Effect of fiber tension on the unwinding resistance of hardening layers of glass-reinforced plastic

The shear fracture toughness characteristics of glass-reinforced plastics used for strengthening metal pressure vessels have been determined by testing metal-GRP rings. The shear fracture toughness characteristics are statistically estimated for a unidirectional GRP as a function of the winding tension.K. É. Tsiolkovskii Moscow Aviation Engineering Institute. Translated from Mekhanika Polimerov, No. 5, pp. 935–938, September–October, 1975.     

Initial stresses in filament-wound reinforced-plastic rings

Methods of experimentally determining the initial stresses in filament-wound GRP rings are examined and the effect of winding tension is investigated. It is shown that by varying the winding tension it is possible to exercise a considerable degree of control over the magnitude and distribution of the initial stresses.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 505–511, May–June, 1969.     

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems for scalar-valued measures on rings of sets that are in general not σ-rings are presented. As a consequence, the rings of subsets of N with density zero and uniform density zero are shown to have the Nikodym property. In addition, vector measure generalizations of the Vitali–Hahn–Saks theorem are given.     

Methods of taking into account the nonlinearity of the deformation properties of the material in calculating thick-walled composite rings

The results of an investigation of the deformation properties of unidirectional composites are presented, and engineering models which take into account the effect of the nonlinearity of the properties in the radial direction on the state of stress of rings under pressure are proposed. The relations obtained are checked theoretically — by means of a refined calculation based on the nonlinear theory of elasticity — and experimentally — by loading rings with internal and external pressure by means of rubber cuffs in specially designed apparatus.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 73–84, January–February, 1976.     

Associative rings

This survey is a continuation of a series of surveys on the theory of rings and modules. Results on the theory of associative rings covered in Referativnyi Zhurnal Matematika during the period 1972–1976 are discussed. The theory of radicals, rings with polynomial identities, rings of fractions, extensions of rings, group rings, properties of various classes of rings, topological and ordered rings, and other topics are considered.Translated from Itogi Nauki i Tekhniki, Algebra, Topologiya, Geometriya, Vol. 16, pp. 91–190, 1978.     

Effect of climatic loading on the residual stresses and carrying capacity of thick-walled glass-reinforced plastic rings

The effect of climatic loading on the carrying capacity of thick-walled glass-reinforced plastic rings with different residual stress levels has been experimentally investigated. It is established that the rings with the greater residual stress level have a lower maximum breaking load. The carrying capacity of the rings is reduced after simulated aging. This effect is shown to be more sharply expressed in the experiments in which the rings were subjected to dynamic loading.Translated from Mekhanika Polimerov, No. 6, pp. 1132–1134, November–December, 1971.     

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.     

Nonassociative rings

Results in the theory of nonassociative rings and related directions reviewed in RZhMatematika during the period 1972–1978 are discussed. Special attention is given to infinite-dimensional Lie algebras, Jordan algebras, alternative rings, Mal'tsev algebras, and varieties, representations, and radicals of nonassociative rings.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 18, pp 3–72 1981.     

Carrying capacity of thick-walled glass-reinforced plastic rings operating under pressure

Experimental data are presented on the carrying capacity and deformability of thick-walled rings made of unidirectional and two-way glass-reinforced plastic subjected to external and internal pressure. A limitation on the carrying capacity of the rings with increase in relative thickness is noted; an explanation of this effect is offered.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1130–1132, November–December, 1971.     

Yield surfaces in local strain theory

The initial yield surfaces for biaxial tension and combined tension and torsion are determined on the basis of the local strain theory. The limit surfaces of the resultant stress on a local plane in tension (torsion) are obtained. A plastic strain probability factor is introduced and its values are calculated for various loading paths.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 594–598, July–August, 1971.     

Isomorphism of a Ring to the Endomorphism Ring of an Abelian Group

This paper presents necessary and sufficient conditions under which isomorphism of endomorphism rings of additive groups of arbitrary associative rings with 1 implies isomorphism of these rings. For a certain class of Abelian groups, we present a criterion which shows when isomorphism of their endomorphism rings implies isomorphism of these groups. We demonstrate necessary and sufficient conditions under which an arbitrary ring is the endomorphism ring of an Abelian group. This solves Problem 84 in L. Fuchs’ “Infinite Abelian Groups.”__________Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 231–234, 2003.     

Experimental study on thin three-layer rings with a pliable filler

The bearing capacity of thin three-layer rings containing a pliable filler and exposed to internal and external stresses has been studied experimentally. The deformation and strength properties of the filler have been examined. The initial stresses in the rings examined have been determined by application of three methods; their effect on the bearing capacity has been estimated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1032–1037, November–December, 1974.     

Thermal effects in a glass laminate in tension

The results of a calorimetric investigation of a glass-reinforced textolite in uniaxial tension are presented. The specimens were deformed on the interval of strain rates from 0.3 to 10.5 mm/min at test temperatures from –30 to 80°C. The thermal effects are shown to depend on strain rate and test temperature.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 599–604, July–August, 1971.     

Experimental study of the effect of friction and bending on the strain distribution around the perimeter of a glass-reinforced plastic ring with unidirectional structure

The effect of friction and bending on the circumferential strain distribution in glass-reinforced plastic rings with unidirectional structure, stretched by two rigid half-disks, has been experimentally investigated. Strain distribution curves for rings of various thicknesses are given. The strain distribution at different levels over the thickness of the ring and the change in compressive strain along the radius have been studied.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 947–949, September–October, 1971.     

On the notion of Cohen–Macaulayness for non-Noetherian rings

There exist many characterizations of Noetherian Cohen–Macaulay rings in the literature. These characterizations do not remain equivalent if we drop the Noetherian assumption. The aim of this paper is to provide some comparisons between some of these characterizations in non-Noetherian case. Toward solving a conjecture posed by Glaz, we give a generalization of the Hochster–Eagon result on Cohen–Macaulayness of invariant rings, in the context of non-Noetherian rings.     

On the difference in the moduli of elasticity of polyamides subjected to different kinds of deformation

Experiments to determine the moduli of elasticity of polyamides (kapron) in tension and compression are described. A substantial difference in these characteristics was detected. The modulus of elasticity in tension is 0.75–0.80 of the value of the modulus in compresion. This difference is explained by the textural characteristics of the polyamides. The use of values of the modulus of elasticity obtained by testing specimens in tension to determine the stiffness of parts working in compression give overestimated strain values.Mekhanika Polimerov, Vol. 1, No. 4, pp. 47–51, 1965     

Homological Computations in PBW Modules

In this paper the Poincaré–Birkhoff–Witt (PBW) rings are characterized. Gröbner bases techniques are also developed for these rings. An explicit presentation of Ext ⁱ (M,N) is provided when N is a centralizing bimodule.     

Local Points of Motives in Semistable Reduction

In this paper we study – for a semistable scheme – a comparison map between its log-syntomic cohomology and the p-adic étale cohomology of its generic fiber. The image can be described in terms of what Bloch and Kato call the local points of the underlying motive. The results extend a proven conjecture of Schneider which treats the good reduction case. The proof uses the theory of logarithmic schemes, some crystalline cohomology theories defined on them and various techniques in p-adic Hodge theory, in particular the Fontaine–Jannsen conjecture proven by Kato and Tsuji as well as Fontaine's rings of p-adic periods and their properties. The comparison result may become useful with respect to cycle class maps.     

Stress relaxation in physically nonlinear polymer materials under simultaneous tension and torsion

Conclusions 1. Application of our method of determining the parameters of physically nonlinear polymer materials from tests in uniaxial tension or in torsion ensures a satisfactory agreement between theoretical and experimental stress-relaxation curves corresponding to other modes of loading.2. Theoretical stress-relaxation curves for shear (tension) calculated on the basis of parameters which have been determined from approximations of stress-relaxation curves for tension (torsion) fall closely within the confidence interval for an individual measurement (with =95%).3. The agreement between theoretical and experimental stress-relaxation curves for a plane state of stress is 2–3 times worse, in terms of the mean-square relative difference, than the agreement between the respective curves for uniaxial tension.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 797–803, September–October, 1977.     

Strengthening of glass-fiber-reinforced plastic under biaxial tension

Conclusions 1. The effect of axial tension, applied at the first stage of loading under biaxial tension, on the increase in the hoop strength of an oriented glass-fiber-reinforced plastic was observed. The increase in the hoop strength depends both on the value of the axial tensile load, and on the angle of winding of the fibers.2. The effect observed is in this case apparently independent of the condition of loading of the sample under biaxial tension.Institute of Mechanics, Academy of Sciences of the Armenian SSR, Erevan. Translated from Mekhanika Polimerov, No. 6, pp. 1025–1029, November–December, 1976.