A method of testing the transverse tensile strength of wound articles

A theoretical and experimental justification is provided for a method of determining the transverse tensile strength of composites on the basis of bending tests on a segment of a circular ring. Test data obtained by different methods are compared.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 4, pp. 759–761, 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.     

Estimating the impact strength of plastics

A method of estimating the impact strength of plastics in transverse two-support bending is proposed. It is shown that if specimens of different size are tested under certain conditions, the ratio of the work done in breaking the specimen to the volume of the specimen between the supports will be the same.Novosibirsk Kuibyshev Structural Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1109–1112, November–December, 1971.     

Experimental determination of the displacement of the neutral surface in polymer specimens stressed in bending

The results of bending tests to determine the displacement of the neutral surface are presented for six different polymers. The specimens were both stressed in pure bending and bent by transverse loads. The values obtained for the displacements indicate that the effect should be taken into account in designing parts for bending. An attempt is made to explain the displacement of the neutral surface in terms of the textural characteristics of the chain molecules.Dnepropetrovsk Metallurgical Institute. Translated from Mekhanika Polimerov, No. 4, pp. 747–749, July–August, 1969.     

Analysis of fracture surfaces in polymethyl methacrylate tested in bending with rotation

Typical fracture surfaces are examined for polymethyl methacrylate specimens subjected to multicycle fatigue testing in circular cantilever bending at T=20, 40, and 60°C. It is established that the fatigue life of smooth specimens is very closely correlated with the size of the diffuse fracture zone. The kinetics of damage accumulation with increase in the number of cycles are investigated by rapidly fracturing prefatigued specimens. The decisive role of diffuse fracture in the fatigue-fracture process is demonstrated. A method of estimating the mean main crack propagation velocity in circular bending is described.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 984–990, November–December, 1973.     

Approximate method of calculating stresses in a rectangular plate locally loaded by a harmonic force

From double trigonometric series for bending moments the slowly converging components are picked out. When the loading facets are small compared with the width of the plate, they are approximately summed by the analytical method. This simplifies substantially the calculation of bending moments and stresses in the zone of small loading facets compared with the usual expansion with respect to the natural vibration forms.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 84–88, 1989.     

Calculating 3D stresses in layered composite plates and shells

Advanced failure criteria for fiber composites account for all six components of the stress tensor. Plate and shell analysis, however, is sensibly performed by assuming the plane state of stress, which results in global displacements, cross-sectional membrane forces, and bending moments of suitable accuracy. Based on these results, equilibrium conditions can be applied to locally determine the stress components in the transverse direction. Therewith, the transverse shear stresses require first derivatives and transverse normal stresses even second derivatives of the membrane stresses. Higher-order finite elements would be necessary if these stress components are to be determined on the element level. To ease this deficiency, a procedure is proposed based on neglecting the in-plane derivatives of the membrane forces and twisting moments as well as the mixed derivatives of the bending moments. This allows us to reduce the order of differentiation by one. Applicability of this procedure is demonstrated by calculating the transverse shear and normal stresses for layered composite structures of different geometric dimensions and various stacking orders under mechanical as well as thermal loads. Comparison with results from 3D analyses shows excellent accuracy and efficiency of the proposed procedure.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Deutsches Zentrum für Luft- und Raumfahrt e.V. (German Aerospace Center), Institute of Structural Mechanics, D-38022 BRAUNSCHWEIG, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 491–500, July–August, 1998.     

On the theory of thermoelastic bending of reinforced shells and plates

The author examines an approach to the construction of a theory of thermoelastic bending of arbitrarily reinforced shells and plates that takes into account the actual structure, the deformation characteristic, and the actual thermomechanical properties of the elements which make up the composite. The final equations are obtained with and without allowance for transverse shear strains. The problem of the thermoelastic bending of a thin, arbitrarily reinforced rectangular plate hinged at the edges, when transverse shear strains can be neglected, is considered as an example.Institute of Hydrodynamics, Siberian Division, Academy of Sciences of the USSR, Novosibirsk. Translated from Mekhanika Polimerov, No. 5, pp. 861–873, September–October, 1972.     

Resistance of composite flywheel rim to radial tensile stresses from centrifugal forces based on results of pure bending of a rim segment

A method is proposed for evaluating the resistance of a flywheel rim to radial stresses in free rotation. The method is based on loading a rim segment in pure bending and calculating the limiting moment and the corresponding limiting angular velocity. Applicability of the method is substantiated theoretically by investigating the similarity of the radial stress diagrams in rotation and pure bending. The method is verified experimentally for the strained state of a rim segment in pure bending.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 521–526, July–August, 1993.     

Theory of the biomechanism of fractures of the diaphysis of long tubular bones

A new theoretical basis is proposed for the biomechanism of fractures of the diaphysis of long tubular bones resulting from bending deformation. Bone damage is shown to result from the concentration of maximum tensile stresses on the tension side and shear stresses in the compression zone. The origin of fan-shaped cracks and oblique fractures, occurring individually or in combination, is explained in these terms.Altai State Medical Institute. Translated from Mekhanika Polimerov, No. 2, pp. 318–322, March–April, 1971.     

Analysis of the transition zone in combined metal/reinforced-plastic shells

The bending stresses in the conical joint zone of cylindrical shells composed of two different materials are determined for the case of internal pressure. The effect of the length of the joint on these stresses is investigated using parameters typical of steel and glass-reinforced plastic.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 465–475, May–June, 1971.     

Bending features of a sandwich panel with asymmetric structure under local loads

The bending characteristics of a composite panel with asymmetric layered structure under local surface loads are obtained. A refined version of the applied theory is developed using the analytical solution of the bending problem of a sandwich plate with arbitrary asymmetric structure under a point load. Local effects are investigated within the limits of a discrete model allowing for the specific character of elastic properties of a soft filler. The advantages of the solution are expressions of bending characteristics — layer curvatures, displacements, and stresses — in a closed form. It is shown that these characteristics can vary several times depending on the asymmetry parameters of the structure. Degeneration peculiarities of the solution, stemming from the slipping of layers or, otherwise, their rigid linking by the Kirchoff—Love hypothesis, as well as from account of the transverse shear and compression of the normal, are examined in line with the degeneration of geometric and physical parameters of the discrete model adopted. The results obtained are illustrated by curves and surfaces for the characteristics studied.Submitted for the 11th International Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).Institute of Polymer Mechanics, Latvian University, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 717–742, November–December, 1999.     

A variant of the refined theory of bending for a laminar plastic beam

The present article considers the bending of a beam fabricated from a material with a low shear rigidity. A bending-theory variant that does not involve the hypothesis of plane cross sections is presented, assuming the material to be incompressible in the direction of the transverse coordinate. Results previously obtained in this area and an appropriate bibliography were given in an earlier article [3]. A solution is given that permits precise satisfaction of the condition for rigid fastening of the end of the beam. An attempt is made to take into account the actual character of the mounting.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 4, pp. 674–681, July–August, 1972.     

Load-Carrying Capacity of Circular Plates Made of a Fiber-Reinforced Composite

The load-carrying capacity of circular plates made of a fiber-reinforced composite and loaded with axisymmetric transverse forces under axisymmetric boundary conditions is investigated. The plates can be freely supported or clamped along their contour. To the known yield condition used, in the plane of main bending moments, there correspond irregular hexagons, which depend on the mechanical properties of composite constituents and some characteristic geometrical parameters. It is shown that, depending on the ratio of ultimate radial and circumferential bending moments, in the plastic state, the circular plates (the central part of the clamped plates) take the form of a cone or a frustum of cone. For each of the cases, the limit load is found, which is a function of the above-mentioned mechanical parameters. The statically allowable fields of bending moments and the corresponding allowable fields of deflection rates are determined. The solutions found are exact. Special cases for the freely supported plates are analyzed, and the results obtained are presented in the form of graphs.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 177–192, March–April, 2005.     

Residual technological stresses in the winding of the stator of large electrical machines

Conclusions Equations were derived for calculating RTS in the gap part and the zone of bending the coils and bars of the stator winding; it was shown that in calculating the RTS in the bending zones, it is necessary to take into account the presence of residual stresses in the copper of the bar. The calculated and experimental results indicate the high concentration of the stresses _X in the bending zones, These regions are most critical from the view-point of possible disruption of the monolithic nature and reduction in the electrical strength of the housing insulation.Paper presented at the Fifth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, October, 1983).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 868–872, September–October, 1983.     

Bending of plates made of oriented glass-reinforced plastics

A plate made of oriented glass-reinforced plastic (GRP) is treated as a regular medium with numerous anisotropic layers. The problem of bending is solved in the elastic formulation of the problem without the use of the hypothesis of undeformed normals and a preliminary specification of the law of distribution of shearing stresses in transverse planes. The important effect of shear strains on the deflections and stresses in plates of oriented GRP is illustrated in the example of a simply supported square plate with transverse isotropy. An estimate is given of the errors introduced by arbitrary specification of the law of distribution of shearing stresses.Mekhanika Polimerov, Vol. 1, No. 3, pp. 129–136, 1965     

Experimental studies on the adhesion strength of a polymer-metal bond depending on the contact zone geometry

Theoretical investigation of the stress-strain state at special points of constructions, e.g., in adhesion joints, has demonstrated that the stress state in the contact zone strongly depends on the configuration of the zone. In order to verify these results, some experiments were carried out. Cylindrical polymer specimens having a circular groove at one of its ends were cemented to steel mushrooms and tested for abruption in tension and cantilever bending. The experiments showed that the adhesive strength depended on the profile of the joint and had a maximum at the optimum value of the angle of the joint and a minimum when the groove was absent. The ratio between the maximum and minimum strength values was 1.5 in tension and 2.5 in bending. The greater effect in the latter case can be explained by the high gradient of the stresses in bending. The experimental results confirmed the possibility of controlling the adhesive strength by changing the contact geometry in accord with the stress-strain calculations.Institute of the Mechanics of Continuous Media, Russian Academy of Sciences, Perm', Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 493–498, July–August, 1999.     

A note on bending of plates including the effects of transverse shearing and normal strains

Summary Earlier results on the effect of transverse shearing strain on the three-dimensional aspects of the distribution of bending stress in plates are complemented by results for the influence of transverse normal strain, due to surface pressure as well as due to a non-vanishing transverse. Poisson's ratio.

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Zusammenfassung Ein früheres Resultat (Int. J. Solids Structures11, 569–573 (1975)) in bezug auf den Einfluß der Querschubverformungen auf die dreidimensionalen Eigenschaften des Biegespannungszustandes werden ergänzt durch Resultate für den Einfluß der Querdehnungen.

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Supported by the Office of Naval Research.     

A refined model for three-point bending of sandwich panels. 1. Deflections and bending stresses

Design formulas for the flexural characteristics of sandwich panels under three-point loading by point forces, taking into account local effects, have been derived. Transverse deformation of the normal in the modified model is deduced in terms of the difference between deflections of face layers. It is considered that the rotation of the normal depends also on shear of the filler. The deflections, local curvatures, and bending stresses, dependent on the face-layer thicknesses and transverse characteristics of the filler, are studied. The danger of initial failure caused by the local moment stresses at the central panel section is shown. Comparative estimates refining the conventional designs are established.Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 747–767, November–December, 1997.     

Finite-difference method of solving the bending problem for glass-reinforced plastic plates with allowance for creep

A new finite-difference method is proposed for solving the bending problem as it applies to thin rectangular orthotropic plates of linear hereditary material. The proposed method makes it possible to obtain a closed approximate solution in explicit form for a series of finite-difference systems of equations corresponding to the problem of the bending of plates of orthotropic glass-reinforced plastic with allowance for the rheological properties of the material under various boundary conditions.Institute of Cybernetics and Computer Center, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 6, pp. 1075–1082, November–December, 1969.