On Resolvable Difference Families

A Steiner 2-design is said to be G-invariantly resolvable if admits an automorphism group G and a resolution invariant under G. Introducing and studying resolvable difference families, we characterize the class of G-invariantly resolvable Steiner 2-designs arising from relative difference families over G. Such designs have been already studied by Genma, Jimbo, and Mishima [13] in the case in which G is cyclic. Developping their results, we prove that any (p, k, 1)-DF (p prime) whose base blocks exactly cover p–1/k(k–1) distinct cosets of the k-th roots of unity (mod p), leads to a Ckp-invariantly resolvable cyclic (kp,k,1)-BBD. This induced us to propose several constructions for DF's having this property. In such a way we prove, in particular, the existence of a C5p-invariantly resolvable cyclic (5p, 5, 1)-BBD for each prime p = 20n + 1 < 1.000.     

Theoretical model of the anisotropy of low-cycle deformability of glass-fiber reinforced plastics

Conclusion A theoretical model is suggested for the anisotropy of low-cycle deformability of glass plastics determined by the anisotropy of the deformational properties of the material in short-term static tension (compression). The effect of the anisotropy of cyclic loss of strength of the deformational properties is taken into account by the introduction of the characterizing function which is taken to be independent of the mechanical properties of the material and of the conditions of low-cycle loading.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 437–442, May–June, 1985.     

Temperature deformation of laminated composite rings

The results of dilatometric measurements on wound circular glass-reinforced plastic rings composed of glass tape and epoxy-phenolic resin are presented. The changes in inside and outside diameter were measured on the temperature interval from 20 to 100°C at various diameter ratios. The theoretical conclusion [1] that anisotropy has a strong influence on the temperature deformation of circular cylinders and rings of composite material is confirmed.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1131–1132, November–December, 1969.     

Method of the anisotropy potential in the linear mechanics of polymers

The potential of the displacements due to the anisotropy of the physical properties of a material (the anisotropy potential) is used in order to reduce the solution of the linear statistical boundary problem of elasticity theory and that of the linear creep of homogeneous anisotropic bodies to two simpler problems: one involving an anisotropic medium, and the other involving an equation analogous to the Poisson equation.S. M. Kirov Ural Polytechnic Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No. 1, pp. 24–31, January–February, 1972.     

Elastic and strength characteristics of a glass-reinforced plastic in compression

The elastic constant and strength characteristics in compression have been experimentally determined for a cold-cured glass-reinforced plastic in the direction of all three principal axes of anisotropy. It is shown that the elastic constants obtained satisfy the constraints imposed on orthotropic materials by the thermodynamic relations.Translated from Mekhanika Polimerov, No. 5, pp. 866–869, September–October, 1970.     

Thermocreep of polyethylene in the cyclic temperature regime

The shear creep and recovery of low-density polyethylene has been investigated in the constant and cyclic temperature regimes. It is shown that in the cyclic regime the relaxation processes are accelerated and the nonisothermal creep strains become progressively greater than the isothermal strains at the maximum temperature of the cycle. In recovery the relaxation spectra are shifted along the time scale relative to the creep spectra, the shifts for simple shear and uniaxial tension being nonidentical.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 227–235, March–April, 1969.     

Fatigue strength of glass-reinforced plastics (GRP) in shear in the plane of reinforcement

The results of an investigation of the fatigue strength of three grades of glass-reinforced plastic are described. It is shown that cyclic loading with gradually increasing stress amplitude can be used to determine the fatigue strength at a given ambient temperature and loading frequency.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 928–931, September–October, 1975.     

Cold flow and melting of plastics under severe friction conditions

Dry friction of a series of crystalline polymers (polypropylene, nylon, PTFE) against steel over a wide range of sliding velocities (4.4–4.4×10^–4 cm/sec) and loads (P=7.5–360 kg) with almost complete mutual overlap of the friction surfaces is studied. It is shown that friction of polymer materials against steel may be accompanied by melting of the crystalline polymer (at high velocities) or cold flow (at low velocities) in the surface layers associated with an orientation effect and the appearance of anisotropy.Mekhanika Polimerov, Vol. 1, No. 5, pp. 95–100, 1965     

Dependence of the acoustic and mechanical properties of polyethylene on temperature and cyclic cooling and heating

The low-temperature stability of polyethylene is confirmed by acoustic and mechanical investigations. Data are given on the dependence of the acoustic and mechanical properties of polyethylene on temperature and repeated cyclic cooling to –50° and heating to +60°C, together with information on the change in Poisson's ratio and volume during deformation.Mekhanika Polimerov, Vol. 1, No. 3, pp. 145–150, 1965     

Effect of hot-drawing conditions on the orientation characteristics of carbon-chain fibers determined by the acoustic method

The orientation characteristics of polypropylene, polyacrylonitrile, and chlorinated PVC fibers, determined by the acoustic method, have been investigated in relation to the fiber drawing conditions (draw ratio, speed, and temperature). It is shown that there is a correlation between the mechanical characteristics and the degree of acoustic anisotropy.Tashkent Institute of the Textile and Light Industries. Translated from Mekhanika Polimerov, No. 3, pp. 552–554, May–June, 1971.     

Deformation of rigidly clamped specimens of acrylic plastics subjected to one-sided cyclic heating

The effect of one-sided rapid cyclic heating on the deformation of rigidly clamped specimens of acrylic plastics has been investigated. It is shown that as the temperature drop increases, so does the bending deformation (concave toward the heated surface) of the unclamped specimens; the greatest temperature change during thermal cycling is concentrated in an active surface layer not more than 1.6 mm thick and is accompanied by the development of tensile stresses in that layer. The characteristics of the reversibility of the deformation upon subsequent annealing are examined.Riga Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, No. 1, pp. 85–90, January–February, 1976.     

Anisotropy of torsional rigidity of sheet polymer composite materials

Wide application of polymer composite materials (PCM) in modern technology calls for detailed evaluation of their stress-strain properties in a broad temperature range. To obtain such information, we use the dynamic mechanical analysis and with the help of a reverse torsion pendulum measure the dynamic torsional rigidity of PCM bars of rectangular cross section in the temperature range up to 600 K. It is found that the temperature dependences of the dynamic rigidity of the calculated values of dynamic shear moduli are governed by the percentage and properties of the binder and fibers, the layout of fibers, the phase interaction along interfaces, etc. The principles of dynamic mechanical spectrometry are used to substantiate and analyze the parameters of anisotropy by which the behavior of a composite can be described in the temperature range including the transition of the binder from the glassy into a highly elastic state. For this purpose, the values of dynamic rigidity are measured under low-amplitude vibrations of the PCM specimens with a fiber orientation angle from 0 to 90°. It is shown that for unidirectional composites the dependence between the dynamic rigidity and the fiber orientation angle is of extreme character. The value and position of the peak depend on the type of the binder and fibers and change with temperature. It is found that the anisotropy degree of PCM is dictated by the molecular mobility and significantly changes in the temperature range of transition of the binder and reinforcement from the glassy into a highly elastic state (in the case of SVM fibers). The possibility of evaluating the anisotropy of composites with other reinforcement schemes, in particular, of orthogonally reinforced PCMs, is shown.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 291–308, May–June, 1999.     

On solution of a class of equilibrium problems

In the article we discuss the question of reducing the Arrow-Debreu model [1, 2] to a problem of mathematical programming; we also study conditions under which the problem is convex. The interest to the question is aroused by the circumstance that the equilibrium problems turn rather difficult for numeric solution. Two approaches are used most frequently. One is based on the monotonicity property (formulated somehow) of the excessive demand [2–5]. If this property is satisfied, then the corresponding differential system, which has the sought equilibrium at the rest point, appears stable. The other approach consists in constructing the so-called heuristic methods (see, for instance, [6]) which have more or less reasonable grounds but in general do not guarantee that a solution is obtainable.The research was supported by the Russian Foundation for Fundamental Research (Grant 93-012-842).Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 35, No. 5, pp. 990–999, September–October, 1994.     

Structural characteristics of materials reinforced with high-modulus fibers

Research on the mechanics of boron and carbon-reinforced plastics is briefly reviewed. The design and testing characteristics of these materials associated with the high degree of anisotropy of their elastic properties, as compared with those of glass-reinforced plastics, are discussed. Problems relating to testing at an angle to the direction of the reinforcement, the effect of misorientation and distortion of the fibers, and the consequences of the low shear strength are considered. Experimental confirmation has been obtained by testing unidirectional (1 : 0), orthogonally reinforced (1 : 1 and 2 : 1), and tridirectional (1 : 1 : 1 in the 0°, +60°, and –60° directions) boron and carbon-reinforced plastics.DeceasedInstitute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 676–685, July–August, 1971.     

Linear Functional Equations in Banach Modules over a C *-Algebra

The paper is a survey on the Hyers–Ulam–Rassias stability of linear functional equations in Banach modules over a C ^*-algebra. Its contents is divided into the following sections: 1. Introduction; 2. Stability of the Cauchy functional equation in Banach modules; 3. Stability of the Jensen functional equation in Banach modules; 4. Stability of the Trif functional equation in Banach modules; 5. Stability of cyclic functional equations in Banach modules over a C ^*-algebra; 6. Stability of cyclic functional equations in Banach algebras and approximate algebra homomorphisms; 7. Stability of algebra *-homomorphisms between Banach *-algebras and applications.     

Polymer fractography and fracture kinetics

On the basis of an analysis of the fractographic data for two polymeric materials (polymethyl-methacrylate and polycaprolactam) it is shown that it is possible to differentiate the effects of local heating and structural changes at the end of the main crack on the reduced lifetime of polymers under cyclic as compared with static loading. A method is proposed for estimating the values of the local temperature and the structure-sensitive coefficient in the cyclic lifetime equation.For communication 2 see [3].Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 869–874, September–October, 1971.     

Asymptotic modeling of thin asymmetric laminates. Boundary-value problems and solution methods

We have investigated the internal dynamic stress-strain state of elastic laminates with perfectly joined anisotropic layers in the long-wave approximation. In contrast to familiar cases, in this treatment we allow an asymmetric arrangement of plies across the thickness and the most general anisotropy. We derive the generalized governing equations for plates by an asymptotic method based on three-dimensional dynamic elasticity. We discuss the similarities and differences between the derived two-dimensional theory and earlier models of S. A. Ambarisumyan and R. M. Christensen. We show that the asymptotic accuracy of the equations depends on the type of anisotropy: (i) general anisotropy; (ii) monodinic anisotropy or orthotropy of the layers.Report presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompositnykh Materialov, Vol. 31, No. 3, pp. 319–325, May–June, 1995.     

Design of orthotropic parts of complex shape by the method of nonplanar sections

Procedures based on the hypothesis of nonplanar sections are used to derive equations for determining the normal stresses at an arbitrary point of a body of complex shape in tension and bending. The anisotropy of the material properties is taken into account by introducing a variable modulus of elasticity. The theoretical results have been checked experimentally.Gor'kii Zhadanov Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 351–354, March–April, 1969.     

Structural stresses in composites reinforced with a system of anisotropic fibers

The effect of the anisotropy of the mechanical and thermophysical characteristics of the reinforcement on the temperature stresses in unidirectional composites has been investigated. The stresses near fibers forming a regular structure in the transverse plane are estimated as a function of the thermoelastic properties of the components and the structure parameters.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 4, pp. 728–731, July–August, 1974.     

Effect of cyclic cooling to low temperatures on the adhesive strength of fiber-thermoplastic matrix joints

The adhesive strength of the interface between the polyarylene sulfone PSK-1 and a steel wire 150 mm in diameter was measured using a pull-out technique after cyclic cooling of the joints from room temperature down to liquid nitrogen temperature. All specimens were prepared under isothermal conditions (300 °C, 30 min) without applying pressure. The number of cycles N of plunging in liquid nitrogen reached 900. All measurements were taken at room temperature with constant loading rate. The joint areas S were varied within a wide range. It was found that ten cooling cycles do not cause any appreciable change in the values of (Figs. 1–3). After 100 cooling cycles, the adhesive strength losses reached 30–45% (Figs. 1–3). After 810 cycles, the fiber-matrix interface is almost totally destroyed (Fig. 1). As the number of cycles N increases, the character of the dependence of the adhesive strength on the joint area changes: when N < 100, the values of are reduced as the interfacial surface area increases; when N = 810, the adhesive strength does not depend on S. The main factor that governs the reduction in adhesive strength is assumed to be residual thermal stresses. Analysis of the data obtained here and earlier shows that the behavior of polymer-fiber systems after cyclic cooling down to low temperatures is the same for both network and linear polymer matrices. The origin of this behavior also seems to be the same for all polymer-fiber adhesive joints.Report presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 156–162, March–April, 1995.This work was done with the support of the International Science Foundation (the G. Soros Foundation), grant NED000.