Moscow University Mechanics Bulletin最新文献

In this paper, the variational principle of Lagrange, the Ritzmethod and piecewise polynomial serendipity shape functions areused to obtain the stiffness matrix and a system of linearalgebraic equations in the micropolar theory of elasticity fororthotropic and centrally symmetric material.

In this paper, the motion of a spherical body with anisotropic magnetizable elastomer in a viscous liquid under the action of a magnetic field of the coil with current is investigated. A mathematical model of such a body motion taking into account the interaction (rolling, sliding) with the inclined plane is proposed. The calculated trajectories of the body movement from the initial position on the coil axis when the magnetic field is turned on are plotted. The parameters are determined at which the movement over the inclined plane occurs. The maximum deviation of the body from the coil axis for various problem parameters is calculated.

With the growth of various microdefects in bodies, complex systems of cracks of arbitrary configuration can be generated. This paper presents a technique for numerical simulation of complex branched cracks, which makes it possible to analyze such systems. Using the method proposed by the authors, it is possible to find the stress and displacement fields as well as the stress intensity factors, the analysis of which leads to the conclusion about the influence of the considered configuration on the crack stability. The paper also contains the comparison with the results of other authors in the problem of a two-link crack.

The paper studies the temperature conditions under which the emergence and self-development of vortex motion in the real atmosphere are possible.

The paper concerns with the equilibrium of the ideal incompressible liquid situated in a moving cylindrical vertical vessel. It is proved that the equilibrium is unstable with probability one if the vessel movement is defined as the vertical random vibration. Random vibration is simulated by stationary Markov chain.

A plane model of a spherical robot containing a platform with a wheel is considered. Dynamic equations are derived for this robot and some assumptions concerning these equations are also discussed. A control is proposed using a multilayer neural network.

The stress-strain state arising under dynamic stretching of a homogeneous sheet of an incompressible ideally rigid-plastic material, which obeys the Mises–Hencky criterion, is studied. The lateral boundary is stressfree and the longitudinal velocities are given at the ends. The possibility of thickening or thinning of the cross section along the length of the sheet is taken into account, which simulates necking and further development of the neck. Two characteristic stretching regimes are revealed: one of them depends on the velocity at which the end sections move away from each other and the other one depends on their acceleration. For the second regime, the asymptotic integration-based analysis allows approximately determining the stress-strain state parameters.

The tensor linear anisotropic constitutive relations of incompressible viscoplastic flow connecting the stress deviator and strain rates and the following scalar relation connecting the quadratic stress invariant and the hardening function are considered. In the case of a perfect plastic material, the latter relation is an anisotropic Mises–Hencky quadratic criterion of plasticity. The mutual dependence of the fourth-rank tensors involved in tensor and scalar constitutive relations is established. As an illustration, the results are given for an orthotropic material.

The generalization of Samarskii–Sobol’ solution in the mode of heat exacerbation and localization is obtained for a quasilinear heat equation in half-space. The analogy of this solution with summer heating of moisture-saturated soil in the permafrost zone is discussed.

Unsteady oscillations of a semi-infinite underground pipeline and elastic soil caused by the propagation of a longitudinal seismic wave along the pipeline are studied. The problem is not self-similar and its solution meets significant difficulties unlike the case of an infinite pipeline. It is shown that the formulation and consideration of this problem performed earlier by Rashidov are incorrect and do not lead to its solution.