Vol 54, No 6 (2019)

The longitudinal vibrations of a rod weakened by transverse cracks are considered. Cracks are assumed to be open and modeled by translational springs. The stiffness of the springs corresponds to the size of the cracks. A method has been developed for identifying the number and position of transverse cracks, as well as the stiffness of the corresponding springs according to two spectra that correspond to two types of conditions at the ends of the rod: free—free and fixed—free. The developed method is based on minimizing the objective function that characterizes the difference between the given (measured) natural frequencies and natural frequencies calculated during the implementation of the algorithm. The objective function is minimized using the Levenberg—Marquardt algorithm. Numerical examples are considered. The stability of the obtained results with respect to noise in the initial data is investigated.

The paper presents the results of a numerical study of the fracture of concrete structures — the protective shell of a nuclear power plant (NPP), under impulse loads. The model of concrete behavior takes into account differences in the limits of compressive and tensile strength, dependence of tensile strengths on the strain rate, plastic properties of concrete, fracture, fragmentation of the shell. Numerical modeling is carried out by finite element method in a three-dimensional statement as part of a phenomenological approach of the mechanics of a continuous medium, using the authors computational software. The dynamics of the fracture of the nuclear power plant protective shell, which has a complex cellular structure and the role of wave processes, is investigated.

A mathematical model of the dynamics of deformation of an overhead power line wire in a spatial setting is developed, the equations are solved on the basis of the finite difference method in an explicit scheme. In some cases, the accuracy of the calculations is compared with the obtained analytical solutions. A numerical study of the loading of a power line under the combined influence of wind and weight load was carried out. A numerical method for calculating wire breakage and the movement of parts after a break is proposed. The mechanism of the appearance of oscillatory motion such as “dancing wires” under the action of a variable wind load. The process of thermal conductivity and the dynamics of line deformation during melting of icing on wires by heating is studied, the transient processes of deformation of the power line are studied.

In various formulations (unbound, coupled, and double-coupled) within the framework of the concepts of “Fixed load” and “Variable load”, analytical solutions to the problem of the loss of stability of a pivotally fixed rod made of an alloy with a shape memory, the material of which undergoes inverse thermoelastic phase transformation under the action of constant compression loads in the presence of initial phase — structural compression strains. The formulation of the concept of “Variable load” is justified, within which the solution for the critical length does not depend on the magnitude of the perturbations.

The influence of the elastic constants of transversely isotropic rocks on the stress concentration values on the well contour is studied. It is shown that in the case of a uniform component initial stress state, the main parameter characterizing the deviation of the stress concentration on the well contour from the concentration characteristic of an isotropic body is the ratio of the independent shear modulus in the plane normal to the isotropy plane to the shear modulus characteristic of one of the subclasses transversally isotropic medium isolated by Saint-Venant, which is a combination of other elastic constants. With this ratio equal to one, stress concentrations for isotropic and anisotropic medium coincide. The well-known fact that this relationship is close to one for most transversely isotropic rocks allows us to use, to a first approximation, an elastic solution for an isotropic body. It is shown that the closeness to one of relation of the ratio of independent shear modulus to combinations of other elastic constants characteristic of other subclasses identified by Saint-Venant is also observed for most rocks, although with slightly less accuracy.

The exploration of non-convex energy landscapes, as arising in phase transitions, is an important task in solid state mechanics. An often employed system in the literature for the study of phase transitions in deformable solids denotes the elastic bar with a non-monotone stress-strain curve. This setting is chosen and modelled by a continuum-on-atomistic model (molecular dynamics coupled with the finite element method). The rod’s material denotes a copper single crystal and undergoes a model phase transition. The resulting non-convex energy landscape is explored by the string method in collective variables. The string method allows for the computation of energy barriers between local minima and to identify minimum free energy paths. The novelty of the present work is the combination of a continuum-on-atomistic method with the string method applied to a problem in mechanics. Numerical examples demonstrate the performance of the numerical model.

There was a mistake in the author mane. The right fifth author is “K. Motaghed A.”