A problem of non – linear deformation of five–layer conical shells with allowance for discrete ribs

A problem of non – linear deformation of multiplayer conical shells with allowance for discrete ribs under non – stationary loading is considered. The system of non – linear differential equations is based on the Timoshenko type theory of rods and shells. The Reissner’s variational principle is used for deductions of the motion equations. An efficient numerical method with using Richardson type finite difference approximation for solution of problems on nonstationary behaviour of multiplayer shells of revolution with allowance distcrete ribs which permit to realize solution of the investigated wave problems with the use of personal computers. As a numerical example, the problem of dynamic deformation of a five-layer conical shell with rigidly clamped ends under the action of an internal distributed load was considered.

Special features of short-duration processes in condensed media

The problem of the short-duration processes is considered on the base of the nonlocal theory of non-equilibrium transport, taking into account inertial effects. The system temporal evolution out of equilibrium connected to the dynamic structure transition described by the Speed-Gradient principle (SG-principle or SGP) developed in control theory and cybernetic physics. In the manuscript, we show that retardation of the system response to the short-duration loading due to inertial effects influences on the system evolution and can change its direction. The response to the shock loading of condensed matter is compared to quasi-stationary loading in a wide range of conditions. The short duration loading can lead the system into the structure unstable state and even give rise to self-organization of turbulent structures in the medium. The use of SGP for the modelling of such processes opens new possibilities to control them.

DIVIDING OF THE FULL REACTION OF THE ADDITIONAL SUPPORT CONTACTING WITH THE PLATE INTO VISCOUS, ELASTIC AND INERTIAL COMPONENTS

An original approach for dividing the reaction of a viscoelastic support into inertial, viscous and elastic components is proposed to assess the effect of various characteristics of additional supports on the deformed state of structural elements. The effectiveness of the proposed approach was tested for a mechanical system consisting of a rectangular isotropic plate of medium thickness, hinged-supported along the contour, and an additional concentrated viscoelastic support, taking into account its mass-inertial characteristics. The deformation of the plate is considered within the framework of Timoshenko's hypotheses. Vibrations of the plate are caused by the applying of an external non-stationary loading. The influence of the additional support is modeled by three independent non-stationary concentrated forces. The paper presents the main analytical relations for obtaining a system of three integral Volterra equations, which is solved numerically and analytically. After performing discretization in time, the system of integral equations is transformed into a system of matrix equations. The resulting system of matrix equations is solved using the generalized Cramer algorithm for block matrices and the Tikhonov regularization method. We point out that the material described is applicable to other objects that have additional supports (beams, plates and shells, which can have different supports along the contour and different shapes in plan). The results of a numerical experiment to determine the components (viscous, elastic and inertial) of the full reaction to the plate, arising due to the presence of an additional support, are presented. The reliability of the proposed approach is confirmed by the coincidence of the results of comparing the reactions found by two methods: numerical-analytical for one complete reaction, as in work [1], and numerical for the full reaction (obtained by adding three components).

INVESTIGATION OF MULTI-CYCLE FATIGUE OF EQUIPMENT AND MACHINERY ELEMENTS UNDER COMPLEX STRESS CONDITIONS AND NON- STATIONARY LOADING

A computational and experimental method for estimating the fatigue life of structural elements of machines operating under complex cyclic stress conditions and non-stationary loading is considered. Comparison of the results of the calculations and experimental data indicated the effectiveness of the kinetic equation of multi-cycle fatigue damage based on the energy concentration of fatigue failure.

Oscillation of Thermal Insulation Three-Layer Cylindrical Pipes under Operating Loads

Equipment and pipes are the main components of a nuclear power plant (NPP) that ensure transfer of heat energy into electric one. The pipes with nominal diameter from DN10 to DN1200 are the main types of pipes that also include different fragments such as bends, cones, tees, branches, etc. Common length of all NPP pipes is hundreds of kilometers. All these components can be combined by one common feature: they are shell structures that found wide application in daily activities. The use of such components in the design and manufacture of equipment and pipelines of NPP power units requires appropriate practical and theoretical studies. The use of filler made of light materials allows for a small increase in the weight of the structure to significantly increase its bending stiffness and improve its thermal insulation properties. The oscillations of three-layer cylindrical pipes are considered in this paper. The equations of motion of a three-layer cylindrical shell with lightweight filler reinforced by stiffening ribs with non-stationary loading have been provided through these efforts. The model of Timoshenko’s theory of shells and rods have been used in this study under analysis of components with flexible structures. Numerical results of oscillations of the three-layer elastic structure were obtained using the finite element method. The impact of the physical and mechanical parameters of the shell layers is investigated on its stress strain state under an axisymmetric internal impulse loading.