Analysis of elastomeric composites based on fiber-reinforced systems. 2. Unidirectional composites

The elastic properties of unidirectionally reinforced composite materials under large deformations are studied. The applied model for deformation of materials is based on the structural macroscopic theory of stiff and soft composites, including micro- and macromechanical levels of analysis of composite media. The properties of unidirectional elastomeric composites are studied in tension and shear in the plane of reinforcement. The microscopic fields in the structural components of composites having poorly compressible and compressible matrices are also analyzed. Changes in the parameters of macroscopic deformation of the composites are examined as functions of the loading parameters and initial conditions of the structure. The evolution of the structural changes in deformed composite materials is described.State Metallurgical Academy of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 29–50, January–February, 1999.     

Stress state of thermosensitive thick cylinders made of anisotropic composites

The class of problems on the axially symmetric stress state of thick cylinders made of anisotropic materials is considered. The problems are solved numerically. The temperature and mechanical fields in the composite cylinders are investigated taking into account the temperature dependence of the matrix and reinforcement characteristics, as well as the variability of density and angle of reinforcement across the thickness.Institute of Mechanics, Ukrainian National Academy of Sciences, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 367–374, May–June, 1999.     

Analysis of elastomeric composites based on fiber-reinforced systems. 1. Development of design methods for composite materials

A method for calculating the elastic properties of fiber-reinforced composites is discussed. The method is based on the structural macroscopic theory for reinforced media [1, 2], which can be used for analysis of stiff and soft composites. As a measure of the elastic properties of composites, the parameters of macroscopic deformations of the base system of Cartesian coordinates are used, with the axes oriented in a certain direction relative to the general reinforcement and loading field. The corresponding macrostresses in the loaded composites are found by a solution of the microboundary problem for a composite macroelement with sides parallel to reinforcement planes of the system. The microboundary-value problem is multiply connected and is formulated based on the information about the homogeneous field of macroscopic displacements specified by the parameters of macroscopic deformation. The problem is solved using the local system of coordinates whose axes are directed along some of the reinforcement trajectories.State Metallurgical Academy of Ukraine, Dniepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 733–745, November–December, 1998.     

Macrorheological theory of hot compaction of composites

The present work presents the results of mathematical modeling of deformation and thermal processes of compaction of viscous compressible materials. An analytical solution of the problem of one-sided compression and extrusion of powder materials is found which enables us to establish different regimes of compaction and extrusion and to find criterial conditions for their realization at a qualitative level. The numerical analysis of the influence of the nonunifomity of the thermal regime and the conditions of heat transfer on the regularities of compaction nd extrusion of the materials is performed. It is shown how the models developed facilitate the solution of practical problems of producing the concrete items.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October 1995.Published in Mekhanika Kompozitnykh Materialov. Vol. 31, No. 6. pp. 840–845. November–December, 1995.     

General structural equilibrium solutions of boundary-value problems in the mechanics of composites

Based on the theory of R-functions, we have constructed general structural equilibrium solutions for stresses identically satisfying both the differential equilibrium equations and the contact conditions at the three-identically boundaries of inhomogeneities of arbitrary shape. These solutions can be used in developing the next generation of numerical and analytical methods in the mechanics of inhomogeneous bodies and the micromechanics of composite materials.Kharkov State Technical University of Construction and Architecture, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 474–481, July–August, 1997.     

Torsion of laminated cylindrical shells with adhesive interlayers

Based on refined equations of the Timoshenko-type shell theory, the contact stresses in torsion of a two-layer cylindrical shell with an adhesive interlayer are numerically studied. The effect of the geometric and physical-mechanical parameters of the load-carrying layers and adhesive interlayer of the shell on the distribution of the interlaminar tangential stress is analyzed. The results are presented graphically.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 501–506, July–August, 1998.     

Waer of composite thin-walled structural elements with consideration of thermal effects

The contact problem on interaction of rigid stamps with anisotropic plates with regard to wear and the corresponding frictional heating is considered. The procedure developed is based on the reduction of the governing equation to a system of Volterra integral equations of the second kind. The numerical analysis allows us to study the effects of both the anisotropic thermoelastic characteristics of materials and the nature of the interaction of the contact-pair elements on the wear process.Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 309–318, May–June, 1999.     

Non-Gaussian analysis and hypergroups

NANU Mathematical Institute, Kiev, Ukraine and MCS University, Lublin, Poland; NANU Mathematical Institute, Kiev, Ukraine and Bielefeld University, Germany. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 3, pp. 51–55, July–September, 1995.     

Torsion of high-elastic cylinders reinforced with a rigid sleeve

The state of stress is analyzed for a cylinder of elastomeric material reinforced with a rigid sleeve and subjected to large torsional strains. Both compressible and incompressible materials are considered.Translated from Mekhanika Polimerov, No. 3, pp. 551–553, May–June, 1969.     

State of stress and strain of plates with two equal openings in the presence of high-elastic deformation

The apparatus of the nonlinear theory of elasticity [1–3] is used to investigate the high-elastic deformation of a plate with two equal circular openings and a massive block with two cylindrical channels. Computer-calculated stress concentration factors are given for compressible and incompressible materials.Translated from Mekhanika Polimerov, No. 4, pp. 687–692, July–August, 1969.     

Calculation of layered structures by the semianalytic method of finite elements

A semianalytic method of finite elements is developed for calculating layered composite structures. The variables are separated on the basis of the Reissner variation principle. A number of plate deformation problems are solved, and a comparison with the known solutions is made. The method can be efficient when dealing with research, as well as engineering, problems.Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 781–785, November–December, 1997.     

A Phragmén–Lindelöf alternative result for the Navier–Stokes equations for steady compressible viscous flow

In this paper, the authors consider the Navier–Stokes equations for steady compressible viscous flow in three-dimensional cylindrical domain. A differential inequality for appropriate energy associated with the solutions of the Navier–Stokes isentropic flow in semi-infinite pipe is derived, from which the authors show a Phragmén–Lindelöf alternative result, i.e. the solutions for steady compressible viscous N–S flow problem either grow or decay exponentially as the distance from the entry section tends to infinity. In the decay case, the authors indicate how to bound explicitly the total energy in terms of data.     

Holographic interferometry study of deformation of cement and concrete under mechanical and thermal loads

Compressive strain of concrete is accompanied by rotation of the rigid aggregate and by local shifts of the cement matrix, which by analogy with local deformation of metals is the cause of a decrease of the real strength of the material. It is shown that deformation of concrete with haydite and granite aggregates in the presence of a heat supply (within limits of positive operating temperatures) is distinguished by damping of deformations in the first case and by local deformation of the aggregate in the second.Presented at the Ninth International Conference on Mechanics of Composite Materials, Riga. October, 1995.Kharkov State Technical Academy of Railroad Transport, Ukraine. Kharkov State Technical Construction and Architecture University, Ukraine. Kharkov Fire Safety Institute Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 202–208, March–April, 1996.     

Consideration of friction between layers in determining the stress-strain state of structures with nonideal layer contact

A mathematical model for calculation of structures in a three-dimensional installation allowing for layer slippage with friction was constructed. The examples examined show that consideration of friction in problems of calculating laminated structures with nonideal layer contact can introduce an essential correction in the stress—strain state of the structure. In slabs with a freely sagging lower surface, friction is perceived for important friction coefficients and increases when the slippage surface approaches the loaded surface. In masses with a rigidly attached lower surface, even insignificant friction coefficients lead to essential redistribution of the stress—strain state.Ukraine Transportation University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 192–199, March–April, 1997.     

A mathematical model of structurally inhomogeneous macroisotropic materials

The proposed mathematical model of microinhomogeneous material statistically distributes mechanical properties and contains mutually uninteresting cracks. The physical interpretation of model parameters is given, and the domain of its applicability is established. Analysis of the stress state in microinhomogeneous material is made and a probable failure criterion is suggested. The obtained results coincide with those known in the literature for partial cases.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Physico-Mechanical Institute, Ukrainian Academy of Sciences, Lviv, Ukraine. Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv, Ukraine. Published in Mekhanika Kompozitmykh Materialov, Vol. 32, No. 4, pp. 480–492, July–August, 1996.     

Averaging the physical properties of fibrous piezocomposites

Elastic, piezoelectric, and dielectric properties of fibrous composites with piezoelectric components are averaged for antiplane strains. Methods for determining coupled electroelastic fields in piezocomposites are proposed. Calculation results of the effective physical characteristics of some composites are given.Sumskii State University, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 1, pp. 116–123, January–February, 1998.     

Regular restrictions of singular quadratic forms

Wroclaw University, Poland. Institute of Mathematics, Kiev, Ukraine. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 2, pp. 79–81, April–June, 1995.     

CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix–vector multiplies with the sampling matrix. For compressible signals, the running time is just O(Nlog²N), where N is the length of the signal.     

Wood-filled thermoplastic composites

Different physical properties of wood-filled thermoplastic materials produced by a special mixing and extrusion process are examined. The results show that the wood content and the kind of plastics are the main parameters that control the physical properties of composites. In general, wood-filled thermoplastic materials exhibit mechanical properties comparable to those of customary wood fiber products, i.e., medium density fiberboard (MDF); however, they show distinctly better behavior than the MDF and natural wood after exposure to moisture.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Universität Kassel, Institut für Werkstofftechnik, Kunstoff-und Recyclingtechnik, Mönchebergstraße 3, 34109 Kassel, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 795–802, November–December, 1998.     

Modern trends in the development of fibrous composites

The two main trends in the development of high-modulus composites are considered. Improved methods of calculation sensitive to the effects associated with the weak shear and transverse characteristics are reviewed. It is shown that the disadvantages of composites with a traditional arrangement of the reinforcement can be overcome. The properties of boron- and carbon-reinforced plastics with a traditional reinforcement structure are described and compared with those of three-dimensionally structured materials with two- or three-strand reinforcing. Whiskerized fiber reinforcement is also considered. A program of further research on high-modulus composites is outlined.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 541–552, May–June, 1972.