卷 88, 编号 2 (2024)

A problem of motion of a point particle on a surface of a homogeneous gravitating ball with a spherical inclusion of a differing density is considered. It is assumed that the body rotates uniformly around its symmetry axis. It is supposed that "besides the gravitation force, the particle is subjected to dry friction.

The gravitational properties outside the ball are described. The dependence of existence, bifurcations, and stability of relative equilibria of the point particle on the body surface on the parameters of the problem is studied. The results are represented both analytically and as numerically obtained bifurcation diagrams.

Besides the well-known fundamental works of Yu.N. Rabotnov in the field of hereditary elasticity and creep theory, one of the aspects of his scientific activity was the mechanics of composite materials and, in particular, a new class of strength criteria for structurally anisotropic composites proposed by him.

The main feature of Yuri Rabotnov’s approach was not an attempt to construct a uniform smooth limiting surface in the stress-space, but taking into account real fracture mechanisms, which, as a rule, are directional in nature.

Now such approaches become crucial in calculation algorithms modeling the fracture process with taking into account the degradation of elastic and strength properties, but in the period of the first Yu.N. Rabotnov’s papers they were pioneering and caused certain discussions. Development and application of some of Rabotnov’s proposed types of strength criteria for fiber-reinforced composites in tension, compression and complex stress state are discussed in this anniversary paper.

The coupled problems of changing the stress-strain and phase state in a thick-walled spherical shell made of a shape memory alloy, the material of which undergoes a direct thermoelastic phase transformation associated with a decrease in temperature uniformly distributed over the entire volume of the material under the action of constant internal or external pressure, are solved. The effects of significant overstressing of the body layers adjacent to the inner boundary and significant unloading of the layers adjacent to the outer boundary associated with the movement of the phase transition completion front through the material were found.

When analyzing the strength of structures made of layered fibrous polymer composite materials; the criteria for failure of a monolayer – a unidirectional reinforced composite – are used. A criterion of strength according to the conditions of matrix fracture is formulated, corresponding to conical limiting surfaces and the lowest destructive loads. The criterion of strength according to the condition of fiber failure, which does not allow the paradox of increasing strength in the region of transition from fiber destruction to matrix failure, is given. Experimental verification of the criteria for volumetric, planar, and one-dimensional loads is carried out. Their better correspondence to empirical data is shown and their advantages in comparison with known criteria are marked. A small number of easily detectable parameters of these criteria contribute to their reliability and stability in strength calculations of composite structural elements.

An analytical solution to the problem of diffraction of a plane acoustic wave on a radially inhomogeneous thick-walled elastic cylindrical shell of finite length is obtained. The cylindrical shell is located in an acoustic half-space filled with an ideal liquid. The boundary of the half-space is an acoustically rigid or acoustically soft surface. The results of calculations of the acoustic field in the far zone are presented.