Moscow University Mechanics Bulletin最新文献

A new class of constitutive equations for complex loading processes is obtained. It has three state functionals. A new method of mathematical modeling and mathematical principle is formulated. According to them, physically correct equations of state are changed by introducing gyroscopic terms that do not perform mechanical work. The constitutive equations of complex loading processes with two state functionals under conditions of force and kinematic loading are constructed. Their connection with the Il’yushin formula and modern theories of plastic flow is obtained. A mathematical model of the domain mechanism of plasticity is formulated. It represents a real deformable continuum as a mixture of an elastoplastic continuum and a Cosserat continuum—flat veinlets (domains of plastic deformation that are the zones of large relative rotations). A physical justification for the inclusion of the asymmetric part of the stress and rotation tensor in the composition of the thermodynamic parameters of the model is given.

A pedestrian navigation system consisting of two foot-mounted strapdown inertial navigation systems (SINS)s is considered. The zero velocity conditions of the foot in the stance phase of a step and a limited distance between the feet are used for SINS corrections. The aim of the work is to study some consistency properties of the extended Kalman filter. It is shown that this consistency depends on a form of the error equations.

The paper is devoted to the development of the displacement discontinuity method for plane problems of fracture mechanics in consideration of the curvature of crack lines. In this paper, some new representations of biharmonic functions are found. This is necessary to obtain the analytical solutions of problems for an elastic plane weakened by a crack in the form of a circular arc. A numerical method is proposed on the basis of these analytical solutions. The numerical values of the stress intensity factor are compared with its known analytical value.

Free oscillations of a conical shell of finite length are considered. This problem was formulated in the 1960s. A modern algorithm without saturation is given in this paper, and specific calculations which show its high efficiency are discussed.

This work presents the construction of a solution to the plane doubly periodic loading problem for an infinite elastic isotropic plane with elliptical inclusions. The plane is under one of three loads: it is stretched in the direction of one of the inclusion axes or it has a pure shear at infinity. The concept of stress concentration tensor is considered and an example of its construction is shown. The solution of the problem is reduced to the search for complex functions from the boundary conditions obtained from the equality of displacements and normal forces of the matrix and inclusions using conformal mappings and integration by the Muskhelishvili method. The effect of noncentral inclusions is expressed by using the small parameter method.

This paper concerned with the motion of two contacting cylinders with dry friction between them. Filippov’s theory of discontinuous differential equations is used to study the system of ordinary differential equations. The forward uniqueness of the solution is proven, the phase portrait is drawn, and its bifurcation is investigated. These results allow describing the motions of the given mechanical system, in particular, the conditions of seizing and permanent rotation.

The problem of motion in a free molecular flow of particles of a rigid body with a fixed point bounded by the surface of an ellipsoid of revolution is considered. Necessary existence conditions for an additional analytic first integral independent of the energy integral are obtained in this problem.

The calibration problem for the accelerometer unit is considered under restrictions on its angular positions (for the plane case). The guaranteeing approach is applied to solve the problem. The solution is found in analytical form.

The paper presents our study on the dilution of precision in the problem of estimating the vehicle’s velocity using a three-beam Doppler lidar. Such a system has been proposed as an addition or replacement to the differential GNSS velocity solution in an airborne gravimetry system. We analytically derive optimal directions of lidar beams and use numerical simulation to obtain their attitude which minimizes the error covariance of estimated vertical velocity.

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.