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.     

The shell theory including transverse shear deformations and thickness change

A variational method for refining the theory of shells based on power series expansion of displacements has been described. The particular case of a cubic approximation for the tangential displacements and a quadratic approximation for the deflections is considered in detail. A constitutive system of differential equations in the canonical form for the axisymmetrical deformation of cyclindrical shells is derived. As an example, axisymmetrical deformations of a cylindrical shell made of an orthotropic composite material are discussed.Martin Luther Universität Halle-Wittenberg, Fachbereich Werkstoffwissenschaften. Germany. Kharkov State Polytechnical University, Department of Dynamics and Strength of Machines. Ukraine. Published in Mekhanika Kompozimykh Materialov, No. 6, pp. 768–780. November–December, 1997.     

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.     

Analysis of elastomeric composites based on fiber-reinforced systems 3. Two-directional composites

Results of investigation of deformation of elastomeric composite materials with a two-directional reinforcement scheme are presented. The study is performed on the basis of a structural macroscopic theory. The matrix of the composites analyzed is of a poorly compressible material. The fibers of both reinforcing systems are simulated as compressible bodies. Dependences of the parameters of tensile and shear strains on the strain values for different geometries of fiber arrangement are obtained.State Metallurgical Academy of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 479–492, May–June, 1999.     

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.     

Remark on the Lyapunov theorem on vector measures

Kharkov State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 4, pp. 78–80, October–December, 1991.     

On Fenchel's problem

Kharkov State University. Translated from Matematicheskie Zametki, Vol. 56, No. 5, pp. 87–97, November, 1994.     

Comparative micromechanical analysis of nonelastic behavior of unidirectional plastics with tetragonal and hexagonal structures

A mathematical model for determining the effective elastic properties and describing the processes of inelastic deformation and damage accumulation of unidirectional fiber-reinforced composites with tetragonal and hexagonal structures is developed. A comparative analysis of the effective elastic moduli of glass, boron, organic, and carbon unidirectional plastics shows that, if the fiber volume fraction does not exceed 0.5, the effective elastic properties calculated by the models presented give closely related results. The calculation results for nonlinear fields of deformation and failure are presented and the limiting strength surfaces of fibrous glass plastics with hexagonal and tetragonal structures are obtained for different transverse loading paths. It is found that the structure of a composite affects significantly its strength properties.Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).Perm' State Technical University, Perm', Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 455–464, July–August, 2000.     

Covariant quantization of null supermembranes in four-dimensional spacetime

Kharkov State University; Kharkov Physicotechnical Institute, Ukrainian SSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 88, No. 3, pp. 358–375, September, 1991.     

Effect of shear stiffness and concrete wedge cone failure on fracture of a fiber-reinforced plastic rod at an intersection with a concrete crack

Experimental results of model speciments in which FRP rods fractured due to local deformation at a crack intersection in a concrete member were analyzed by a 3D nonlinear finite element method in which orthogonal anisotropy of the FRP rod was considered. The analytical results indicated that accurate prediction of shear modulus of the FRP rod and size of concrete wedge cone failure around the FRP rod was significant to predict deformation and fracture of the FRP rod. FRP rods as reinforcement in concrete members, the small shear modulus, because of the orthogonal anisotropy and the wedge cone failure, may prevent the FRP rod from fracturing at a very low tensile stress due to the local deformation at the crack intersection.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 21, No. 2, pp. 158–166, March–April, 1996.     

Low-frequency asymptotics of the Green's functions of magnets with spontaneously broken symmetry

Physicotechnical Institute, Ukrainian SSR Academy of Sciences, Kharkov; Kharkov State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 89, No. 2, pp. 293–303, November, 1991.     

Continual approximations of displacements in thick layered plates upon decomposition of thermomechanical loads into bilateral symmetric and antisymmetric components

Continual models of deformation of thick layered plates, where the general order of resolving equations does not depend on the number of layers, are constructed with account of the specific character of the unflexural and flexural deformation caused by the symmetric and antisymmetric components of bilateral loads and temperature. Account of the load decomposition during the process of refining a certain reasonable initial solution, consisting in the analytical iterative integration, makes it possible to obtain rather precise continual approximations of stresses and displacements over the transverse coordinate and thus to revise the known continual models.Ukrainian State Academy of Water Management, Rovno, the Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 743–756, November–December, 1999.     

Hadamard's problem and coxeter groups: New examples of Huygens' equations

Moscow Physical Technical Institute. Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 1, pp. 3–15, January–March, 1994.     

Mechanisms for flow and forced high elasticity of cross-linked polymers

A quantitative model is proposed for flow and forced high elasticity of cross-linked polymers based on the cluster model of amorphous state structure. The flow process is seen as the loss of displacement stability by the clusters, while forced high elasticity is related to the mechanical devitrification of the softpack matrix. Fractal analysis was used to show a turbulent regime for the forced high elasticity of cross-linked polymers.Kabardino-Balkariya State University, Nal'chik. Russia. Donetsk Physics and Mechanical Sciences University. Ukraine. Branch of the Institute of Ecology. Kashkhatau, Kabardino-Balkariya. Russia. Center for Composite Materials, Moscow State Open University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 270–278, March–April, 1996.     

Aharonov-Bohm oscillations in relativistic Fermi and Bose systems

Kharkov State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 83, No. 1, pp. 115–128, April, 1990.     

Synthesis of averaging methods in stochastic boundary-value problems of the mechanics of microheterogeneous solids

The method of periodic components is further developed, which allows us, on unified positions, to predict the effective characteristics and structural strain fields in partially or fully disordered composites. The stochastic boundary-value problem of elasticity theory for microheterogeneous solids with a statistically homogeneous structure is treated. The heterogeneous solid is considered to be macroscopically homogeneous and macroanisotropic (or quasi-isotropic) with geometric form and properties of the structural components determined and given. The structural elements are assumed to have perfect interfaces, i.e., the displacements and tractions are continuous across the interface. The boundary-value problem was solved by the method of local approximation. Numerical results were obtained for composites with a stochastic structure.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 3–12, January–February, 1999.     

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.     

Problems of the theory of deformation of polymeric materials under complex loading

Research on problems of the theory of deformation of polymeric materials under complex loading based on a synthesis of creep theories and the local strains theory is reviewed.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.M. V. Lomonosov Moscow State University. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 434–443, May–June, 1972.     

Methods of finite element analysis of arbitrary buckling forms of sandwich plates and shells

Two statements of the problem of arbitrary buckling forms (BFs) (including synphasic, antiphasic, mixed flexural, flexural-shear, and shear forms in the tangential directions) of general-form sandwich shells and two schemes of its solution by the FEM are given. The first of the schemes is based on the use of refined linear equations for determination of the precritical stress-strain state and linearized equations of neutral equilibrium with all parametric addends necessary to determine the critical loads and reveal the possible BFs. The second one uses the general geometrically nonlinear relations of elasticity theory for investigation of the whole deformation process up to buckling in terms of a modified incremental (stepwise) statement of the problem. Examples of solution of particular problems are given.Center for Study of Dynamics and Stability, Tupolev Kazan' State Technical University, Kazan', Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 473–486, July–August, 2000.