Large deformations of homogeneous and fiber-reinforced cylinders under the action of centrifugal forces

The problem on large deformations of round cylinders made of homogeneous and fiber-reinforced elastomeric materials under the action of inertia forces caused by rotatory motion is solved. The solution is given in a plane axisymmetric statement, where the deformation parameters of the cylinders depend only on the radial coordinate. Based on the mathematical model presented, the deformation of revolving cylinders made of homogeneous elastomeric materials and reinforced with fibers in the axial, circumferential, and radial directions is investigated. The ultimate rotational speeds for cylinders with different reinforcement schemes and tight and loose fits are found at which their limiting configurations are reached. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 347-366, May-June, 2009.     

Quantum duality in quantum deformations

In accordance with the quantum duality principle, the twisted algebra is equivalent to the quantum group and has two preferred bases: one inherited from the universal enveloping algebra and the other generated by coordinate functions of the dual Lie group . We show howthe transformation can be explicitly obtained for any simple Lie algebra and a factorable chain of extended Jordanian twists. In the algebra , we introduce a natural vector grading , compatible with the adjoint representation of the algebra. Passing to the dual-group coordinates allows essentially simplifying the costructure of the deformed Hopf algebra , considered as a quantum group . The transformation can be used to construct new solutions of the twist equations. We construct a parameterized family of extended Jordanian deformations and study it in terms of ; we find new realizations of the parabolic twist. Dedicated to the birthday of my teacher, Yurii Novozhilov __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 112–125, July, 2006.     

Amplitude modulation of a low-coherence source, applications to distance and dynamic displacement sensing

The possibilities of the radio-frequency amplitude modulation of a low-coherence source for distance and displacement measurements are discussed. This intensity-based method, used within a Michelson interferometer, is a novel alternative to perform dynamic deformation measurements. The theoretical background is presented, together with the experimental verification of the principle. Besides, the results of the first quasi-dynamic tests are shown and the perspectives of the technique discussed. This method is specially useful for the dynamic monitoring of civil structures, where large measurements bases are needed. Furthermore, the application of the amplitude modulation for distance measurements is demonstrated experimentally.     

Steps in the Classification of Cohen–Macaulay Modules Over Singularities of Type xt + y3

Let k be an algebraically closed field of characteristic 3 and i, j, t some positive integers such that 1 i < j < t, i + j t. Then there exist a finite number of nonisomorphic indecomposable maximal Cohen–Macaulay modules N over k[[x, y]] /(x^t + y³) such that N / y N is a direct sum of copies of k[[x]] /(xⁱ), k[[x]] /(x^j) and we describe them completely.     

On Continuous and Differential Hochschild Cohomology

We show that there are canonical isomorphisms between Hochschild cohomology spaces , where is the algebra of smooth functions on a manifold M and the space of skew multivector fields over M. This implies that continuous and differential deformation theories of coincide.     

Discrete Structure of Some Schlesinger Systems on the Riemann Sphere

In the present work we investigate the group structure of the Schlesinger transformations for isomonodromic deformations of the Fuchsian differential equations. We perform these transformations as isomorphisms between the moduli spaces of the logarithmic sl(N)-connections with fixed eigenvalues of the residues at singular points. We give a geometrical interpretation of the Schlesinger transformations and perform our calculations using the techniques of the modifications of bundles with connections, or, the Hecke correspondences for the loop group SL(N)C(z).     

Theoretical Modeling of Mechanical Resistance and Stability and Related Characteristics of Polymeric Systems with Branching/Cross-Linking

A theoretical (thermodynamic) method for the estimation of mechanical characteristics of polymeric systems is proposed. This method uses the statistical polymer method for modeling of branched/cross-linked structures. The weak interaction between macromolecules is modeled in the approach of their mutual interpenetration. The proposed method is used for the estimation of mechanical resistance and stability of microporous polymeric materials. An engineer method for the evaluation of mechanical stability and resistance of polymeric materials is derived.     

Deformations of pressure vessel domes in asymmetric winding

The deformation of pressure vessel domes in asymmetric winding with the use of two families of yarns is accompanied by shear deformations and torsion. For the case of large deformations, a system of equations for describing the stress-strain state of an asymmetrically reinforced netlike shell of revolution loaded with an internal pressure is obtained. It is shown that the shear deformations depend on the deformations of both the yarn families and the deformations of meridians and parallels of the shell. As an example, the dome of a pressure vessel in a deformed state is calculated for an initial equilibrium shape determined on the assumption that the yarns are inextensible. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 425–432, July–August, 2006.     

Inverse Problems of the Mechanics of Thin-Walled Composite Structures

New formulations and methods for the solution of the inverse problems of thin-walled layered and reinforced shells and plates are discussed. Rational projects with regard for the requirements of nonflexural deformations in layered structural members, the given deformability of particular surfaces, the realization of a strictly momentless state, an equally stressed reinforcement, and the breaking strength of the binder at the interfaces are investigated. A brief review of the known solutions to these problems is given, and solutions to some new problems are described.     

Peculiar features in the rheological behavior of electrorheological suspensions

Studies have been made of concentrated (up to 60%) diatomite suspensions in transformer oil, the structure and theological properties of which depend on an applied electric field. Studies have been conducted of steady-state and transient regimes of straining involving continuous and periodic shear. The structure in such suspensions is formed in the presence of an electric field of 10^–3 –10² duration. The suspensions under continuous stationary strain behave as non-Newtonian fluids with a yield stress dependent on electric intensity. Under periodic deformation conditions the test suspensions exhibit elasticity which abruptly diminishes with increasing deformation amplitude.