Rubric: "01.02.00 Mechanics"
The purpose of this article is to deduce general and approximate equations for the torsional vibration of the viscoelastic round bar rotating around the symmetry axis with the constant angular velocity. Within the research we develop the algorithm allowing to define the bar deflected mode. The received approximate equations enabled to numerically solve the problem of the bar torsional vibrations. Moreover, we carry out a comparative analysis of the results obtained for exponential and weakly singular kernels of the viscoelastic operator. As a result, we estimate the rotation influence on the bar vibrations
Khudoynazarov K., Abdirashidov A., Burkutboyev . Torsional vibrations of the viscoelastic round bar rotating with the constant angular velocity. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 38-51
The article offers the calculation algorithm of deflected mode of an absolutely flexible bar interacting with the external air flow. The algorithm is based on the replacement of the continual mechanical system by the discrete set of rectilinear finite elements and concentrated masses. The authors show differential equations of mass motion with allowance for an aerodynamic load and dissipative forces and integrate them by numerical method. That made it possible to find both the equilibrium position of the flexible bar in the flow, and the critical flow velocity which causes violent bar vibrations in case of its excess.
Sorokin F., Nizametdinov F. Numerical simulation of absolutely flexible bAR motion in the air flow. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 3-16
The suggested thermocreep theory for thin multilayer plates is based on analysis of general three dimensional nonlinear theory of thermalcreep by constructing asymptotic expansions in terms of a small parameter being the ratio of a plate thickness and a characteristic length. Here we do not introduce any hypotheses on a distribution character for displacements and stresses through the thickness. Local problems were formulated for finding stresses in all structural elements of a plate. It was shown that the global (averaged by the certain rules) equations of the plate theory were similar to equations of the Kirchhoff–Love plate theory, but they differed by a presence of the three-order derivatives of longitudinal displacements. The method developed allows to calculate all six components of the stress tensor including transverse normal stresses and stresses of interlayer shear. For this purposes one needs to solve global equations of thermal creep theory for plates, and the rest calculations are reduced to analytical formulae use.
Dimitrienko Y., Gubareva E., Yurin Y. Asymptotic theory of thermocreep for multilayer thin plates. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 18-36
A lot of heat-shielding materials used in engineering have porous structure. When there is an intensive thermal exposure, there occurs a necessity to consider thermal energy transfer by means of radiation in pores of such materials. We contructed a mathematical model describing heat exchange by radiation in a spherical cavity. Its form can be considered as an average statistical form in relation to forms of closed pores in solid bodies. For the quantitative analysis of this model we used the method of the least squares and introduced an equivalent coefficient of thermal conductivity in the conditional continuous environment filling a pore. This allows to regard the material with porous structure as a continuous non-uniform solid body.
Zarubin V., Pugachev O., Savelyeva I. Application of the least squares method to the problem of radiation transfer in a spherical cavity. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 53-65
The research explored questions of the convergence of iterative processes and correctness of the solutions on the example of the problem about a steady-state flat square lid-driven cavity flow of incompressible viscous liquid. The problem is solved for Reynolds numbers of 15000 < Re < 20000 and steps of grid 1/128 > h > 1/2048. The findings of the research illustrate that not for all relationships between Re and h the convergence of iterative processes is stable and the resulting steady-state solutions are qualitatively correct. We conducted a qualitative analysis of the solutions of the problem in the coordinate system (Re, 1/h) in terms of the convergence of iterative process, solution correctness and the required computing time. According to the literature and the results of systematic calculations we conclude that the stability of the convergence of iterative process on the coarse grid depends on the degree of influence of the artificial viscosity and/or the condition number of the matrix of difference elliptical linear algebraic equations, and on the detailed grid it depends on the grid Reynolds number. At high Reynolds numbers steady calculations can be carried out either on very coarse grids, or on very detailed ones. The width of the zone of instability in terms of parameter 1/h increases with increasing Reynolds number. Since the coarse grid solution is incorrect, and the use of detailed grid leads to very high costs of computer time, the further increase of the Reynolds number in the problem is associated with increasing the order of approximation of the differential equations.
Fomin A., Fomina L. On stationary solution of the problem of an incompressible viscous fluid at high Reynolds numbers. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 92-109
On the basis of mathematical model of thermal interaction between inclusion and the matrix we estimated influence of inclusions deviations from spherical shape on the effective thermal conductivity coefficient of the composite and associated with such deviation a possible occurrence of the anisotropy of the composite with respect to the property of thermal conductivity. Using the dual variational formulation of the stationary problem of heat conduction in an inhomogeneous body we built bilateral estimates of effective thermal conductivity.
Zarubin V., Kuvyrkin G., Savelyeva I. Effective thermal conductivity of a composite in case of inclusions shape deviations from spherical ones. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 3-17
This article deals with the finite-element RKDG method (Runge-Kutta Discontinuous Galerkin) and its application for numerical integration of three-dimensional system of equations of ideal gas on unstructured grids. By means of the described algorithm we solved two test tasks. For each task we conducted the analysis and compared the task solution with well-known analytical solutions or with tabular data. We also give error assessment in the solution.
Dimitrienko Y., Koryakov M., Zakharov A. Application of RKDG method for computational solution of three-dimensional gas-dynamic equations with non-structured grids. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 75-91
During the last decades we are witnessing climate changes. Scientists assume global warming to be the result of man-generated increase of green house gases in the atmosphere, the most important one being СО2. The article deals with the problem and describes cutting-edge solutions for stabilising climate. The research makes use of a seasonal global combined threedimensional hydrodynamic model of climate. This model of climate includes model of the World Ocean with real depths and configuration of continents, model of evolution of sea ice and energy — moisture balance model of the atmosphere. The first stage covers estimation of climate change through 2100 following IPCC A2 СО2 increase scenario. The calculations yield rise of average annual surface temperature of the atmosphere by 3,5 С. A number of calculations have been made to estimate possibility of stabilising climate at the level of 2010 by means of controlled release of sulphate aerosol into stratosphere. The aerosol will reflect and disperse a part of the coming solar radiation. We have calculated concentration (albedo) of the aerosol from 2010 to 2100 which will enable us to stabilise the average annual temperature of the surface layer of atmosphere. We have shown that by this way it is impossible to achieve the seasonal uniform approximation to the existing climate, although it is possible to significantly reduce the greenhouse warming effect. Provided that the aerosol is distributed evenly in space in stratosphere, we can stabilize the average annual temperature of the atmosphere, herewith in middle and low latitudes the climate will be colder by 0,1…0,2 С and in high latitudes it will be warmer by 0,2…1,2 С. Besides, these differences are essentially seasonal in nature, they increase in winter. If we stop releasing the aerosol in 2080 the average annual global temperature of the atmosphere will rise, reaching the former value without the aerosol by the year 2100.
Parkhomenko V. Modelling global climate stabilisation by controlled emission of stratospheric aerosol. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 115-126
The article describes a mathematical model of photon transport and generating the secondary electromagnetic fields in structures of complex geometry and package. A draft of the model design is given. The results of computing the photon flux in different elements of the model structure are demonstrated. It is shown that multiple-material stack-up of the enclosure can dramatically weaken the photon flux, scattering not only soft but hard photons as well. Intensity of absorption has pronounced maxima. There is space charge and the electrostatic field generated in the gas atmosphere inside the model. Electrostatic field can reach high amplitude in a small spatial domain inside the enclosure of the model.
Berezin A., Zhukov D., Zhukovskiy M., Konukov V., Krainukov V., Markov M., Pomazan Y., Potapenko A. Modeling the electromagnetic effects in complex structures exposed to pulse radiation. Маthematical Modeling and Coтputational Methods, 2015, №2 (6), pp. 58-72