On the extremal value of the thermoelastic energy of a material with an inclusion subject to mechanical and thermal action

Under prescribed thermoelastic stresses and known properties of the matrix and the inclusion in an elastic medium with an inhomogeneity, we find the shape of inhomogeneity that leads to an extremal value of the thermoelastic energy. From the necessary conditions for an extremum of the thermoelastic energy functional we find a condition for seeking the interface. For the case of isotropic cornponents and under loads of stretching (compression) type and uniform heating of the medium the shape of the inclusion can be found explicitly within a certain range of initial parameter values. The results of numerical study are presented and analyzed. One table. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 26–34.     

On the thermal runaway of combustible fluids in lagging material

This paper presents the mathematical foundations for a simpletheory for investigating the phenomenon of ignition of flammablefluids in lagging material that are used for insulation of hotpipework, for transport of heat transfer fluids, or other similarsituations. Experiments with porous material impregnated witha flammable fluid have simulated the self-heating known to occurwhen combustible liquids leak from a hot pipe into lagging surroundingthe pipe or are split from another source on to the lagging.A theory to explain these findings is presented which showsthat there is a watershed temperature beyond which substantialself-heating will take place. Although the theory does not takeaccount of diffusion, it simulates the main physics of the phenomenon–thatis, combustible fluid, which normally in the open air wouldevaporate and not be a hazard, can, within a porous medium,remain dispersed within the porous structure long enough forthe exothermic oxidation to develop into ignition.     

Temperature field of a layer of a fibrous composite material under conditions of external thermal radiation

On the basis of an expression for the scattering phase function of an individual fiber, relations modeling radiative properties of fibrous composites are obtained. We calculate the temperature state of a layer of such a material under condition of external thermal radiation. Dependences of temperature distributions on the volume fraction of fibers in the composite, their reflectance, and size are investigated. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 185–193, January–March, 2008.     

Propagation of acoustic waves in a fibrous fluid-filled material

The homogenization method is used for the analysis of acoustic wave propagation in a unidirectional fibrous material for the acoustic control of the fiber arrangement in manufacturing composites. Acoustic equations for a rigid periodic structure filled by a nonviscous fluid are obtained by two-dimensional asymptotic expansions. A regular square and triangular arrangement of the fibers with a round cross-section are considered. The analysis reveals that the velocity of acoustic waves is significantly affected by both the volume content and the fiber arrangement.Moscow State Academy of Chemical Engineering, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 651–655 September–October, 1997.     

Investigation of the processes of thermal and mechanical degradation of polymers using mass spectrometers. Review

The review covers work with mass spectrometers during the last 5 years involving the study of the processes of thermal and mechanical degradation of polymers. Special attention is given to the effect of defects in the macromolecules on the development of the thermal and mechanical degradation processes. It is suggested that the defects of the chemical structure of the macromolecules have an important influence not only on the thermal degradation but also on the development of mechanical failure. The possible uses of mass spectrometry in investigating interfaces are also examined. The initial experiments along these lines are discussed.     

Determination of effective thermal expansion coefficients of unidirectional fibrous nanocomposites

We present an efficient numerical scheme (based on complex variable techniques) to calculate the effective thermal expansion coefficients of a composite containing unidirectional periodic fibers. Moreover, the mechanical behavior of the fibers incorporates interface effects allowing the ensuing analytical model of the composite to accommodate deformations at the nanoscale. The resulting ‘nanocomposite’ is subjected to a uniform temperature variation which leads to periodic deformations within the plane perpendicular to the fibers and uniform deformations along the direction of the fibers. These deformation fields are determined by analyzing a representative unit cell of the composite subsequently leading to the corresponding effective thermal expansion coefficients. Numerical results are illustrated via several physical examples. We find that the influence of interface effects on the effective thermal expansion coefficients (in particular that corresponding to the transverse direction in the plane perpendicular to the fibers) decays rapidly as the fibers become harder. In addition, by comparing the results obtained here with those from effective medium theories, we show that the latter may induce significant errors in the determination of the effective transverse thermal expansion coefficient when the fibers are much softer than the matrix and the fiber volume fraction is relatively high.     

Intensity of mechanical action and mechanical degradation of rigid polymers

The authors have investigated the relation between the degradation of rigid carbon-chain polystyrene, polyvinyl acetate, and polymethyl methacrylate polymers with the kinetics of mechanical degradation during vibromilling. They determine the critical value of the intensity necessary for the onset of the degradation process.Moscow Technological Institute of Light Industry. Translated from Mekhanika Polimerov, No. 2, pp. 362–364, March–April, 1974.     

Post buckling response of functionally graded materials plate subjected to mechanical and thermal loadings with random material properties

In this paper, the second order statistics of post buckling response of functionally graded materials plate (FGM) subjected to mechanical and thermal loading with nonuniform temperature changes subjected to temperature independent (TID) and dependent (TD) material properties is examined. Material properties such as material properties of each constituent’s materials, volume fraction index are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear kinematic using modified C⁰ continuity. A direct iterative based C⁰ nonlinear finite element method (FEM) combined with mean centered first order perturbation technique (FOPT) proposed by last two authors for the composite plate is extended for Functionally Graded Materials (FGMs) plate with reasonable accuracy to compute the second order statistics (mean and coefficient of variation) of the post buckling load response of the FGM plates. The effect of random material properties with amplitude ratios, volume fraction index, plate thickness ratios, aspect ratios, boundary conditions and types of loadings subjected to TID and TD material properties are presented through numerical examples. The performance of outlined present approach is validated with the results available in literatures and independent Monte Carlo simulation (MCS).     

Optimization of dynamic mechanical response of a composite plate using multi-field coupling with thermal constraints

We consider the problem of optimizing the dynamic response of a mechanically loaded, rectangular, electrically conductive anisotropic composite plate by applying an electromagnetic field, which exploits the electro-magneto-mechanical field coupling phenomenon. An important aspect of the formulated nonlinear partial differential equation (PDE)-constrained optimization model is the presence of a thermal constraint that prevents polymer matrix degradation in the composite material due to Joule heating produced by the electromagnetic field. A black-box optimization approach based on the active set algorithm is employed. A system of governing PDEs is solved using a series of sequential numerical procedures that includes the method of lines, Newmark time-stepping scheme, quasilinearization, integration of two-point boundary-value problems, and a superposition method followed by orthonormalization. Implementation in hyper-dual arithmetics facilitated automatic differentiation and computation of the gradient. Optimization results show that application of an electromagnetic field with optimal characteristics enables one to significantly reduce the amplitude of the plate vibrations while controlling for Joule heating.     

Correlation between the strength and thermal conductivity of glass-reinforced plastics

The effect of changes in the component ratio and porosity of glass-reinforced plastics on their strength and thermal conductivity is considered. A correlation is shown to exist between the bending strength and thermal conductivity of a glass laminate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 749–751, July–August, 1969.     

Effect of material properties on the stability of transversely isotropic shells with an elastic filler subjected to the action of mechanical loads and temperature

The effect of the low shear strength of the material (glass-reinforced plastic) on the stability of cylindrical shells with an elastic filler is investigated in relation to axial compression, external pressure, and heating. The equations of the thermoelastic problem of the theory of monotropic shells, constructed with allowance for the effect of tangential shearing stresses, are used in the calculations.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. L'vov Polytechnic Institute. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 903–907, September–October, 1970.     

On the irregularity strength of trees

For any graph G, let n_i be the number of vertices of degree i, and . This is a general lower bound on the irregularity strength of graph G. All known facts suggest that for connected graphs, this is the actual irregularity strength up to an additive constant. In fact, this was conjectured to be the truth for regular graphs and for trees. Here we find an infinite sequence of trees with λ(T) = n₁ but strength converging to . © 2004 Wiley Periodicals, Inc. J Graph Theory 45: 241–254, 2004     

Mechanism by which tension on the fibrous filler affects the structure and the strength of wound glass-plastics

Conclusions 1. We have studied how the structure of glass-plastics wound with twisted threads is affected by tension on the fibrous filler. The trend of changes in fiber content and porosity, as well as an increasingly nonuniform distribution of the reinforcing filler over the thickness, has been established.2. The effect of a nonuniform filler distribution over the thickness on the tensile strength has been evaluated. The calculated and the experimental curve of strength as a function of the tension have been compared, the former taking into account variable porosity, fiber content, and nonuniformity of fiber distribution over the thickness.3. It has been demonstrated that the change in the strength characteristics of a wound glass-plastic as a function of the tension on the reinforcing filler during winding is due to a combined complex effect of such factors as the overall fiber content and porosity, a nonuniform fiber distribution over the thickness, the fiber orientation, and the degree of mechanical damage in threads due to their interaction with the active components of the winding machine.Report presented at the Third All-Union Conference on Polymer Mechanics. Riga, November 10–12, 1976.Translated from Mekhanika Polimerov, No. 3, pp. 439–444, May–June, 1977.     

Impregnation of fibrous fillers with polymeric binders 6. Effect of parameters of ultrasound treatment on strength properties of wound fibrous composites

Conclusion Tests of annular PCM specimens — fiberglasses and organoplastics formed by the method of wet winding using low-frequency ultrasound — were conducted. Three alternate US-impregnation schemes were investigated. Optimal alternate schemes and insonification parameters were established experimentally: frequency, amplitude, intensity, and time. Optimization was carried out on the basis of investigation of the relationships between the values of the tensile, compressive, bending, and interlayer-shear strengths, and also the relative content of filler as a function of treatment parameters. It was shown that deviation of insonification parameters from the optimal leads to a reduction in strength characteristics, as well as to a different character of specimen failure in tension and interlayer shear.The effect of US modification in producing PCM is provided by an increase in structural uniformity, and improvement of the strength and production characteristics of the polymer matrix, as well as by a reduction in the composite's effectiveness as a result of a reduction in the content of air inclusions and improvement of the binder's distribution across the section of the filler.For previous communication, see [9].Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 724–731, July–August, 1989.