Computational Continuum Mechanics

An actual trend in the field of experimental solid mechanics is the extension of the test specimen range. This article considers a force-controlled loading test of a hollow "Brazilian disk" with two inclined cracks. Tests of this type of specimens provide important information on brittle and quasi-brittle fracture under mixed loading conditions (Modes I and II). For practical application of these specimens, it is necessary to know the stress state parameters in the vicinity of the crack tip, such as KI, KII and T-stress. Unfortunately, due to the complex geometry of the specimens, there are no analytical expressions for evaluating these parameters, which are generally computed via finite element modeling with post-processing of the results. However, due to a significant algorithmic complexity of this procedure, the application of new types of specimens remains limited. To simplify the computational experiments for new types of specimens, we propose an approach, which is based on the approximation of the dependence of the desired stress state parameters on the problem parameters, namely, the dimensions of the disk, the length of the cracks, and their inclination angle with respect to the loading axis. The approximation of the desired parameters is found by solving a linear problem of the least root-mean-square deviation. To obtain an accurate approximation, it is necessary to use higher degree polynomials, although an excessive number of monomials leads to a rapid increase in the number of coefficients in the approximator and, as a result, to a rapid deterioration of the problem conditioning, which eventually reduces the accuracy and stability of the approximation. To avoid overparameterization, we consider three methods for constructing bases with a specified number of monomials.. The accuracy of the constructed approximators is evaluated by making comparison with the data obtained from numerical modeling and verified experimentally. As numerical experiments have shown, the approximation error is about 1% for each of the desired stress state parameters. The obtained approximators are available as a MATLAB script, open for free download at GitHub.

Кирилл Павлович Уфимцев

Денис Александрович Кузнецов

Алексей Валерьевич Шутов

Аппроксиматоры для ускоренного вычисления параметров напряженного состояния в нестандартных образцах с трещинами

用于加速计算含裂纹非标准试样应力状态参数的逼近器

Cylindrical periodic shells are widely used in modeling various building structures, pipelines, offshore drilling rig supports, wind farms and other structures. Increasing their wear resistance and preventing the occurrence of risk-bearing operating modes is an urgent problem. In this paper, we investigate one of the potentially dangerous modes caused by axisymmetric vibrations of a circular cylindrical shell of Kirchhoff–Love type with additional inertia in the form of periodic "mass belts" of zero width. The shell is assumed to be infinite and its free harmonic vibrations are analyzed using a Floquet-type exact analytical solution. The dependence of pass bands and stop bands on the mass of the concentrated loads is investigated. At a certain combination of parameters, the points of intersection and quasi-intersection of the boundaries of these bands can coincide. The neighborhood of such a special point is considered in view of the fact that the boundaries of the pass and stop bands of an infinite periodic shell can be obtained and investigated by considering free vibrations of its separated symmetric segment of periodicity. This makes it possible to essentially reduce the volume of calculations, to simplify the determination of the coordinates of this special point, as well as to facilitate the analysis of the vibration field, the integral energy flux and its components. In such a way, the consideration of energy flows and its components not only significantly complements the picture of vibration fields, but also allows us to assess more adequately the nature of vibrations. It is shown that in the vicinity of a singular point there is a sharp change in the character of vibrations, which can lead to dangerous modes of operation of real structures.

Георгий Викторович Филиппенко

Энергетический анализ осесимметричных колебаний цилиндрической оболочки, нагруженной периодическими сосредоточенными массами

能量分析受周期集中质量载荷的圆柱壳轴对称振动

An extremal problem of determining the upper (kinematic) limit of the load-bearing capacity of a flat disk reinforced with continuous fibers and rotating in a quasi-steady state is formulated. At the inner edge, the disk blade is rigidly attached to the shaft (or hub), and reinforced vanes can be attached to its outer edge. The materials of the composition phases are assumed to be rigid-plastic, having different yield limits in tension and compression; the binder matrix material may be cylindrically orthotropic. Under conditions of a generalized plane stress state, the yield curves of the components of the composition in the principal stresses are piecewise linear. Reinforcement structures have radial and axial symmetry. The plastic deformation of the composition is calculated using the relations of the structural model of the mechanics of composites, which takes into account the plane stress state in all phase materials. The problem was discretized and a numerical algorithm for solving it was developed, based on the use of linear programming methods. Various variants of discretization of the problem under consideration have been studied. The convergence of the numerical solution and its good agreement with the previously obtained analytical solution are demonstrated. Numerical examples of calculating the maximum angular velocity of rotation of disks for different reinforcement structures of their fabric are analyzed. Cases of laying fibers along straight trajectories (geodesic lines), along logarithmic spirals, as well as along radial and circumferential directions are considered. In this case, the isotropic materials of the components of the composition obey the associated flow law corresponding to the yield criterion Hu. The influence of reinforcement parameters (directions and densities) on the bearing capacity of rotating disks has been studied. The comparison was carried out for composite disks of the same mass and with the same relative volume of reinforcement.

Андрей Петрович Янковский

Численный метод определения несущей способности плоских вращающихся армированных дисков

确定平面旋转加固盘承载力的数值方法

One of the applications of shape memory alloys is automotive industry, where they can be used as a material for working bodies of actuators. The movement of the working body is provided by the accumulation of direct transformation deformation during cooling and the shape memory effect during heating. In this paper, the behavior of the actuator, which consists of the rod made from shape memory alloy and the series-connected elastic displacement body, is studied in the framework of the combined model of nonlinear deformation taking into account isotropic and translational hardening. Inelastic deformation produced by the structural transformation in the martensitic state and during thermoelastic phase transitions is described with the use of a loading surface in the stress deviator space. The maximum value of the intensity of phase-structural deformation averaged over the martensitic part of the representative volume is assumed as a non-integral isotropic hardening parameter in the loading surface equation. The formation of martensitic elements during direct thermoelastic transition as well as their evolution are considered. The results of numerical modeling of the working stroke are compared with the data obtained without translational hardening, and the conditions, at which translational hardening can be ignored, are determine. Analysis shows that deformation by a structural mechanism and translational shift of the loading surface are possible under the action of the applied payload and during the working stroke. It has been found that during the working stroke the translational shift of the center of the loading surface significantly affects the stress level in the shape memory rod and the displacement of the point of connection of the working body and translational body. The maximum values of these parameters are reached at the end of the working stroke and are independent of the hardening modulus. The effect of the translational hardening on the results of simulation significantly reduces with an increase in the initial deformation of the working body and an increase of the ratio of the working body flexibility to the elastic body flexibility. It is shown, that during the idle stroke the center of the loading surface is not displaced. The consideration for translational hardening does not affect the selection of parameters providing closeness of the cycle, i.e. the return of the system to its initial state after idling.

Наталья Валерьевна Гаганова

Моделирование привода с рабочим телом в виде стержня из сплава с памятью формы и упругим элементом смещения с учетом трансляционного упрочнения

考虑平移硬化的形状记忆合金杆驱动器与位移弹簧元件的建模

Volcanic eruptions and accompanied lava flows pose a significant threat to population, buildings and regional infrastructure. Lava may occupy large spatial domains, for which a detailed three-dimensional modeling of its flow is reduced to solving discrete problems of high dimensionality and is not always effective. For sufficiently small ratio of the vertical dimension of the flow to its horizontal dimension, the mathematical models which are based on the depth-averaged equations of motion of a viscous medium are used. In this study, such a model consists of equations for lava thickness, two-dimensional equations of its motion, crystal growth kinetic equations and a heat balance equation that takes into account nonlinear convective and radiative energy exchange with the external environment, dissipation energy and latent heat of crystallization. The mathematical model was implemented numerically in the open-source package OpenFOAM. This package makes it possible to use modern high-performance computing clusters for conducting numerical experiments and to adapt the problem to specific physical aspects of the simulated natural process. The codes were verified by comparing the analytical solution of the problem and the solution obtained in terms of the model involving equations of motion of a two-phase incompressible fluid in spatial domain. The effect of the rheological characteristics of the flow represented by the Newtonian model was studied in comparison with the flow simulated using the Bingham model and the nonlinear Herschel–Bulkley model. The nonlinear rheology of the fluid of interest accounts for the dependence of the actual viscosity of a lava flow on temperature, shear rate, and yield stress (the yield stress and the flow behavior index are the functions of temperature). Parallel computer codes were implemented on the basis of OpenMPI for the computing clusters with shared and distributed memory running in Linux OS. Profiling of codes for multi-core CPUs with shared memory was carried out.

Publication Information	Publisher: Institute of Continuous Media Mechanics，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2019，Proportion of original research papers: ，Self Citation Rate:， Gold OA Rate:

Computational Continuum Mechanics

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Аппроксиматоры для ускоренного вычисления параметров напряженного состояния в нестандартных образцах с трещинами

Энергетический анализ осесимметричных колебаний цилиндрической оболочки, нагруженной периодическими сосредоточенными массами

Численный метод определения несущей способности плоских вращающихся армированных дисков

Моделирование привода с рабочим телом в виде стержня из сплава с памятью формы и упругим элементом смещения с учетом трансляционного упрочнения

Численное моделирование извержения вулкана Этна с применением усредненной по глубине модели потока лавы

Аппроксиматоры для ускоренного вычисления параметров напряженного состояния в нестандартных образцах с трещинами

Энергетический анализ осесимметричных колебаний цилиндрической оболочки, нагруженной периодическими сосредоточенными массами

Численный метод определения несущей способности плоских вращающихся армированных дисков

Моделирование привода с рабочим телом в виде стержня из сплава с памятью формы и упругим элементом смещения с учетом трансляционного упрочнения

Численное моделирование извержения вулкана Этна с применением усредненной по глубине модели потока лавы

ISSN	1999-6691
h-index	6