Adaptive classification method and measurement of intermittent random process characteristics

Results are presented of an analytic construction and investigation of adaptive data classification algorithms for intermittent turbulence. A decision making rule is presented, relationships are derived to estimate the classification accuracy. A three-level procedure is described for processing the intermittency, including the calculation algorithms for the initial point, self-teaching, and optimal classification. It is shown that the method proposed permits realization of total automation of intermittency data processing.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 119–123, 1987.     

Variant of statistical interpretation of the formation of viscoelastic deformations of polymers

A variant of a statistical probability interpretation of elementary micromechanisms of formation of viscoelastic deformations of polymers is examined with the aid of the concept of dissymmetric media and the dissymmetry coefficient. A new rheological relationship is obtained, a particular case of which is the known equation of a typical linear viscoelastic body. A method is given for determining the relaxation spectrum for different intensity functions figuring in the rheological relationships. The results of the calculation are compared with the experimental data, exemplified by the creep of polyamide P-68.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 392–396, May–June, 1973.     

Combined stepwise stressing of creeping material,obeying the theory of hardening

Irreversible creeping deformations of a physically nonlinear material under combined stepwise stressing were investigated. A new variant of the theory of local deformations was used and the physical relationships were based on the theory of hardening. The deformation components were calculated on a BÉSM-3M digital computer and were found to be in good agreement with experimental data. Curves are given representing the intensity of deformations as a function of time.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 393–398, May–June, 1970.     

Duality for Equilibrium Problems under Generalized Monotonicity

Duality is studied for an abstract equilibrium problem which includes, among others, optimization problems and variational inequality problems. Following different schemes, various duals are proposed and primal–dual relationships are established under certain generalized convexity and generalized monotonicity assumptions. In a primal–dual setting, existence results for a solution are derived for different generalized monotone equilibrium problems within each duality scheme.     

Stability of cylindrical plexiglas shells exposed to dynamical axial loads

The dynamical stability of a cylindrical Plexiglas shell exposed to axial compression is studied by means of a nonlinear formulation. Main attention is paid to a study of the waves formed when the stability gets lost. Empirical relationships between the critical load and the geometrical and mechanical parameters of the shell are derived.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 740–743, July–August, 1972.     

Adhesive strength

The relationship of the actual to theoretical strengths of adhesive bonds and means of increasing actual adhesive strength are analyzed in terms of the molecular theory of adhesion. Certain relationships for the destruction of adhesive bonds are examined. The lack of substance in the objections to the molecular theory of adhesion is shown.V. I. Lenin All-Union Institute of Electrical Technology, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 303–310, March–April, 1970.     

A class of lifted path and flow-based formulations for the asymmetric traveling salesman problem with and without precedence constraints

In this paper, we present a new class of polynomial length formulations for the asymmetric traveling salesman problem (ATSP) by lifting an ordered path-based model using logical restrictions in concert with the Reformulation–Linearization Technique (RLT). We show that a relaxed version of this formulation is equivalent to a flow-based ATSP model, which in turn is tighter than the formulation based on the exponential number of Dantzig–Fulkerson–Johnson (DFJ) subtour elimination constraints. The proposed lifting idea is applied to derive a variety of new formulations for the ATSP, and we explore several dominance relationships among these. We also extend these formulations to include precedence constraints in order to enforce a partial order on the sequence of cities to be visited in a tour. Computational results are presented to exhibit the relative tightness of our formulations and the efficacy of the proposed lifting process.     

Periodic deformation and viscous flow of polymer solutions and melts

The effect of nonlinear periodic deformation on the relaxation spectra and viscous-elastic characteristics of polymer melts and solutions is considered. The experimental and calculated relationships between the dynamic characteristics and effective viscosity and the amplitude of the rate of periodic deformation were compared.For Communication 1, see [6].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Institute of Mechanics Problems, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 357–366, March–April, 1970.     

Deformability modelling of foam elongation

The relationships concerning the deformation of rigid cellular foams during elongation are reviewed under the conditions of a monotonous load increase. The cellular structure behavior is modelled by the operation of a certain piston structure. The proposed equation leads to a satisfactory approximation of the experimental stress-strain diagram for polystyrene and poly(vinyl chloride) foams.V. A. Kucherenko Central Scientific-Research Institute of Building Constructions, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 154–157, January–February, 1972.     

Bivariate Birnbaum–Saunders distribution and associated inference

Univariate Birnbaum–Saunders distribution has been used quite effectively to model positively skewed data, especially lifetime data and crack growth data. In this paper, we introduce bivariate Birnbaum–Saunders distribution which is an absolutely continuous distribution whose marginals are univariate Birnbaum–Saunders distributions. Different properties of this bivariate Birnbaum–Saunders distribution are then discussed. This new family has five unknown parameters and it is shown that the maximum likelihood estimators can be obtained by solving two non-linear equations. We also propose simple modified moment estimators for the unknown parameters which are explicit and can therefore be used effectively as an initial guess for the computation of the maximum likelihood estimators. We then present the asymptotic distributions of the maximum likelihood estimators and use them to construct confidence intervals for the parameters. We also discuss likelihood ratio tests for some hypotheses of interest. Monte Carlo simulations are then carried out to examine the performance of the proposed estimators. Finally, a numerical data analysis is performed in order to illustrate all the methods of inference discussed here.     

Features of viscoelastic behavior of materials based on heat-resistant polymers

Conclusions In the example of polybenzoxazole, the relationships of viscoelastic behavior have been investigated for monolithic heat-resistant polymers over a wide range of temperatures (from 22° to 230°C) and initial deformations (from 0.5 to 2.5%). The experimental data on stress relaxation, covering the regions of linear and nonlinear viscoelasticity, are approximated by the basic equation of the primary cubic theory of Il'yushin, using the singular kernel of Rzhanitsyn. For the first time, the region of stable mechanical capability of monolithic heat-resistant polymers has been defined with due regard for relaxation characteristics.Paper presented at Fourth All-Union Conference on Polymer Mechanics and Composite Materials (Riga, October 1980).Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 978–983, November–December, 1980.     

Numerical identification of properties of particle-reinforced composite materials

The paper deals with numerical identification of the average elastic properties of particle-reinforced composite materials. The finite element method for the determination of deformation energy of the characteristic volume element was used. In earlier analytical investigations, an approximation function of the averaged elastic properties of the composite was derived. An identification procedure allows the estimation of the unknown approximation parameters from numerical experiments. The obtained functions describe precisely the numerical data for any relationships between constituents of the material.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Computer Analysis of Structures, Riga Technical University, Riga PDP-1658, Latvia. Institute of Materials Science, Department of Materials Science, Martin-Luther-University Halle-Wittenberg, D-06099 Halle, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 383–390, May–June, 1998.     

Elastic modulus of a nonpolar polymer

A theoretical calculation of the elastic modulus of a nonpolar polymer (polyethylene) is carried out after deriving the appropriate relationships. Intramolecular forces (retarded rotation) play a far more important part than intermolecular forces. A simple method is proposed for finding the entropy and energy forces from the corresponding elastic moduli. The intra- and intermolecular energy effects are separated for one particular case.K. D. Ushinskii Yaroslav State Pedagogical Institute. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 450–454, May–June, 1973.     

Generalized z-Distributions and Related Stochastic Processes

The class of generalized z–distributions is defined and their properties are investigated. Ornstein–Uhlenbeck–type and self–similar generalized z–processes are constructed and described. Esscher transforms of the generalized z–processes and the mixed generalized z–processes are characterized. Finally, construction and some properties of generalized z–diffusions are also discussed.     

Determination of contact stresses in problems on bending of a package of transversely isotropic bars

A mechanomathematical model for bending of packages of transversely isotropic bars of rectangular cross section is proposed. Adhesion, slippage, and separation zones between the bars are considered. The resolving equations for deflections and tangential displacements are supplemented with a system of linear differential equations for determining the normal and tangential contact stresses, and boundary conditions are formulated. A scheme for analytical solution of two contact problems—a package under the action of a distributed load and a round stamp—is considered. For these packages, a transition is performed from the initial system of differential equations for determining the contact stresses, where the unknown functions are interrelated by recurrent relationships, to one linear differential equation of fourth order and then to a system of linear algebraic equations. This transition allows us to integrate the initial system and get expressions for the contact stresses.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 761–778, November–December, 2004.     

Connections between stability and asymptotic stability of nonlinear switched systems

Here are considered nonlinear switched systems in which the switching occurs among a class of subsystems that are characterized by input–output properties stated in terms of L_p spaces of signals. The relationships between the L_p stability of each subsystem and the internal stability of the switched system are studied. In particular, conditions on the dwell time of the switching signals that guarantee the asymptotic stability of the overall system are provided. The connections among these conditions and the L_p input–output properties of the subsystems are investigated.     

Viscosity of melts obtained from polymers with a wide spread of particle size

By comparing existing relationships between the maximum viscosity and the molecular weight and between the effective viscosity and the shear velocity, the effect of the molecular-weight distribution of linear polymers on the shear velocity is analyzed.Scientific-Industrial Combine Plastopolimer. Scientific-Research Institute of Polymerized Plastics, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 753–756, July–August, 1972.     

Cracking resistance and long-term strength of dispersion-hardened composites

Conclusions The previously proposed relationships were used to develop a method of predicting the endurance of dispersion-hardened composites on the basis of results of tensile tests on the material at a constant strain rate. It is shown that stress raisers in the form of cut out or defects which weaken the working cross section, greatly reduce the endurance of the material. The proposed method of evaluating the effect of stress raisers on the endurance of polymer materials is based on the assumption on the initiation of a crack-like defect and its propagation in accordance with the loss of linear fracture mechanics.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 869–877, September–October, 1989.     

Changes in the strength characteristics of human intervertebral disks under compression

Conclusions 1. The strength of intervertebral disks undergoes significant changes during the human lifetime. The data obtained allow the distinction of three periods: 1) a period of strength gain (newly born babies-18 years); 2) a stable period (20–40 years); and 3) a period of strength loss (from 50 to the death). The safety factor of strength of the intervertebral disks is the highest during the first two decades and decreases during the following age periods.2. The sex has a significant influence on the strength characteristics of the intervertebral disks.3. Changes in the limiting load of the intervertebral disks of the spine are characterized by a caudocranial gradient and the changes in the strength and the safety factor of strength, by a cranio-caudal gradient. The existing relationships do not depend on age or sex and reflect the significance of the functions of support and motion in different sections of the spinal column.4. The strength of the intervertebral disks depends on the degree of the degenerative-distrophic process, the mineral content of the tissues, the water content, and the ability of the disk tissues to retain water.S. V. Kurashov Kazan' State Medical Institute. Translated from Mekhanika Polimerov, No. 5, pp. 897–902, September–October, 1976.     

Shear creep of orthogonally reinforced spherofibrous composites

Our previous theory for the viscoelasticity of spheroplastics and two-phase structural models was used to construct stress creep and relaxation operators for shear of orthogonally reinforced spherofibrous composites. The operators were constructed using the Volterra principle, Rabotnov's fraction exponential kernels, and approximate analytical relationships for the integral composite characteristics. Operators were taken incorporating data on the rheonomic characteristics of the composite, components with hybrid, hollow, and other fiber types. Approximate formulas were obtained for operators convenient for studying stress creep and relaxation in elements of three-dimensional structures.A. A. Blagonravov Mechanical Engineering Institute, Russian Academy of Sciences, Moscow. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 770–779, November–December, 1996.