Mechanics

Axisymmetric Problem Lemba for the Cosserat Medium

Authors: Tran L. T., Tarlakovsky D. V.

The article deals with elastic homogeneous isotropic half-space filled with the Cosserat medium. At the initial instant of time and at infinity, there are no perturbations. At the boundary of the half-space, normal pressures are given. All the components of the stress-strain state are supposed to be limited. A cylindrical coordinate system is used with an axis directed inward into the half-space.

Creep and Long-Term Strength Modeling for Thick-Walled Tubes under Combined Loading with Axial Force, Torsional Moment and Internal Pressure

Authors: Radchenko V. P., Tsvetkov V. V.

We have developed a method for solving the boundary-value problem of rheological deformation and creep rupture of thick-walled tube under combined loading with axial force, torsional moment and internal pressure. Energetic variant of the theory of creep and long-term strength is used to describe creep process. Experimental verification of proposed method has been performed using known test data for creep and long-term strength of thick-walled tubes made of D16T alloy and Steel~20. Calculated dependencies for total axial strain and torsion angle on time are obtained.

Instantaneously not Elongated Directors in Three-Dimensional Kinematics of the Coulomb – Mohr Medium

Authors: Radaev Y. N.

Three-dimensional flows of perfectly plastic medium are considered within the framework of the Coulomb -- Mohr continuum model. The model is to be used in applied problems related to limit states and flows of sands, rocks and any other kind of granular media. The present study is based on a notion of asymptotic directions of the stress tensor and the strain tensor increment and as well on instantaneously not elongated directors which are orthogonal to the asymptotic directions and lie in the plane normal to the intermediate principal stress axis.

Stress and Strain Fields in a Plate of Stress State Dependent Material Properties

Authors: Lomakin E. V., Shchendrigina O. P.

The paper analyzes the properties of the constitutive relations proposed to describe the behavior of materials whose deformation diagrams depend on the type of external forces. In this case, various forms of nonlinearity arise, related to the dependence of the properties of materials on the type of the stressed state, the nonlinearity of the deformation diagrams, and the relationship between the shear and volume deformation processes.

Low-Frequency Vibration Modes of Strongly Inhomogeneous Elastic Laminates

Authors: Kaplunov J. D., Prikazchikova L. A.

The dynamic behaviour of thin multi-layered structures, composed of contrasting “strong” and “weak” layers, is considered. An asymptotic procedure for analysing the lowest cutoffs is developed. A polynomial frequency equation is derived, along with the linear equations for the associated eigenforms corresponding to displacement variation across the thickness. For a five-layered laminate with clamped faces two term expansions for eigenfrequencies and eigenforms are compared with those obtained from the exact solution of the original problem for thickness resonances.

On the Complex Dynamics in Simplest Vibrational Systems with Hereditary-Type Friction

Authors: Igumnov L. A., Metrikin V. S.

The dynamics of a number of vibrational systems, accounting for the forces of hereditary-type dry friction and a vibration limiter, are studied in the paper. The interaction between the vibration limiter and the vibrational system is assumed to obey Newton's hypothesis. A general mathematical model has been developed, which is a strongly nonlinear non-autonomous system with a variable structure. The dynamics of the mathematical model is studied numerically-analytically, using the mathematical apparatus of the point mapping method.

On Some Models of Indentation for Functionally-Graded Coatings

Authors: Vatulyan A. O., Plotnikov D. K., Poddubny A. A.

The paper presents approximate models of deformation for an inhomogeneous elastic strip. Approximate models reflect the distribution features of the inhomogeneous structure properties over the thickness. The models are based on hypotheses about the nature of the change in the components of the displacement field, which allows to consider arbitrary laws of heterogeneity: continuous, as well as discontinuous or having a strong gradient. Solutions of the contact problem for different inhomogeneity laws are constructed. Comparative analysis of the models is carried out.

Studying of Elastoplastic Properties of Coal Specimens Using Indentation Technique

Authors: Vatulyan A. O., Lyapin A. A., Kossovich E. L.

A numerical study on elsatoplastic properties in problem of coals specimen nanoindentation by Berkovich pyramid is presented. The stress-strain state of specimen during indentation is calculated using finite element method including complex elastoplastic behaviour on the basis of Drucker-Prager model. The effective axisymmetrical indenter of cone shape is introduced and used for the simulation. The influence of basic geometrical and material parameters of the solid model on the indentation curve is studied. In addition, some new form of indentation curve approximation is proposed.

Approximate Theory of a Laminated Anisotropic Plate Vibrations

Authors: Belyaev A. K., Zelinskaya A. V., Ivanov D. N., Morozov N. F., Naumova N. V., Tovstik P. E., Tovstik T. P.

The multi-layered plate vibration is investigated. A two-dimensional asymptotic model of the second order accuracy with respect to the small thickness parameter is proposed with account for the transverse shear and the normal fibre extension. The model is appropriate for a monoclinic plate described by 13 elastic moduli which is heterogeneous in the thickness direction. In particular, the model can be applied to a multi-layered plate consisting of orthotropic layers of arbitrary orientation. In this case the elastic moduli are piece-wise constant functions.

On the Unsymmetrical Buckling of Shallow Spherical Shells under Internal Pressure

Authors: Bauer S. M., Voronkova E. B.

This work isdevoted to the numerical study of unsymmetrical buckling of shallow spherical shells and annular plates with varying mechanical characteristics subjected to internal pressure. We suppose that the edge of the shell is clamped but moving freely in the shell’s plane. For the annular plate a roller support is considered for the inner edge of the plate, i.e. the edge that can slide along the figure axes without changing the slope. The unsymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate.

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