Nonsymmetrical temperature fields and stresses in cylinders made of nonuniform composites

The class of problems for determining nonsymmetrical temperature fields and stress in thick-walled hollow nonuniform cylinders is considered. A resolution set of differential equations is constructed for determining steady-state temperature fields, stresses, and displacements in asymmetrically heated cylinders which are arbitrarily nonuniform with respect to thickness with one plane of elastic symmetry. An approach is suggested for effective numerical solution of this class of problems. Problems are analyzed for thick-walled cylinders whose relative volume content of reinforcing elements varies in the radial direction. Known relationships of composite mechanics are used in order to find effective mechanical and thermophysical parameters for the material. Examples are provided for solving specific problems which point to the requirement of considering nonuniformity with respect to thickness.To be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 494–500, July–August, 1995.     

Determination of the mechanical indices of composite materials by testing multilayered samples

The mechanical indices of materials such as composites reinforced by braids and ribbons are difficult to determine by standard methods. Moreover, the indices of such materials may be greatly altered when they are converted into various structures. It has been suggested that these indices be determined by analyzing the structure testing data. The determination of linear and nonlinear elastic, plastic, and viscoelastic parameters of reinforced materials is discussed. A very simple structure, namely, cylindrical shells made by symmetric winding, is studied as an example. Equilibrium conditions are used to obtain resolving equations relative to the mechanical indices. Convergence of iteration methods is examined. The effect of the scatter of experimental data on the calculated results is analyzed.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 607–615, September–October, 1995.     

Effect of mineral fillers on properties of composite matrix material

The influence of mineral fillers on thermomechanical properties of matrix material of composites is investigated. Different methods to determine elastic properties and thermal expansion coefficients of composite materials have been considered and compared. Injection moulded polyester samples containing varying concentrations of talc filler are tested and properties such as Young 's modulus, thermal expansion coefficients, and volumetric shrinkage during cure are measured. Results obtained by theoretical models and from experiments are compared and discussed.To be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 435–445, July–August, 1995.     

Modeling process operations in the forming of parts made of flat metal-polymer composites

The forming of complex three-dimensional parts (tubular structures, sections, shells) from flat sheets of metal-polymer composites is examined. Results are reported from a series of experimental studies of the strain and strength characteristics of these composites, and features of the fabrication of shells of single and double curvature are analyzed. One method of solving the problem of bending shells of complex shape with large displacements (deflections) beyond the elastic limit of the material is proposed and substantiated empirically.Paper to be presented at the IX International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 417–427, May–June, 1995.     

Deformation of elastic polyurethanes with a bimodal cellular structure

This article examines the cellular structure and mechanical properties of elastic foamed polyurethanes with a bimodal cellular structure (BFPUs). It is shown that the sizes of the oval cells (3–12 mm) in the elastic foamed polyurethenes that are studied are a tenth of an order greater than the sizes of the polyhedral cells (0.1–0.6 mm). Conversely, for rigid foamed polyurethanes, the polyhedral cells are more than a tenth of an order larger than the oval cells (microcells). The equations of the compression curve of BFFUs are found, and it is established that the deformation of BFPUs is determined by the deformation function of the cellular structure and the viscoelastic properties of the polymer matrix. The deformation functions of the cellular structure and the relaxation properties of BFPUs are determined. It is shown that choosing BFPUs with a cellular structure improves the comfort properties of the foamed material: the softness coefficient increased by 8–19% in the investigated case, while the support coefficient increased by 15–35%.Paper presented at the IX International Conference on the Mechanics of Composite Materials (Riga, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 330–339, May–June, 1996.     

Dynamic compressive strength of epoxy composites

The strength of laminated and unidirectionally reinforced composite materials was investigated in conditions of dynamic uniaxial compression with a strain rate of 50–1000 sec^–1 using the split Hopkinson pressure bar method. It was shown that in conditions of dynamic compression, glass/epoxy, aramid/epoxy, and carbon/epoxy composites exhibit elastic-brittle behavior with anisotropy of the strength and elastic properties. The effect of the strain rate on the strength characteristics of fiberglass-reinforced plastics was demonstrated.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6, pp. 776–782, November–December, 1995.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).     

Numerical modelling of hardening polymers

An approach to complex modelling of structural, temperature and stress — strain states of hardening polymers is suggested. The approach does not basically need new experimental data. Numerical methods are used. The approach is employed with some programs. Some of the results of test calculations are given in the article.Presented at the 9th International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6. pp. 846–851. November–December, 1995.     

Application of the variation principle for the problem of buckling of a nonlinearly elastic ring nonuniform along its thickness

There has been considerable recent attention given to the stressed and buckled states of items with complicated configuration made of different nonlinearly elastic materials joined by complete adhesion. However, effective analytical solutions for such problems have been hindered by mathematical difficulties. Approximate methods have thus been developed for such problems. A variational combined principle has been formulated in this communication. A nonlinear geometrical approach has been used for formulating a mixed-type functional with physical relationships given by Euler equations, nonlinear equilibrium equations, and nonlinear boundary conditions for a piecewise-nonuniform nonlinearly elastic body composed of finite elements (particles). As an example, buckling along the nonuniform thickness of nonlinearly elastic rings was analyzed hypothetically assuming plane cross-sections. Options for two-, three-, four-, five-, and six-layered rings in a periodical structure have been reviewed. The critical buckling forces for an even number of layers have been found to be equal to each other. The ratios of the critical forces, elasticity moduli, and proportionality levels were determined for all five variants by the Runge-Kutta method.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 262–268, March–April, 1995.     

Analysis of the anisotropic properties of honeycomb sandwich plates

A mathematical model has been described and an approach proposed to the diagnostics of the anisotropic properties of the relative elasticity constants of three-layer (sandwich) plates with a honeycomb filler. Compact analytical relationships between the anisotropy coefficients and the geometrical dimensions of the cells have been obtained. A practical approach has been proposed for the selection of rational parameters of the honeycomb structure, at which its anisotropic properties would be in the chosen region of the functional space. The conditions have been formulated at which the constructive anisotropy, inherent to honeycomb structures, degenerates to isotropy for some relative elastic constants.Paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 482–487, July–August, 1995.     

Theory of spherofibrous composites. 2. Fundamental equations

Fundamental equations of the theory of spatially reinforced media with a matrix reinforced by spherical particles are proposed on the basis of a linearly reinforced layer and tl.e hypothesis of a longitudinal state. For an arbitrary orientation of the fibers, the generalized elasticity equation for composites was found to contain 21 elastic constants and approximate formulas were derived for their determination.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga. Latvia (October, 1995).Communication 1. see preceding article.A. A. Blagonravov Institute of Mechanical Engineering. Russian Academy of Sciences, Moscow. Russian. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 306–316, May–June, 1996.     

Production and characterization of UHMWPE fibers/LDPE composites

The production of unidirectionally fiber-reinforced composites (tapes) consisting of high-strength/high-modulus UHMWPE fibers and LDPE matrix is described. Two production techniques are applied: impregnation by aqueous powder dispersion and dry powder impregnation. The produced composites exhibit excellent mechanical properties. Depending on the fiber volume content which can be obtained: tensile strength (in fiber direction) 460–1100 MPa, elastic modulus 11–22 GPa, and elongation at break 4.9–8.3%.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Technical University of Berlin. Institute of Nonmetallic Materials. Polymer Physics Group.-Englishe Str. 20, D-10587 Berlin. Germany. Published in Mekhanik Kompozitnykh Materialov, Vol. 32, No. 6. pp. 719–728, November–December, 1996.     

Predicting the Deformability of Expanded Polystyrene in Short-Term Compression

A regressive model is presented for the relationship between the compressive stress and strain of expanded polystyrene (EPS) on a 0–35% strain range. On the whole, the model agrees well with experimental data. A practical way is suggested for determining the coefficients of the model from the known density of EPS plates and their compressive stress at a 10% strain. The model allows one to predict the critical compressive stress and the elastic modulus of EPS.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 157–162, March–April, 2005.     

Calculation of deformative and thermal properties of multiphase composite materials filled with composite or hollow spherical inclusions by the effective medium method

A theoretical investigation was carried out to examine the possibilities of a structural approach to prediction of elastic constants, creep functions, and thermal properties of multiphase polymer composite materials filled with composite or hollow spherical Inclusions of several types. The problem of determining effective properties of the composite was solved by generalizing the effective medium method, a variant of the self-consistent method, for the case of a four-phase kernel-shell-matrix-equivalent homogeneous medium model. Exact analytical expressions for the bulk modulus thermal expansion coefficient, thermal conductivity coefficient, and specific heat were obtained. The solution for the shear modulus is given in the form of a nonlinear equation whose coefficients are the solution of a system of 12 linear equations.To be presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 462–472, July–August, 1995.     

Asymptotic modeling of thin asymmetric laminates. Boundary-value problems and solution methods

We have investigated the internal dynamic stress-strain state of elastic laminates with perfectly joined anisotropic layers in the long-wave approximation. In contrast to familiar cases, in this treatment we allow an asymmetric arrangement of plies across the thickness and the most general anisotropy. We derive the generalized governing equations for plates by an asymptotic method based on three-dimensional dynamic elasticity. We discuss the similarities and differences between the derived two-dimensional theory and earlier models of S. A. Ambarisumyan and R. M. Christensen. We show that the asymptotic accuracy of the equations depends on the type of anisotropy: (i) general anisotropy; (ii) monodinic anisotropy or orthotropy of the layers.Report presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompositnykh Materialov, Vol. 31, No. 3, pp. 319–325, May–June, 1995.     

Majorant estimates for solutions of quadratic difference systems with lag

Systems of differential equations with lag with quadratic right-hand sides are considered. A compact matrix form for representing these systems in the general form is suggested. Upper and lower bounds for solutions of systems of quadratic differential equations with arbitrary lag are obtained by using quadratic Lyapunov functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 542–545, April, 1995.     

Electromechanical properties of laminated piezoelectric composites

The general expressions for the effective elastic, piezoelectric, and dielectric coefficients of a laminated piezocomposite composed of laminates in parallel connection are shown. By means of the asymptotic averaging method [12] these effective coefficients are calculated. The effective coefficients as well as physical properties such as electromechanical piezoelectric coupling coefficients, acoustic impedance, and wave velocity for a two-phase composite, where one phase is ceramic and the other one is polymer, are analyzed. A comparison with another results is shown.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 410–417, May–June, 1996.     

Limiting stresses in spatially reinforced composites with components-having different structural geometries nd elastic properties

A model which is proposed for calculating structural stresses in spatially reinforced composites and an invariant-polynomial criterion for evaluating their limiting values are used to predict the effect of the elastic and strength properties of the components and their relative content on the limiting stress-strain state of composites of different structures. Emphasis is given to tri-orthogonal and 4D cubic structures, in addition to structures with hexagonal and angle-ply fiber reinforcement schemes in the plane and perpendicular to it. The types of composite loading typical of standard tests are examined in separate numerical experiments for shear, tension, compression, and their proportional combination. A computational variant of a criterional estimate of the limiting stresses is substantiated for an anisotropic composite of variable strength. The limiting-stress surface is obtained along with contour maps showing stress isolines as a function of the properties of the components and the geometry of the structure. The maps are suitable for practical use. The cases of maximum resistance to shear, tension, compression, and combination loading of 3D and 4D composites are compared to the analogous cases for two-dimensional structures.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 616–639, September–October, 1995.     

Attractors of dynamical systems with control: topology of purposeful formation

The definitions of homogeneous and mosaic attractors of codimension one are given. A topological method for their purposeful formation by using the feedback control laws of controlled dynamical systems is suggested.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 129–132, January, 1995.     

Iterative reduction of the Dirichlet problem to the Neumann problem

An iteration procedure for reduction of the Dirichlet boundary-value problem to the Neumann problem is suggested. Estimates of the rate of convergence are established.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 362–369, March, 1995.This paper was supported by the Foundation for Fundamental Research of the Ukrainian State Committee on Science and Technology and by the American Mathematical Society.     

Viscoelastic parameters of certain polymers in the temperature interval 4.2–240°K

The principal elastic constants of Nylon 6, Nylon 7, Nylon 6.10, Nylon 11, Nylon 12, PVC, PMMA, polystyrene, and polyvinylfluoride have been calculated from data on the velocity of ultrasonic longitudinal and shear waves measured at a frequency of 5 MHz on the temperature interval 4.2–240°K. It is shown that at cryogenic temperatures the dynamic moduli of elasticity are, to a considerable extent, determined by the characteristics of the chemical structure of the polymers. It is suggested that the Poisson's ratios of the polymers depend on their free volume.Scientific-Research Institute of Plastics, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 604–609, July–August, 1973.