The effect of the nonuniformity properties of a material in problems of elastic equilibrium and stability of shells

On the basis of two improved models of shells that are nonuniform by thickness (based on assumptions of Timoshenko type stated separately for each layer and assuming a uniform stress-deformed state of a thin-walled element of the layered structure) we study the stressed state and stability of three-layer cylindrical shells with a nonsymmetric packet. We show the equivalence of the two models in describing the reaction of layered shells to uniform external actions. We give an analysis of the dependence of the stress-deformed state and the reserve stability of shells on the structure of the packet.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 89–93.     

Water Wave Packets Over Variable Depth

In this paper, we develop higher‐order nonlinear Schrödinger equations with variable coefficients to describe how a water wave packet will deform and eventually be destroyed as it propagates shoreward from deep to shallow water. It is well‐known that in the framework of the usual nonlinear Schrödinger equations, a wave packet can only exist in deep water, more precisely when kh > 1.363 , where k is the wavenumber and h is the depth. Using a combination of asymptotic analysis and numerical simulations we find that in the framework of the higher‐order nonlinear Schrödinger equations, the wave packet can penetrate into shallow water kh < 1.363 or not even reach kh > 1.363 , depending on the sign of the initial value in deep water of a certain parameter of the wave packet that measures its speed.     

Determination of the thermal stresses in anisotropic shells of revolution

Using the relations of the improved model of layered anisotropic shells based on the straight line assumption taking account of the thermal compression over the thickness we obtain a resolvent system of equations for shells whose properties depend on temperature. We carry out a study of the stresses in a two-layer cylindrical shell formed by winding as a function of the winding angle. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 82–85.     

Monitoring the packet gap of real-time packet traffic

Real-time packet traffic is characterized by a strict deadline on the end-to-end time delay and an upper bound on the information loss. Due to the high correlation among consecutive packets, the individual packet loss does not well characterize the performance of real-time packet sessions. An additional measure of packet loss is necessary to adequately assess the quality of each real-time connection. The additional measure considered here is the average number of consecutively lost packets, also called the average packet gap. We derive a closed form for the average packet gap for the multiclassG/G/m/B queueing system in equilibrium and show that it only depends on the loss behavior of two consecutive packets. This result considerably simplifies the monitoring process of real-time packet traffic sessions. If the packet loss process is markovian, the consecutive packet loss has a geometric distribution.     

Free oscillations of shells of complex geometry with finite shear stiffness

By applying isoparametric approximations we develop a finite-element method for studying the oscillations of shells whose middle surfaces are Monge surfaces. As the starting point we take the model of shells of Timoshenko type. To solve the eigenvalue problem we apply the method of iterations in a subspace. Two figures. Five tables. Bibliography: 14 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 13–17.     

On queueing delays of dispersed messages

We study the message queueing delays in a node of a communication system, where a message consists of a block of consecutive packets. The message delay is defined as the time elapsing between the arrival epoch of the first packet of the message to the system until after the transmission of the last packet of that message is completed. We distinguish between two types of message generation processes. The message can be generated as abatch or it can bedispersed over time. In this paper we focus on the dispersed generation model. The main difficulty in the analysis is due to the correlation between the system states observed by different packets of the same message. This paper introduces a new technique to analyze the message delay in such systems for different arrival models and different number of sessions. For anM/M/1 system with variable size messages and for the bursty traffic model, we obtain an explicit expression for the Laplace-Stieltjes transform (LST) of the message delay. Derivations are also provided for anM/G/1 system, for multiple session systems and for fixed message sizes. We show that the correlation has a strong effect on the performance of the system, and that the commonly usedindependence assumption, i.e., the assumption that the delays of packets are independent from packet to packet, can lead to wrong conclusions.     

Optimal position of a strut on a cylindrical shell

A solution is given for the problem of the optimal design of a rigid structure consisting of a spherical shell and two cylindrical shells linked by a strut. The volume of the structure is minimized under constraints on the maximal equivalent stresses in each of the shells and on the geometric parameters of the strut. Among the regulating parameters are the thickness of the shells, the geometric parameters of the strut, and the length of the first of the cylindrical shells. The problem is solved by the method of geometric programming.Translated from Matematicheskie Metody i Fiziko-Mekhanicheski Polya, No. 29, pp. 76–80, 1989.     

The stressed state of elastoplastic shells with nonthrough cracks

We study the problem of the stressed state and limiting equilibrium of shells with nonthrough surface cracks. Several assumptions make it possible to reduce the three-dimensional problem to the two-dimensional problem and the latter to a system of singular integral equations whose solution is constructed using numerical methods. For cylindrical and spherical shells weakened by nonthrough cracks situated along the coordinate lines we carry out a numerical analysis of the dependence of the crack opening on the load and the geometric and physico-mechanical parameters of the shells.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 147–151.     

Axisymmetric deformation of bimetallic shells of revolution in the supercritical region

Geometrically nonlinear relationships of the theory of thin layered shells are applied to analyze axisymmetric strain of bimetallic shells of revolution in a temperature field. One-dimensional nonlinear boundary-value problems are solved by a combination of the linearization method and the discrete orthogonalization method. A numerical approach is proposed to solve the boundary-value problems in the supercritical strain region.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 72, pp. 52–56, 1990.     

Theory of vibration-damping polymeric coatings

Conclusions 1. An approximate method for calculating the characteristics of vibration-damping polymeric coatings of complex construction, based on equations of the theory of multilayer plates and shells, has been developed.2. The dimensionless parameters of the theory of multilayer plates and shells, g and h/r, are the basic quantities which determine the effectiveness of a damping coating.3. An increase in number of layers in the coating, while preserving the overall thickness of the packet and an assigned ratio between the thicknesses of the polymeric and rigid layers, exerts only a small effect on the effectiveness of the coating.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 2, pp. 269–276, March–April, 1978.     

Deformation of a system of cylindrical shells under the action of an internal nonstationary pressure wave

We study the problem of nonstationary deformation of a system of imbedded cylindrical shells under the action of an internal compression wave. The rigorous method of solution we apply makes it possible to obtain a system of Volterra integral equations with retarded arguments in the deflections of the shells. We give the results of computations for the case of a linear source and a source of finite size with limiting hardness properties. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 60–66.     

On the equations of thermoelasticity of thin shells with breaks in the middle surface

Applying the apparatus of generalized functions, we obtain a complete system of equations of thermoelasticity for thin shells with breaks. The shells are subject to heat sources located arbitrarily along a curve or throughout a region. We find the solution of the steady-state heat-conduction problem for an unbounded cylindrical shell with a break along a meridian. The results of numerical analysis are given. Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 135–139.     

Multiwavelet packets and frame packets ofL 2(ℝ d )

The orthonormal basis generated by a wavelet ofL ²(ℝ) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis ofL ²(ℝ ^d ) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized to this setting. Further, we show how to construct various orthonormal bases ofL ²(ℝ ^d ) from the multiwavelet packets.     

Nonlinear contact problems for thin-walled elements of constructions

Some one-dimensional contact problems for plates and shells are considered for one-side contact with a rigid base. Contrary to analogous papers about the zone of contact, we use applied theories of contraction of Winkler type, which are obtained from equations of elasticity theory by asymptotic methods together with bending equations of thin-walled elements. The possibility of deviation of shells needs a definition of a contact zone in the process of solution of the problem from the condition of continuity of bending and its derivatives up to the second order inclusive. Some conclusions are made with respect to the optimal projects of reinforcement of shells taking into account their deviation.Translated from Dinamicheskie Sistemy, No. 8, pp. 40–45, 1989.     

Wavelets on S3 and SO(3)—Their construction,relation to each other and Radon transform of wavelets on SO(3)

The paper at hand is concerned with creating a flexible wavelet theory on the three sphere S³ and the rotation group SO(3). The theory of zonal functions and reproducing kernels will be used to develop conditions for an admissible wavelet. After explaining some preliminaries on group actions and some basics on approximation theory, we will prove reconstruction formulas of linear and bilinear wavelet transformed L²‐functions on S³. Moreover, specific examples will be constructed and visualized. Second, we deal with the construction of wavelets on the rotation group SO(3). It will be shown that the Radon transform of a wavelet packet on SO(3) gives a wavelet packet on S² for every fixed detection direction. Copyright © 2010 John Wiley & Sons, Ltd.     

Solution of heat-conduction problems for thin shells and plates by application of a generalized variational approach

By applying a generalized variational approach we construct an approximate system of equations for heat conduction for thin shells and plates and develop a method of solving them. We give the results of numerical studies for a particular problem.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 66–70.     

Phase Field Modeling of Fracture in Plates and Shells

The numerical modeling of failure mechanisms in plates and shells due to fracture based on sharp crack discontinuities is extremely demanding and suffers in situations with complex crack topologies. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. In this paper, we extend ideas recently outlined in [1, 2] towards the phase field modeling of fracture in dimension-reduced continua with application to Kirchhoff plates and shells. The introduction of history fields, containing the maximum reference energy obtained in history, provides a very transparent representation of the coupled balance equations and allows the construction of an extremely robust operator split technique. The performance of the proposed models is demonstrated by means of representative numerical examples. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reduction of a polling network to a single node

We consider a discrete-time tree network of polling servers where all packets are routed to the same node (called node 0), from which they leave the network. All packets have unit size and arrive from the exterior according to independent batch Bernoulli arrival processes. The service discipline of each node is work-conserving and the service discipline of node 0 has to be HoL-based, which is an additional assumption that is satisfied by, a.o., m _i -limited service, exhaustive service, and priority disciplines. Let a type i packet be a packet that visits queue i of node 0. We establish a distributional relation between the number of type i packets in the network and in a single station system, and we show equality of the mean end-to-end delay of type i packets in the two systems. Essentially this reduces an arbitrary tree network to a much simpler system of one node, while preserving the mean end-to-end delay of type i packets.      

On an approach to the design of reinforced shells that is optimal in terms of reliability

We consider questions of optimal design of shallow spherical shells reinforced by a grid of struts taking account of reliability. It is assumed that the independent random variable acting on the structure is distributed according to the Weibull law.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 60–63.     

Queueing and Fluid Analysis of Partial Message Discarding Policy

We consider a stream of packets that arrive at a queue with a finite buffer. A group of consecutive packets constitutes a frame. We assume that when an arriving packet finds the queue full, not only is the packet lost but also the future packets that belong to the same frame will be rejected. The first part of the paper deals with a detailed packet level queueing model; we obtain exact expressions for the stationary queue length distribution and the goodput ratio (i.e. the fraction of arriving frames that experience no losses). The second part deals with a fluid model and the fluid analysis leads to simple closed form expressions for the stationary workload process and the fluid goodput ratio.