculation model of the impact indenting electrode interaction with an AMg6 aluminum alloy plate on the electrodynamic treatment of weld joints is described. The problem was solved in the Lagrange two-dimensional statement with an ANSYS/LS-DYNA program. Calculation results for residual stress and plastic strain regions formed on the elastoplastic indenting electrode impact are presented.

The mathematical model of dynamics of dust plasma considering polydisperse structure of the condensed phase

Work is devoted to studying of non-stationary processes in the complex plasma representing a suspension of solid particles in the uncharged gas. This model constitutes the closed system of the multiphase mediums dynamics equations in two-dimensional statement which involves the bearing medium and the condensed phase movement equations.

ДИНАМИКА ЖИДКОСТИ В ПОДВИЖНОМ СОСУДЕ С НАКЛОННЫМИ РЕШЕТКАМИ

Forced oscillations of a rectangular tank p artially filled with liquid are considered in this work. Two inclined screens are located in the tank as inserts. The system of Reynolds–averaged Navier–Stokes equations is solved numerically with the SST k - ω turbulence model. The volume of fluid (VOF) method is taken for simulation of gas–liquid interface. The problem is solved in two-dimensional statement. Unstructured triangular mesh converted to a fine structured rectangular mesh is used near the screens. A comparison of two turbulence models with experimental data is carried out, and the optimal model for the pressure loss coefficient calculation is chosen. The effect of the inserts inclination angle on the pressure loss coefficient is investigated at different values of the oscillation amplitude of the tank and different heights of the screen slats. It is obtained that the pressure loss coefficient dependence on the inclination angle at small Keulegan–Carpenter number has the local maximum depending on the oscillation amplitude and the geometric parameters of the screens. Comparison with the known analytical dependence of the pressure loss coefficient dependence on the inclination angle that obtained for the stationary flow through the inclined screen is conducted. It is found that this dependence needs to be verified for the case of oscillation tank at big screen inclination angle and small Keulegan–Carpenter number.

Mathematical Model of Heat Transfer in Morphological Part of Vegetation at Influence by Thermal Radiation from Surface Forest Fire Front

Numerical research results of heat transfer in layered tree trunk influenced by heat flux from forest fire are presented. The problem is solved in two-dimensional statement in Cartesian system of co-ordinates. The typical range of influence parameters of heat flux from forest fire is considered. Temperature distributions in different moments of time are obtained. Condition of tree damage by forest fire influence is under consideration in this research.