Stress state in multilayer cylindrical tubes made of elastically compressible linear viscoelastic material

Through the use of Abel's operators and э operators, the authors obtained an implicit solution for N-layered cylindrical tubes with alternating elastic and viscoelastic layers under conditions of elastic compressibility of the viscoelastic medium. Explicit expressions were written for the reactive pressures in 3- and 2-layered cylindrical tubes with alternating elastic and viscoelastic layers; these are analyzed in detail. Based on the solution obtained earlier for a condition where the viscoelastic operator corresponding to Poisson's coefficient is taken as a constant, it has been shown that the hypotheses discussed will lead in time to qualitatively different stress states. The overall results obtained are illustrated on an example.     

On the sonic composites with scatterers made from auxetic material

A finite size periodic array of resonators made from auxetic material embedded into an epoxy matrix is analyzed in this paper. According to the Bragg's theory, the sound attenuation band is due to the superposition of multiple reflected waves inverse proportional to the central distance between resonators. The sound attenuation in such composites is studied using a method that combines the features of the cnoidal method and the genetic algorithm [1-3]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solution of the problem of the plane deformation of a tube made of physically nonlinear quadratic viscoelastic material

An exact solution is obtained for the problem of the plane deformation of a tube of quadratically nonlinear viscoelastic material characterized by four kernels. For given boundary pressures the solution contains functions determined from simple creep and relaxation tests for stresses and strains lying in the region of linearity of the relation. In accordance with the method of approximations for nonlinear materials [9], an approximation is given for a series of convolution integrals of increasing multiplicity in transforms and inverse transforms together with an error estimate.Moscow Institute of Electronic Engineering. Translated from Mekhanika Polimerov, No. 1, pp. 117–123, January–February, 1973.     

Axisymmetric trawl cod-ends made from netting of a generalized mesh shape

The equations governing the geometry of axisymmetric trawl cod-endsmade from netting of meshes of a particular generalized structureare derived. From this, by suitable setting of the initial meshbar lengths, the equations governing the geometry of cod-endsthat are of importance to the fishing industry can be readilydeduced. It is assumed that arbitrary membrane forces act normalto the edges of the mesh elements, that there is no shear forceacting on the edge of a mesh element and that the twine thatmakes up the netting is extensible. The case where there isslackness in the mesh bars in the circumferential directionis dealt with and it is demonstrated how the finite structureof a knot can be taken into account. The case where the membraneforces arise solely as a result of and can be expressed by theappropriate components of the tensions in the mesh bars is alsoexamined and numerical solutions are found for a range of examples.     

Design and analysis of planar shape deformation

Shape deformation refers to the continuous change of one geometric object to another. We develop a software tool for planning, analyzing and visualizing deformations between two shapes in . The deformation is generated automatically without any user intervention or specification of feature correspondences. A unique property of the tool is the explicit availability of a two-dimensional shape space, which can be used for designing the deformation either automatically by following constraints and objectives or manually by drawing deformation paths.     

Quantification of the evolution of shape storage and recovery in thermally responsive shape memory polymers

This study demonstrates the relevance of strain and stress storage/recovery profiles for the thermomechanical behaviour of thermally responsive Shape Memory Polymers (SMPs). It is shown how these experimentally determined profiles may be used for the development, calibration and validation of continuum-based models describing the shape memory effect in polymeric materials. The presented methodology applies both to small and finite strain deformation problems under the assumption of constant strain and cooling/heating rates. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free vibrations of thin annular plates made from functionally graded material

Subject of the consideration is thin annular plate made of a two-phase functionally graded composte. The plate has periodically inhomogeneous microstructure slowly varying in space: the λ-periodic structure along circular coordinate, but smoothly graded apparent (averaged) properties in the perpendicular, radial direction. The aim of the contribution is to derive and apply a deterministic macroscopic model describing the free vibrations of this plate. Modeling procedure is based on tolerance averaging technique. We received, equations system with smooth coefficients. We made numerical solution of this problem, using finite difference method, and analyze influence of material proportion and microstructure size on first frequency of free vibrations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the degree of holomorphic mappings from an annulus into an annulus

We establish an estimate for the degree of a holomorphic mapping f : K 1 K ₂ (here, K ₁ and K ₂ are doubly-connected domains) in terms of the modulus of a family of curves in K ₂. This estimate generalizes a result obtained by Kobayashi.Published in Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 8, pp. 1135–1138, August, 2004.     

Large deformation shape uncertainty quantification in acoustic scattering

We address shape uncertainty quantification for the two-dimensional Helmholtz transmission problem, where the shape of the scatterer is the only source of uncertainty. In the framework of the so-called deterministic approach, we provide a high-dimensional parametrization for the interface. Each domain configuration is mapped to a nominal configuration, obtaining a problem on a fixed domain with stochastic coefficients. To compute surrogate models and statistics of quantities of interest, we apply an adaptive, anisotropic Smolyak algorithm, which allows to attain high convergence rates that are independent of the number of dimensions activated in the parameter space. We also develop a regularity theory with respect to the spatial variable, with norm bounds that are independent of the parametric dimension. The techniques and theory presented in this paper can be easily generalized to any elliptic problem on a stochastic domain.     

Nonaxisymmetric bulging of cylindrical shells made from polymeric material on prolonged loading

Forms of bulging of cylindrical shells prepared from polymeric materials caused by the action of a constant compressing load in the direction of the generatrix are discussed. The functions of the initial irregularities and the additional radial deflection and stresses are characterized by the Fourier series in a complex representation. When the problem in a geometrically and physically nonlinear formulation was solved, it was found that the form of the deformed surface is transformed, and the bulging of the shell at the critical instant takes place asymmetrically. This agrees with the experimental results.     

Temperature stresses in plates made of reinforced laminated material

The heat conduction equations and the basic equations of the quasi-static axisymmetric problem of thermoelasticity are obtained for thin plates with heat transfer and cylindrical anisotropy. The nonsteady temperature stresses are determined for an infinite plate with a circular opening and an annular plate, both made of reinforced laminated material.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Translated from Mekhanika Polimerov, No. 4, pp. 721–726, July–August, 1970.     

Splitting of resonant and scattering frequencies under shape deformation

It is well known that the main difficulty in solving eigenvalue problems under shape deformation relates to the continuation of multiple eigenvalues of the unperturbed configuration. These eigenvalues may evolve, under shape deformation, as separated, distinct eigenvalues, and the splitting may only become apparent at high orders in their Taylor expansion. In this paper, we address the splitting problem in the evaluation of resonant and scattering frequencies of the two-dimensional Laplacian operator under boundary variations of the domain. By using surface potentials we show that the eigenvalues are the characteristic values of meromorphic operator-valued functions that are of Fredholm type with index 0. We then proceed from the generalized Rouché's theorem to investigate the splitting problem.     

On the interrelation between dissipation and chemical energies in modeling shape memory alloys

We use the principle of maximum dissipation for thermo-mechanically coupled modeling of poly-crystalline shape memory alloys (SMA). This modeling scheme demands approaches for both Helmholtz free energy and dissipation. For time-independent processes, dissipation is usually modeled by the norm of the internal variable's rate times a factor. We show that for SMAs this factor is not an additional modeling parameter. In contrast, it can be calculated from the Helmholtz free energy. This reduces the number of model parameters and provides furthermore an interesting effect of the model which allows to display the material behavior in an even more realistic manner. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)