Moscow University Mechanics Bulletin最新文献

From the standpoint of the theory of small elastoplasticdeformations, the stress-strain state of the continuous mediumalong various unloading trajectories from the state achieved as aresult of a simple active process is analyzed. It is shown that ifthe unloading is disproportionate, then the constitutive relationsconnecting the deviators of stresses and strains are tensoriallynonlinear, i.e., the unit tensors of these deviators do notcoincide. It is demonstrated that in the Il’yushinfive-dimensional deviatoric space there exists only one fullunloading point, and it belongs to the line segment of thepreceding active loading. A measure of the nonproportionality ofthe unloading is introduced, characterizing the degree ofdeviation of the path of the passive deformation process from thepreviously mentioned line segment. This measure is calculated fortwo piece-linear unloadings using the example of a constantannular tube subject to the simultaneous action of ((rtheta))-torsion and axial ((rz))-shear.

In this paper, a variational principle of Lagrange, the Ritz method, and piecewise polynomial shape functions of brick family ‘‘linear’’ element are used to obtain reduced and selective integration techniques in a form of the tensor-block stiffness matrices to prevent the locking effect for nearly incompressible, isotropic, and centrally symmetric material of the micropolar theory of elasticity.

This paper shows the possibility of solving the problem of the transition between periodic and point attractors in the bistable Rosenzweig–MacArthur model with modifications for the dynamics of root hemiparasitic plants and their hosts.

The article presents a three-dimensional linear model of the vestibulo-ocular reflex in darkness. The model is based on established relationships between the vestibular system and the extraocular muscles. The effectiveness of the model is evaluated through comparison with experimental observations. The model successfully reproduces realistic patterns of slow-phase vestibulo-ocular nystagmus during head rotations.

An exact analytic solution to the problem of joint nonstationary oscillations of a semi-infinite underground pipeline and elastic soil caused by the propagation of a longitudinal seismic wave along its axis is obtained in the case when the pipeline end is clamped. The emerging stress-strain state for subsonic and supersonic modes of seismic wave propagation is studied. The results of this study can be used to calculate the deformation of oil and gas pipelines under seismic loads.

A point transformation determining the equivalence of systems of equations of two-dimensional shallow water over horizontal and sloping bottoms is obtained. The symmetries of these systems of equations are found.

Traveling wave solutions to the deep bed filtration system are constructed for a model with different velocities of a carrier fluid and suspended particles. The solution in quadratures is obtained when the velocity of the carrier fluid and that of the particles differ by a concentration-dependent factor. For some special cases, the physically realizable domains are found in the space of governing parameters. The solutions that may be interpreted as a clogging wave structure are presented.

This article considers a series of three experiments on the elastoplastic deformation of the V95 alloy, which is sensitive to the type of stress state. Experimental studies were carried out on a CL-EVM (complex loading) test machine on thin-walled tubular specimens during their deformation along two-link strain trajectories with 90 degree break angles. Experimental studies were carried out in the deviatoric plane (text{E}_{1}-text{E}_{3}) with simultaneous combined action of axial force and torque on tubular specimens ((P-M) experiments). The scalar and vector properties of the V95 aluminum alloy are studied. It is found that, for the implemented complex strain trajectories in the form of two-link polygonal chains for the V95 material, the isotropy postulate is not fulfilled accurately enough in terms of scalar and vector properties.

We consider new holonomic tensor measures of strain and stresses and build nonlinear elasticity models for which the problems of stretching of a thin wide plate and uniaxial stretching of a rod from incompressible materials are solved. These models are congruent with classical ones when deformation is small, and they essentially demonstrate various properties at large deformations.

The problem under consideration is to find periodic trajectories lying on the boundary of the limit reachability region of a linear time-invariant third-order system with one controlling action bounded in absolute value. It is assumed that the characteristic equation of a homogeneous system has one negative real root and two complex conjugate roots, the real parts of all three roots are the same. The results make it possible to construct the boundary of the limit reachability region (for an infinitely long control time) in the form of analytical expressions on the system parameters.