Behavior of waveguide modes in a neighborhood of the critical cross section

A curved waveguide of variable thickness filled with an inhomogeneous medium is considered. Shortwave asymptotic equations are obtained which describe the waveguide modes near the critical cross section. The amplitudes of waves reflected from the critical cross section and also of waves filtering through the postcritical section of the waveguide are obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 181–188, 1974.     

Determination of contact stresses in problems on bending of a package of transversely isotropic bars

A mechanomathematical model for bending of packages of transversely isotropic bars of rectangular cross section is proposed. Adhesion, slippage, and separation zones between the bars are considered. The resolving equations for deflections and tangential displacements are supplemented with a system of linear differential equations for determining the normal and tangential contact stresses, and boundary conditions are formulated. A scheme for analytical solution of two contact problems—a package under the action of a distributed load and a round stamp—is considered. For these packages, a transition is performed from the initial system of differential equations for determining the contact stresses, where the unknown functions are interrelated by recurrent relationships, to one linear differential equation of fourth order and then to a system of linear algebraic equations. This transition allows us to integrate the initial system and get expressions for the contact stresses.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 761–778, November–December, 2004.     

Account of the Cross-Sectional Deplanation of a Composite Bar in Determining the Critical Force

A method for determining the critical force for an axially compressed composite bar with account of deplanation of its cross sections is considered. It is proposed to consider the cross-sectional deplanation, which decreases the critical force, by lowering the basic flexural stiffness of the bar by the value resulting from this effect. General relationships for calculating this value for composite bars are obtained. Numerical results are presented, which show the decrease in the critical force as a function of some parameters for transversely isotropic bars of rectangular cross section.     

Action of a concentrated load on an elastic ring pressed into a circular hole in an anisotropic plate

A solution is obtained for the elastic equilibrium problem for an anisotropic plate with a circular hole into which is pressed a ring of arbitrary cross section symmetrical about the middle surface of the plate. Before deformation the outside radius of the ring differs from the radius of the hole in the plate by the amount of the permissible elastic displacements. A normal concentrated load is applied to the ring. The ring is analyzed in accordance with the theory of thin curved bars. A numerical example is given.I. Franko L'vov State University. Translated from Mekhanika Polimerov, No. 6, pp. 1054–1059, November–December, 1973.     

Stability of orthotropic cylindrical shells under variable pressure

A method of determining the critical stresses is developed for elastic orthotropic cylindrical shells subjected to nonuniform pressure. It is assumed that the external pressure varies over the cross section and is constant along the length of the cylinder. A shell stability analysis is given for the case of a weakly varying load.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 897–902, September–October, 1970.     

Effect of the two-way reinforcing system on the load-carrying capacity of glass-reinforced plastic shells

The load-carrying capacity of thin cylindrical glass-reinforced plastic shells loaded by axial compression and external pressure has been investigated in relation to the characteristics of the two-way reinforcing system. The critical loads are expressed in terms of the characteristics of a parallel-reinforced layer with a coefficient that takes into account the reinforcing system and the shape of the cross section. The relations among the reinforcing layers optimal for the load-carrying capacity are determined and it is shown that independent two-way reinforcing substantially improves the load-carrying capacity of solid shells and shells with a nonload-bearing core.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1052–1058, November–December, 1969.     

Effect of the size of the specimen cross section on the long-term strength of polyethylene

The scale effect has been investigated in relation to the long-term strength of specimens of high-density polyethylene. Time dependences of the tensile strength at ordinary temperatures have been obtained. It is shown that the long-term strength depends on the dimensions of the specimen cross section. The deformation of the specimens depends on their size and the shape of the gage cross section.Higher Chemical Technology Institute, Sofia. Translated from Mekhanika Polimerov, No. 4, pp. 741–743, July–August, 1973.     

Elasticoplastic bending of rectangular plates reinforced with fibers of constant cross section

The problem on the elastoplastic transverse bending of Kirchhoff plates of variable thickness reinforced with fibers of constant cross section is formulated and its qualitative analysis is performed. An analytical solution to the problem is constructed in the case of cylindrical bending, and, by using the Bubnov-Galerkin method, an approximate solution for a rectangular plate is obtained. Based on calculations of plates reinforced with boron fibers and steel wire, it is shown that the load-carrying capacity of the structural member in elastoplastic bending is several times (or even by an order of magnitude) higher than in purely elastic one.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 17–36, January–February, 2005.     

Calculating the total resistance for a tube with a variable cross section

A study has been made on the decisive effect from the exit cone on the total resistance of a variable cross section tube composed of alternating divergent and convergent parts, whose radii vary on a cosine law. Numerical calculations have been performed for steady-state stabilized laminar flow of a viscous incompressible liquid. The frictional and pressure resistance coefficients have been calculated. The contribution from those resistances to the total resistance has been examined.Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 120–124, 1990.     

Experimental-theoretical studies of the stability of orthotropic shells with a filler in axial compression

Conclusions 1. An analysis has been made of the solution to the problem of the stability of multilayer cylindrical shells having a filler and simple calculation formulas have been obtained for determining the critical forces.2. The stability of fiberglass-plastic shells with rubber-like fillers has been studied experimentally.3. Comparative experimental-theoretical studies of critical forces have been made, and the stability coefficients have been ascertained for the shell class under consideration.Translated from Mekhanika Polimerov, No. 3, pp. 485–489, May–June, 1978.     

Averaging the electrical properties of fiber-reinforced metal composites

Using the regular structure model, we average the electrical properties of unidirectional fiber-reinforced metal composites and propose procedures for determination of the effective electrical conductivity tensor of these materials. For the general case of packing of fibers of arbitrary cross section, the problem is reduced to calculation of some functionals determined in solutions of the integral equation of the corresponding boundary current problem for the structure. In the special case of symmetric packing of fibers of circular cross section, the solution is written in the form of series in elliptic functions.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 533–539, July–August, 1995.     

Stability of elastoplastic flat arches

The stability of flat arches with pinned and fixed ends under a uniformly distributed load is investigated on the assumption that the material obeys a linear hardening law and the geometric relations are nonlinear. The equations obtained are solved for a sinusoidal arch with a rectangular cross section using the Bubnov-Galerikn method and the method of elastic solutions. Equations are obtained for the load and deflection at which transition from the purely elastic to the elastoplastic state occurs.Tartu State University. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 887–896, September–October, 1968.     

Criterion for existence of a continuous invariant cross section of an affine extension

Necessary and sufficient conditions are established for the existence of a continuous invariant cross section of a linear inhomogeneous extension, the linear part of which has no nontrivial bounded motions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1146–1151, August, 1990.     

Mechanical behavior of cylindrical laminated plastic shells

The static and dynamic behavior of a cylindrical glass-reinforced plastic shell with an open cross section under long-term loading and unloading has been experimentally and theoretically investigated. The experimental results are compared with the theoretical data obtained using a geometrically nonlinear theory based on the Kirchhoff hypothesis. For calculation purposes the glass-reinforced plastic is assumed to be a homogeneous orthotropic linearly elastic material.Building Research Institute, Prague. Translated from Mekhanika Polimerov, No. 1, pp. 110–115, January–February, 1976.     

Distribution of shearing stresses under three-point flexure in beams made of composite materials

Conclusions 1. When short beams made of composite materials with span-to-height ratios within the 4.0–5.0 range are tested in three-point flexure, the profile of shearing stresses over the height of a beam cross section departs appreciably from a parabolic one over approximately 40% of the span length.2. The zones of a perturbed state of stress, which appear in short beams tested in three-point flexure, render this method unusable for determining the interlayer shear strength of composite materials on "ultrashort" specimens.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 56–62, January–February, 1977.     

Displacement of a compressed packing ring of oval cross section

The author discusses the state of deformation of a packing ring of oval cross section. He suggests a method of calculating the elongations of the horizontal and vertical diameters of the oval from the results of an interpretation of photoelastic patterns with finite deformations. The calculated values agree with experimental measurements.Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 368–370, March–April, 1974.     

Elastic characteristics of graphitoplastics and impregnated graphites

The effect of aging on the moduli of elasticity of graphitoplastics and resin-impregnated graphites has been directly investigated. The dependence of the modulus of elasticity in tension and compression on the normal stress in the specimen cross section has been studied for the same materials.Novocherkassk Sergo Ordzhonikidze Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1127–1130, November–December, 1970.     

On the convergence of the multigroup,discrete-ordinates solutions for subcritical transport media

Summary In the multigroup, discrete-ordinates approximations to the linear transport equation, the integration over the directional variable is replaced by a numerical quadrature rule, involving a weighted sum over functional values at selected directions, with the energy dependence discretized by replacing the cross section data by weighted averages over each energy interval. The stability, consistency, and convergence rely fundamentally on the conditions that the maximum fluctuations in the total cross section — and in the expected number of secondary particles arising from each energy level — tend to zero as the energy mesh becomes finer, and as the number of angular nodes becomes infinite. Our analysis is based on using a natural Nyström method of extending the discrete-ordinates, multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ generalizations of the collectively compact operator approximation theory of P. M. Anselone to deduce stability and convergence of the approximates.This research was started while the first author (H.D.V., Jr.) was an Alexander von Humboldt Research Fellow in the Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Federal Republic of Germany. Generous support was also provided by a Faculty Development Leave from Texas Tech University for the 1982–83 Academic Year.     

Failure of composite tubes in the Chinese lantern mode under a weight-type load

The failure of unidirectional composite tubes in the Chinese lantern mode is analyzed in the case of a tube compressed by a weight type load, which retains its magnitude after splitting of the tube. Calculation formulas are derived for predicting the critical load. The main regularities of the solution obtained are illustrated with specific examples. It is shown that the nature of the acting load must be considered in the analysis of unidirectional composite tubular bars with axial reinforcement.Bauman Moscow State Technical University, Russia. Scientific Research Institute of Mechanical Engineering, Moscow, Russia. Translated from Mekhanika Komspozitnykh Materialov, Vol. 35, No. 3, pp. 319–324, May–June, 1999.