Moscow University Mechanics Bulletin最新文献

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.

A boundary value problem is considered in a functionally gradedelastic strip. A three-term asymptotic expansion of a transferfunction is obtained for the Poincaré–Steklov operator thatmaps normal stresses to normal displacements on a part of thestrip boundary. Padé approximations are determined for theobtained asymptotic series. An approach to computing the transferfunction using the asymptotic series and the Padé approximationsis proposed, which reduces computational costs.

The initial-boundary value problems of acceleration from a state of rest of a two-constant viscoplastic medium (Bingham body) in a half-plane is investigated when the tangential stress is given at the boundary as a piecewise continuous monotonically nondecreasing function of time. As an additional condition at an unknown interface between a flow zone that increases with time in thickness and a stationary semi-infinite rigid zone, the requirement is chosen that the solution of this problem with a tendency to zero of the yield strength of the material at each point and at each moment of time tends to the solution of the corresponding viscous flow problem known as the generalized vortex layer diffusion problem. The exact analytical solutions are found for tangential stress and velocity profiles in nonstationary one-dimensional flow. The cases of self-similarity and so-called quasi-self-similarity are distinguished. The nature of the tendency at (ttoinfty) of the thickness of the layer, in which the shear is realized, to infinity is of particular interest.

We consider the classical problem of elasticity theory concerning the conditions of strain compatibility, which ensure the determination of a continuous field of displacements of an elastic body by the strain field. We construct generalized Cesàro representations that allow defining the displacement field through integrodifferential operators on the components of the strain tensor deviator with an accuracy up to quadratic polynomials. It has been established that the quadratures both for the pseudovector of local rotations and for the bulk strain are completely determined by the strain deviator field. We present the conditions for the existence of the listed quadratures, which are written in the form of five third differential order compatibility equations for the five components of the strain deviator tensor.

In this paper, a variational principle of Lagrange, the Ritzmethod, and piecewise polynomial serendipity shape functions areused to obtain a stiffness matrix and a system of linear algebraicequations in the micropolar theory of elasticity for anisotropic,isotropic, and centrally symmetric material in case of anonisothermal process.

We continue the systematic analytical study of a nonlinear Maxwell-type constitutive equation for shear flow for thixotropic viscoelastic media accounting for interaction of deformation process and structure evolution, namely, the influence of the kinetics formation and breakage of chain cross-links, agglomerations of molecules and crystallites on viscosity and shear modulus and deformation influence on the kinetics. We formulated it in the previous article and reduced it to the set of two nonlinear autonomous differential equations for two unknown functions (namely, the stress and relative cross-links density). We examine the phase portrait of the system for arbitrary (increasing) material function and six (positive) material parameters governing the model and prove that the (unique) equilibrium point is stable and the only three cases are realized: the equilibrium point is either a stable sink, or a degenerated stable sink, or a stable spiral sink. We found criteria for every case in the form of explicit restrictions on the material function and parameters and shear rate.