Viscosimetric flow of an incompressible elastoviscoplastic material under the presence of a lubricant on the boundary surfaces

Generalizing the model of large deformations by accounting for the viscous properties of materials, we obtain the analytical solutions of some quasistatic boundary value problems concerning the viscosimetric flows of an elastoviscoplastic material in the gap between the rigid coaxial cylindrical surfaces when, in the neighborhood of one of the rigid cylinders (either internal or external), there is a layer of an elastic non-Newtonian lubricant, and the rigid adhesion conditions are satisfied on boundary surfaces. The conditions are studied of origination of a flow in the lubricant layer and in the basic material. The values of the maximum velocity are specified under which the flow does not tresspass the lubricant layer.     

Deformation of cylindrical composite shells under combined dynamic loading

Conclusions A procedure has been shown for calculating the stress-strain state of cylindrical multilayer shells made from composite materials under the combined action of dynamic axial compression and dynamic external pressure, as well as with different variants of combined loading with static and dynamic forces. An investigation has been made of the effect on the mode of the buckled shell surface of the ratio of the application rate of dynamic loads; ranges of loading rates have been established in which stresses predominate caused either by axial compression or external pressure. It has been shown that, as a result of preliminary static loading, a marked change occurs in the initial imperfections of the shell mode which affects subsequent dynamic buckling. To calculate the time when the first defect occurs and its location in the shell body, a procedure has been devised for layer-by-layer strength analysis employing a tensor-polynomial criterion. It was demonstrated that the level of preliminary static loading noticeably affects the time until the first failure of the layer, not only a reduction of this time being possible with an increase in the static loads, but also an increase in it.We should also point out the work in [10] where it is shown that it is possible to weaken the susceptibility of the shell to initial imperfections when internal pressure is applied.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 461–473, May–June, 1981.     

Nonisothermal deformation of an elastoviscoplastic flat heavy layer

We give a solution to the thermoplasticity problem on the slide of a heavy layer from an inclined plane under heating. The reason for the creep effect is the development of a viscoplastic flow due to the dependence of the yield strength of the layer material on temperature. In the framework of large deformation theory we indicate a law of propagation for the elastoplastic boundary, calculate stresses, deformations, and deformation velocities both in the thermoplastic deformation region and the flow region.     

Deformation of a composite plate on an elastic foundation by local loads

Bending of an elastic annular composite plate with a light filler lying on an elastic foundation is considered. The plate is subjected to local loads. To describe the kinematics of the package, asymmetric across its thickness, the hypotheses of broken normal is accepted. The reaction of foundation is described based on the Winkler model. A system of equilibrium equations is constructed, and its exact solution in displacements is found. Numerical solutions for a metal-polymer sandwich plate are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 109–120, January–February, 2007.     

Calculation of thin-wall closed profiles of composite materials under a complex loading

Uniclosed caisson structures with deformable perimeters, which are asymmetric in terms of geometry and stiffness and which are subjected to a complex loading (bending in two planes and torsion with respect to the longitudinal axis) are examined in terms of a cylindrical coordinate system Z, S. The possibility of partitioning the general problem of the stress and strain state into elementary problems by fulfilling conditions of orthogonality is demonstrated. The coordinates of the center of rotation are determined. The need for consideration of the deformation of the cross-sectional perimeter, which defines the warping function and normal bitorque stresses under torsion is indicated. The law governing the distribution of tangential stresses, which contains both a constant component that corresponds to Bredt's theory, and also a part corresponding to Vlasov's theory, is derived.Moscow State Aviation Institute (Technical University), Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 349–359, May–June, 1997.     

The pressing of an elastoviscoplastic material between rigid coaxial cylindrical surfaces

An analytical solution of the problem of the pressing of an incompressible elastoviscoplastic material between two rigid coaxial cylindrical surfaces is obtained using the theory of large strains. The velocity of motion of the elastic core, the change in the dimensions of the zones of irreversible deformation and the stresses and strains both in the elastic core and in the flow region are calculated as a function of the variable pressing force.     

Deformation of generic submanifolds in a complex manifold

This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1-parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis of the jet spaces of embeddings satisfying certain nondegeneracy properties, and also make use of Thom's transversality theorem, as well as the stratification of real-algebraic sets. Optimal results on the order of nondegeneracy are given.     

Deformation and stress distribution in a layered plastic

The stress distribution over the unidirectionally reinforced layers is investigated in relation to the layer thickness ratio and the direction of loading of a two-way reinforced plastic. An expression is obtained for the modulus of elasticity of the layered plastic in an arbitrary direction relative to the directions of reinforcement. The effect of the geometry of the structure of the layered material on its deformation properties is experimentally illustrated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 563–570, May–June, 1972.     

On the uniform stress state inside an inclusion of arbitrary shape in a three-phase composite

The stress field inside a two-dimensional arbitrary-shape elastic inclusion bonded through an interphase layer to an infinite elastic matrix subjected to uniform stresses at infinity is analytically studied using the complex variable method in elasticity. Both in-plane and anti-plane shear loading cases are considered. It is shown that the stress field within the inclusion can be uniform and hydrostatic under remote constant in-plane stresses and can be uniform under remote constant anti-plane shear stresses. Both of these uniform stress states can be achieved when the shape of the inclusion, the elastic properties of each phase, and the thickness of the interphase layer are properly designed. Possible non-elliptical shapes of inclusions with uniform hydrostatic stresses induced by in-plane loading are identified and divided into three groups. For each group, two conditions that ensure a uniform hydrostatic stress state are obtained. One condition relates the thickness of the interphase layer to elastic properties of the composite phases, while the other links the remote stresses to geometrical and material parameters of the three-phase composite. Similar conditions are analytically obtained for enabling a uniform stress state inside an arbitrary-shape inclusion in a three-phase composite loaded by remote uniform anti-plane shear stresses.     

On the stress distribution in a rectangular thick plate of a composite material with curved structure under forced vibration

The stress distribution in a rectangular plate of a multilayer composite material with a periodically curved structure under forced vibration is studied. It is assumed that the plate is hinge supported at opposite sides. The investigation is carried out within the exact three-dimensional linear theory of elasticity. The mechanical relationships of the plate material are described by the continuum theory of Akbarov and Guz'. The numerical results obtained by the finite element method show that even in low-frequency dynamic loading of the plate the extreme values of stresses, which appear as a result of the curving in the plate structure, considerably exceed those in the corresponding static loading.Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 447–454, July–August, 1999.     

Deformation of a system of cylindrical shells under the action of an internal nonstationary pressure wave

We study the problem of nonstationary deformation of a system of imbedded cylindrical shells under the action of an internal compression wave. The rigorous method of solution we apply makes it possible to obtain a system of Volterra integral equations with retarded arguments in the deflections of the shells. We give the results of computations for the case of a linear source and a source of finite size with limiting hardness properties. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 60–66.     

Free-edge stress analysis of general composite laminates under extension, torsion and bending

In this study, based on the reduced form of elasticity displacement field for a long laminate, an analytical method is established to exactly obtain the interlaminar stresses near the free edges of generally laminated composite plates subjects to extension, torsion, and bending. The constant parameters being in the displacement field, which describe the global deformation of a laminate, are appropriately calculated by using the improved first-order shear deformation theory. Reddy’s layerwise theory is subsequently employed for analytical and numerical examinations of the boundary layer stresses within arbitrary laminated composite plates. Various numerical results are developed for the interlaminar normal and shear stresses along the interfaces and through the thickness of laminates near the free edges. Finally the effects of end conditions of laminates and geometric parameters on the boundary-layer stress are studied.     

Multicriteria optimization of a composite cylindrical shell under an external pressure and longitudinal thermal stresses

The multicriteria optimization of the structure and geometry of a laminated cylindrical shell under the action of external pressure and longitudinal thermal stresses is considered. From the known monolayer properties of the composite and the given values of variable structural and geometric parameters, the thermoelastic properties of the anisotropic layered composite are determined. The criteria to be optimized — the critical external pressure and thermal stresses — depend on two variable parameters and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subdomain are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 495–502, July–August, 2006.     

Deformation of short composite beam using refined theories

High-order flexural theories for short laminated composite beams subjected to mechanical and thermal loading are presented. The formulation allows for warping of the cross-section of the beam and eliminates the need for using arbitrary shear correction coefficients as in other theories. Based on higher-order shear deformation theories, the governing equations are obtained using the principle of virtual work (PVW). The justification for use of higher-order shear deformation theories is established for short and composite beams where cross-sectional warping is predominant.