Yield condition for circular cylindrical shells made of a fiber-reinforced composite

A yield condition is obtained for circular cylindrical shells made of a definite class of fiber-reinforced composite material whose components possess plastic properties. It is shown that, in the plane of generalized stresses — the axial bending moment and the circumferential force (when the axial force is absent) — the yield curve consists of two linear and four curvilinear sections. By approximating the curvilinear sections, we get a piecewise linear yield condition described by a hexagon in the plane indicated. The nonlinear equations and the corresponding piecewise linear equations of the yield condition for particular cases are given in the form of tables. In solving specific boundary-value problems, we consider a circular cylindrical shell simply supported at its ends and loaded with a uniform internal pressure, for which the load-carrying capacity is determined in relation to the mechanical properties of composite components and some characteristic geometrical parameters. The results of numerical calculations are represented in the form of graphs. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 655–666, September–October, 2006.     

A continuous model for investigation of physically nonlinear deformation of orthotropic sandwich plates

A phenomenological yield condition for quasi-brittle and plastic orthotropic materials with initial stresses is suggested. All components of the yield tensor are determined from experiments on uniaxial loading. The reliability estimates of the criterion suggested is discussed. For a plastic material without initial stresses, the given condition transforms into the Marin—Hu criterion. The defining equations of the deformation theory of plasticity with isotropic and “anisotropic” hardening, associated with the yield condition suggested, are obtained. These equations are used as the basis for a highly accurate nonclassical continuous model for nonlinear deformation of thick sandwich plates. The approximations with respect to the transverse coordinate take into account the flexural and nonflexural deformations in transverse shear and compression. The high-order approximations allow us to model the occurrence of layer delamination cracks by introducing thin nonrigid interlayers without violating the continuity concept of the theory. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. pp. 329–340, May–June, 2000.     

Correlation between the strength of fiber-reinforced plastics and the adhesive strength of fiber—Matrix joints

The relationship between the strength (σc) of unidirectional fiber-reinforced plastics in different stressed states and the interfacial strength of their components is investigated. The shear adhesive strength (τ0) of fiber—matrix joints determined by the pull-out technique is used as a measure of the interfacial strength. To obtain the correlation curves betweenσc andτ0, the experimental results are used, where both the plastic and adhesive strength change under the influence of a single factor. In this case, such factors are the fiber surface treatment, nature and composition of polymer matrices, and test temperature. It is shown that the strength of the glass, carbon, and boron plastics increases practically linearly with increased interfacial strength. Such a behavior is observed in any loading conditions (tension, shear, bending, and compression). Sometimes, a small (10–20%) increase in the adhesive strength induces a significant (50–70%) growth in the material strength. Therefore, the interface is the “weak link” in these composites. The shape of theσc—τ0 curves for composites based on the high-strength and high-modulus aramid fibers and different thermoreactive matrices depends on the nature of the fiber and the type of stress state. In many cases, the composite strength does not depend on the interfacial strength. Then, the fiber itself is the “weak link” in these composites. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 291–304, May–June, 2000.     

A note on slant submanifolds of nearly trans-Sasakian manifolds

The geometry of slant submanifolds of a nearly trans-Sasakian manifold is studied when the tensor field Q is parallel. It is proved that Q is not parallel on the submanifold unless it is anti-invariant and thus the result of [CABRERIZO, J. L.—CARRIAZO, A.—FERNANDEZ, L. M.—FERNANDEZ, M.: Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125–138] and [GUPTA, R. S.—KHURSHEED HAIDER, S. M.—SHARFUDIN, A.: Slant submanifolds of a trans-Sasakian manifold, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47 (2004), 45–57] are generalized.     

Topics in isotopic pairs and their representations. II. The general supercase

Isotopic pairs—algebraic objects suitable for describing some forms of non-Hamiltonian (magnetic-type) interactions of Hamiltonian systems at the quantum level—are considered with maximum generality within the framework of the vector superalgebra formalism. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 1, pp. 149–158, April, 1997.     

Self-adhesion of amorphous polymers and their miscible blends

The amorphous film surfaces of polystyrene (PS), poly(2,6-dimethyl 1,4-phenylene oxide) (PPO), and their miscible blends are brought into overlap contact below the glass transition temperature T _g for 10 min and 24 h in order to obtain PS—PS, PPO—PPO, and blend—blend self-adhesive joints. It is shown that after the contact of the blend surfaces, i.e., when the molecules of both PS and PPO are present at the interface, it is possible to attain higher values of shear strength as compared with those at PS—PS and PPO—PPO interfaces. This points to the contribution of a specific interaction between the segments of PS and PPO to the strength development at the interface. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 1, pp. 127–135, 2000.     

Weyl connections and the local sphere theorem for quaternionic contact structures

We apply the theory of Weyl structures for parabolic geometries developed by Čap and Slovák (Math Scand 93(1):53–90, 2003) to compute, for a quaternionic contact (qc) structure, the Weyl connection associated to a choice of scale, i.e. to a choice of Carnot–Carathéodory metric in the conformal class. The result of this computation has applications to the study of the conformal Fefferman space of a qc manifold, cf. (Geom Appl 28(4):376–394, 2010). In addition to this application, we are also able to easily compute a tensorial formula for the qc analog of the Weyl curvature tensor in conformal geometry and the Chern–Moser tensor in CR geometry. This tensor was first discovered via different methods by Ivanov and Vasillev (J Math Pures Appl 93:277–307, 2010), and we also get an independent proof of their Local Sphere Theorem. However, as a result of our derivation of this tensor, its fundamental properties—conformal covariance, and that its vanishing is a sharp obstruction to local flatness of the qc structure—follow as easy corollaries from the general parabolic theory.     

On identities of the Rogers-Ramanujan type

A generalized Bailey pair, which contains several special cases considered by Bailey (Proc. London Math. Soc. (2), 50, 421–435 (1949)), is derived and used to find a number of new Rogers-Ramanujan type identities. Consideration of associated q-difference equations points to a connection with a mild extension of Gordon’s combinatorial generalization of the Rogers-Ramanujan identities (Amer. J. Math., 83, 393–399 (1961)). This, in turn, allows the formulation of natural combinatorial interpretations of many of the identities in Slater’s list (Proc. London Math. Soc. (2) 54, 147–167 (1952)), as well as the new identities presented here. A list of 26 new double sum–product Rogers-Ramanujan type identities are included as an Appendix. 2000 Mathematics Subject Classification Primary—11B65; Secondary—11P81, 05A19, 39A13     

On the non-emptiness of the fuzzy core

The seminal contribution of Debreu and Scarf (Int Econ Rev 4:235–246, 1963) connects the two concepts of core and competitive equilibrium in exchange economies. In effect, their core-equilibrium equivalence result states that, when the set of economic agents is replicated, the set of core allocations of the replica economy shrinks to the set of competitive allocations. Florenzano (J Math Anal Appl 153:18–36, 1990) defines the fuzzy core as the set of allocations which cannot be blocked by any coalition with an arbitrary rate of participation and then shows the asymptotic limit of cores of replica economies coincides with the fuzzy core. In this note, we provide an elementary proof of the non-emptiness of the fuzzy core for an exchange economy. Hence, in motivation, our result is similar to the contribution of Vohra (On Scarf’s theorem on the non-emptiness of the core: a direct proof through Kakutani’s fixed point theorem. Brown University Working Paper, 1987) and Shapley and Vohra (Econ Theory 1:108–116, 1991) for the core. Unlike the classical Debreu–Scarf limit theorem (Debreu and Scarf in Int Econ Rev 4:235–246, 1963) and its numerous extensions our result does not require any asymptotic intersection—or limit—of the set of core allocations of replica economies. The author would like to thank the Netherlands Organisation for Scientific Research (NWO) for financial support.     

Strength and deformation characteristics of poly(ethylene terephtalate)/elastomer blends

Changes in the toughness of crystalline poly(ethylene terephtalate) upon addition of two elastomers — ethylene-propylene-diene terpolymer and ethylene-α-octene copolymer — are investigated. Blends with increasing elastomer content (up to 30 wt.%) were obtained and modified by γ-radiation up to a 300-kGy absorbed dose. The interrelation between the toughness and certain tensile characteristics (elastic modulus, yield stress, ultimate stress, elongation at break, and specific fracture energy) of the blends, with various structural features of components (crystallinity and the degree of cross-linking) and morphology of the blends, is discussed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 521–534, July–August, 2008.     

Spatial braiding of cylindrical articles

The effective deformative characteristics of spatially reinforced composites made by spatial braiding along the generatrices of a one-sheet hyperboloid are analyzed. The geometrical relationships determining the structure of a unit cell of a braided composite are derived. The effective thermoelastic characteristics are calculated by the method of orientational averaging. The dependences of the bending and torsional stiffnesses of thick-walled cylindrical rods — made by the method suggested and by winding — on the braiding/winding angle are compared. The numerical estimations are given for rods made of carbon (CFRP) and aramid (AFRP) epoxy plastics. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompzitnykh Materialov, Vol. 36, No. 3, pp. 341–354, May–June, 2000.     

Quantitative Generalized Bertini-Sard Theorem for Smooth Affine Varieties

Let X ⊂ ℂⁿ be a smooth affine variety of dimension n – r and let f = (f₁,..., f_m): X → ℂ_m be a polynomial dominant mapping. We prove that the set K(f) of generalized critical values of f (which always contains the bifurcation set B(f) of f) is a proper algebraic subset of ℂ_m. We give an explicit upper bound for the degree of a hypersurface containing K(f). If I(X)—the ideal of X—is generated by polynomials of degree at most D and deg f_i ≤ d, then K(f) is contained in an algebraic hypersurface of degree at most (d + (m – 1)(d – 1)+(D – 1)r)_n-rD_r. In particular if X is a hypersurface of degree D and f: X → ℂ is a polynomial of degree d, then f has at most (d + D – 1)_n-1D generalized critical values. This bound is asymptotically optimal for f linear. We give an algorithm to compute the set K(f) effectively. Moreover, we obtain similar results in the real case.     

Extended finite operator calculus—an example of algebraization of analysis

“A Calculus of Sequences” started in 1936 by Ward constitutes the general scheme for extensions of classical operator calculus of Rota—Mullin considered by many afterwards and after Ward. Because of the notation we shall call the Ward's calculus of sequences in its afterwards elaborated form—a ψ-calculus. The ψ-calculus in parts appears to be almost automatic, natural extension of classical operator calculus of Rota—Mullin or equivalently—of umbral calculus of Roman and Rota. At the same time this calculus is an example of the algebraization of the analysis—here restricted to the algebra of polynomials. Many of the results of ψ-calculus may be extended to Markowsky Q-umbral calculus where Q stands for a generalized difference operator, i.e. the one lowering the degree of any polynomial by one. This is a review article based on the recent first author contributions [1]. As the survey article it is supplemented by the short indicatory glossaries of notation and terms used by Ward [2], Viskov [7, 8], Markowsky [12], Roman [28–32] on one side and the Rota-oriented notation on the other side [9–11, 1, 3, 4, 35] (see also [33]).     

I sottogruppi del gruppo modulare con coefficienti del corpo di Jacobi-Eisenstein e un teorema sui gruppi finiti

Sommario Introduzione — § 1 – 1. L'indice μ(n) dei sottogruppi Г_μ(n) del gruppo Γ di sostituzioni lineari unimodulari con coefficienti del campo diJacobi-Eisenstein — 2. Il poliedro fondamentale del sottogruppo Г_μ(1−ε) — § 2 – 3. I campi fondamentali dei gruppi Г_μ(n) — 4. Impossibilità di limitare con un numero finito di piani e sfere di riflessione i poliedri fondamentali dei gruppi Г_μ(n), conn intero razionale pari, diverso da 2 — § 3 – 5. Relazioni fondamentali fra le sostituzioni generatrici del gruppo di sostituzioni lineari con coefficienti del corpo K_ε con determinante ±1 — § 4 – 6. Sulla indipendenza delle sostituzioniS,T,U, generatrici del gruppo finito G_2μ(n) e sulle loro relazioni caratteristiche nel gruppo G_2μ(n) — § 5 – 7. Dimostrazione del teorema fondamentale sui gruppi G_2μ(n). Lemmi preliminari — 8, Dimostrazione del teorema fondamentale nel caso di moduli primi con 2(1−ε) — § 6 – 9. Il teorema fondamentale per i modulim(1−ε), 3m, 2m, 2m(1−ε), 6m conm primo con 6 – 10. Immagine geometrica dei gruppi G_2μ(1−ε) — § 7 – 11. Il gruppo delle sostituzioni unimodulari , [c/1+4ma]=+1, e il caso eccezionale dei moduli 4m – 12. Il gruppo delle sostituzioni unimodulari [c/1+3m(1−ε)a]₃=+1 e il caso eccezionale dei moduli 3(1−ε)m.     

On the hyperbolic unitary geometry

Hans Cuypers (Preprint) describes a characterisation of the geometry on singular points and hyperbolic lines of a finite unitary space—the hyperbolic unitary geometry—using information about the planes. In the present article we describe an alternative local characterisation based on Cuypers’ work and on a local recognition of the graph of hyperbolic lines with perpendicularity as adjacency. This paper can be viewed as the unitary analogue of the second author’s article (J. Comb. Theory Ser. A 105:97–110, 2004) on the hyperbolic symplectic geometry.     

Some argument inequalities for certain analytic functions

For analytic functions f(z) in the open unit disk U and convex functions g(z) in U, Nunokawa et al. [NUNOKAWA, M.—OWA, S.—NISHIWAKI, J.—KUROKI, K.—HAYAMI, T: Differential subordination and argumental property, Comput. Math. Appl. 56 (2008), 2733–2736] have proved one theorem which is a generalization of the result [POMMERENKE, CH.: On close-toconvex analytic functions, Trans. Amer. Math. Soc. 114 (1965), 176–186]. The object of the present paper is to generalize the theorem due to Nunokawa et al..     

The relation between intuitionistic and classical modal logics

Intuitionistic propositional logicInt and its extensions, known as intermediate or superintuitionistic logics, in many respects can be regarded as just fragments of classical modal logics containingS4. The main aim of this paper is to construct a similar correspondence between intermediate logics augmented with modal operators—we call them intuitionistic modal logics—and classical polymodal logics We study the class of intuitionistic polymodal logics in which modal operators satisfy only the congruence rules and so may be treated as various sorts of □ and ◇. Supported by the Alexander von Humboldt Foundation. Translated fromAlgebra i Logika, Vol. 36, No. 2, pp. 121–155, March–April, 1997.     

Experimental and theoretical investigation of a composite beam for bridge structures

Results of an experimental and theoretical investigation of composite beams as elements of bridge superstructure are presented. Experiments on beams of two types — made of wood and the same beams with a composite sheath — were carried out. The rigidity of the beams of the second type was about twice as high as that of the first ones. The classical bending model of composite beams gave deflections smaller than experimental ones. To reconcile these results, the model is refined by including the effect of shear. The deflections are represented as classical ones multiplied by a shear factor which depends on the bending and shear stiffnesses and the span length of the beams. As a result, a good agreement between calculations and experiments is achieved. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 449–462, July–August, 2006.     

Thermal conductivity of micro-and nanostructural epoxy composites at low temperatures

The thermal conductivity of epoxy composites containing not only the traditional fillers quartz, talc, carbon black, and aerosil, but also the very promising carbon nanomaterials is investigated. Two kinds of carbon nanomaterials — multi-wall (MWNT) and single-wall (SWNT) carbon nanotubes — were considered. The influence of their content (from 0.05 to 3.0 wt.%) on the thermal conductivity of MWNT-epoxy composites was studied. The thermal conductivity of epoxy composites was examined in the temperature range from −150 to 150°C. It was found that the introduction of 0.1–1.0 wt.% MWNT enhanced the thermal conductivity of pure epoxy resin by about 40%. A further increase in content of the nanotubes decreased the thermal conductivity. This can be explained by the worsening of nanotube dispersion at their high concentrations. The maximum growth in the thermal conductivity of the epoxy composites, on the entire range of temperatures considered, was observed at a 0.1 wt.% content of MWNT. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 117–126, January–February, 2008.     

Modal operators on commutative residuated lattices

We prove some fundamental properties of monotone modal operators on bounded commutative integral residuated lattices (CRL). Moreover we give a positive answer to the problem left open in [RACHŮNEK, J.—ŠALOUNOV á, D.: Modal operators on bounded commutative residuated Rℓ-monoids, Math. Slovaca 57 (2007), 321–332].