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     

Flexure of beams with low shear strength on an elastic foundation

The deflection of a beam on an elastic foundation is determined with allowance for shears and without postulating a law of shear-stress distribution. The accuracy of approximating this law with a quadratic parabola is estimated. The effect of shears on deflection is investigated in relation to beams of different length made of materials of the oriented glass-reinforced plastic type with low shear strength.Mekhanika Polimerov, Vol. 3, No. 5, pp. 881–887, 1967     

Combined bending and compression of circular cylindrically orthotropic plates with low shear strength

Equations are derived for the combined bending and compression of cylindrically orthotropic plates with allowance for shear and without postulating a shear distribution lawf/it(z). Solutions of the equations obtained are given for various boundary conditions. The error introduced by postulating the distribution lawf/it(z) is estimated. The effect of the ratio of the Young's moduli in the circumferential and radial directions E/E_r and the ratio of the Young's modulus E_r and the shear modulus G on the deflection w and the critical load T_cr is investigated. It is shown that for plates made of materials such as oriented glass-reinforced plastics the shear correction is very important. It is noted that buckling (due to shear) can occur even when the Young's moduli of the material are infinite.Mekhanika Polimerov, Vol. 4, No. 1, pp. 116–123, 1968     

Effect of sign-variable thermocycling on the mechanical properties of carbon-fiber plastics with various layups

Conclusion An economic method for the ST of carbon-fiber-reinforced plastics is proposed in this study. It is established as a result of investigations of the mechanical properties of carbon-fiber-reinforced plastics with different layups, which are subjected to ST in the range to 100 cycles, that in the majority of cases, the number and duration of thermal cycles has no effect on the stiffness and strength in tension, compression, bending, and shear. The effect of number of thermal cycles was manifested only on the stiffness in tension and bending and also on the tensile, compressive, and bending strengths of the material with the obliquely reinforced structure loaded in the direction of the diagonal. It is permissible to use the dynamic method to assess variations in the stiffness of a material subjected to ST.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 1, pp. 66–76, January–February, 1993.     

Distortion of cross sections during deformation of oriented glass-reinforced plastics

Test pieces equipped with wire strain gauges were used to investigate the distortion of cross sections of bars made of oriented glass-reinforced plastics (GRP) in tension and bending. The need for modified design formulas, obtained without use of the simplifying hypothesis of plane sections, is demonstrated. The previously obtained theoretical results of [2, 3] are experimentally confirmed. The effect of the free ends on beam deflection is found to be unimportant.Mekhanika Polimerov, Vol. 1, No. 5, pp. 107–113, 1965     

Effect of building structure on the distribution of random bending strength of multilaminate reinforced plastics

A probabilistic structural model has been constructed for predicting the bending strength distribution in multilaminate reinforced plastics. The number and random strength/elastic properties of the layers or repeating structural elements are parameters of the structure. The random properties of the repeating structural elements are characterized by the scheme and geometry of the unidirectional layers. Two failure conditions have been analyzed: multistep failure caused by successive failure of separate layers and failure caused by the failure of the weakest component. The effect of the number of layers and the instability of the strength and elastic properties on the basic statistical properties of the bending strength was analyzed numerically for typical structures and for both failure conditions. The quantitative significance of the size effect determined by the thickness of the plastic was investigated. The main theoretical results were checked experimentally for unidirectional reinforced carbon plastic under uniaxial bending. The experimental distribution agrees well with the predicted distribution.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 3, pp. 336–344, May–June, 1993.     

Creep and long-time strength of oriented glass-reinforced plastics in interlaminar shear

The creep and long-time strength in interlaminar shear and the creep in compression in the direction of the reinforcement have been experimentally investigated for certain types of oriented glass-reinforced plastics. The specimens in the interlaminar creep tests took the form of short beams loaded in bending. The experimental creep data for shear and compression are well described by the hereditary theory with a kernel of the Abel type (shear) or in the form of a Rabotnov function (compression). If the stresses are constant in time, good agreement with experiment is also given by Findley's form of the aging theory. A deformation criterion of interlaminar shear strength is also obtained. The experimental curves and values of the creep and long-time strength constants are presented.Translated from Mekhanika Polimerov, No. 6, pp. 1003–1012, November–December, 1971.     

The bending of clamped beams made of materials with low resistance to shear

Oriented glass-reinforced plastics have low resistance to shear. This means that the calculation of beams made of these materials on the basis of the hypothesis of plane cross sections is not possible. We compare several methods of calculating shear and verify them on the basis of experimental data obtained for beams made of oriented glass-reinforced plastics with one or both ends clamped. We also discuss the boundary conditions in the clamped cross section and the effect of axial force in the case of fixed supports.Mekhanika Polimerov, Vol. 3, No. 4, pp. 730–736, 1967     

Resistance of three-layered structures to static and cyclic bending

Conclusions The above studies of two types of three-layer structural elements showed that the types have different resistances to static deformation in bending. Regardless of the materials, the use of structures which are symmetrical in regard to stiffness makes it possible to obtain a stiffness and strength for the structure which are 10–15% lower than the stiffness and strength of the external plates if the thickness of the latter does not account for more than 25% of the thickness of the structure. This finding, in turn, permits a substantial reduction in the weight of the structure by the use of a lower-density material for the internal layer. Resistance to static bending is determined mainly by the resistance of the structure to shear stresses. The mechanism of fatigue fracture differs appreciably from the fracture mechanism in static deformation. Regardless of the thickness of the structural elements, fatigue fracture for both types of structure occurs as a result of the acting normal compressive stresses. The endurance limit of the hybrid structure is determined by the fatigue resistance of the external layers, and its value is nearly equal to the resistance of the pure materials.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 878–882, September–October, 1986.     

Experimental evaluation of the strength of one-piece Kapron nuts

The strength of one-piece Kapron nuts has been investigated in static loading tests. Graphs of the load versus the number of turns, which reflect the distribution of the load over the turns, are presented. The types of failure of threads of five standard sizes with different profiles are analyzed. It is concluded that there is an important difference between the usual thread calculation model based on the strength of the turns in shear, bearing and bending and the actual loading of the turns of polyamide nuts cooperating with steel screws.Dnepropetrovsk Metallurgical Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 752–754, July–August, 1968.     

Experimental investigation of the transverse shear effect in the bending of cantilevered plates with low shear stiffness

The state of stress of cantilevered plates made of different materials (steel and glass-reinforced plastic) has been experimentally investigated. The results obtained are compared with the known theoretical solutions. It is shown that in certain cases it is necessary to take into account the effects associated with the low shear stiffness of the plate.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov; Kamenets-Podol'skii General Engineering Department of Khmel'nitskii Technological Institute. Translated from Mekhanika Polimerov, No. 4, pp. 736–738, July–August, 1971.     

Bending of prestressed glass-reinforced plastic beams

Initial waviness of the fibers and prestressing are investigated in relation to their effect on flexural stiffness and strength for beams with low shear strength. It is shown that prestressing the reinforcement increases the flexural stiffness but at the same time adds to the shear correction as a result of an increase in the modulus of elasticity E_x in the direction of reinforcement and the insensitivity of the shear modulus G_xz to prestress. It is established that prestressing increases the shear strength and the degree of anisotropy . Materials of two types are investigated: unidirectional (AG-4S) and cloth-reinforced (SKT-11).Mekhanika Polimerov, Vol. 3, No. 5, pp. 888–893, 1967     

横向剪切对双模量复合材料叠层矩形板非线性弯曲的影响

本文探讨了动力松弛(DR)法在双模量复合材料叠层矩形板非线性弯曲问题中的应用。在分析中分别采用叠层板大挠度经典理论和计及大转动(在Von Karman意义上)的复合材料叠层板剪切变形理论。我们发现,对于考虑横向剪切变形的非线性弯曲问题,如何计算虚拟密度以控制数值计算的稳定性,仍然需要进一步研究。本文提出了一种虚拟密度的计算方法,从而保证了本课题数值计算的稳定性。文中介绍了用DR法求解双模量复合材料叠层板非线性弯曲的主要步骤,给出了由轻度双模量材料(Born-Epxy(B-E))和高度双模量材料(Aramid-Rubber(A-R)和Polyester-Rubber(P-R))的两层正交叠层简支矩形板在正弦分布载荷及均布载荷作用下的非线性弯曲特性的数值结果。将所得结果和小挠度分析结果及普通复合材料的结果作了比较,并分析了横向剪切变形对无量纲中心挠度的影响。     

Influence of Different Factors on the Stiffness and Strength of Multilayer Composite Elements

In the paper, the bending stiffness and strength of multilayer structural elements in relation to the mechanical properties of layers and their number layout and sizes are investigated and the corresponding correlations are established. It is found that the most rational structure of a multilayer element in bending is a symmetric three-layer structure formed from two materials with the thickness of the core less than the half-thickness of the element. The values of normal stresses in the layers of a multilayer beam in bending depends on its bending stiffness and the position of layers relative to the neutral axis. The influence of the number of layers on the stiffness of the structural element and on the magnitude of normal stresses is insignificant.     

Shear strength of webs with holes

In lightweight design the webs of beams which are loaded by bending are often provided with holes. Aim of this article is to present a method to calculate the shear strength of webs with certain holes. The semi-analytical method is derived with respect to the results of geometrically and physically non-linear numerical simulations in which the shear strength of the web is calculated. The method consists of a plastic failure approach for rather thick webs and a framework analogy to model the failure of a solid web after onset of buckling. To take the influence of the holes into account the shear strength of the solid web is reduced as a function of geometry parameters. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Design of closed thin-walled composite shapes for bending

A study is made of the possibility of dividing the complex bending of a structure into elementary components, and an examination is made of closed wing-type monocoque structures with a rigid contour. The structures studied are asymmetric with respect to their geometric and stiffness characteristics. They are subjected to bending without torsion and are referred to a cylindrical coordinate system (Z, S). The longitudinal displacements are determined on the basis of the method of conjugate displacements by integrating the Cauchy equation and circulation equation, with the displacement along the contour (due to its stiffness) being represented in the form of a series containing terms describing the bending of the structure. The shear strains are similarly represented. The resolvent equations are obtained by using the principle of the minimum potential strain energy of the contour.Deceased.Moscow State Aviation Institute (Technical University). Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 82–89, January–February, 1997.     

Some problems of the theory and analysis of anisotropic plates and shells with low shear stiffness

Certain problems associated with the theory and analysis of plates and shells made of materials with low shear stiffness are discussed.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Translated from Mekhanika Polimerov, No. 4, pp. 693–714, July–August, 1970.     

Adhesive ability of a heat-resistant double-chain polymer and the strength of CFRP based on it

The adhesive ability of a heat-resistant polyiminoquinazolindione (PIQD) binder, based on a double-chain polymer, and the physicomechanical characteristics of unidirectional CFRPs made with it are investigated. It is shown that, at room temperature, the strength of model adhesive joints (PIQD-steel wire) and of the CFRPs in shear and bending is rather low — about half of that of similar specimens based on an epoxy binder. At the same time, all their mechanical characteristics, to a large measure (50%), are retained at temperatures up to 450°C, which considerably exceeds the heat resistance of all polymer matrices used at the present time. The elastic modulus of the CFRPs in bending practically remains the same up to 450°C. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 535–546, July–August, 2008.     

Filament-wound rings tested by the application of concentrated loads

The stiffness and strength of rings and ring segments of fiber-reinforced materials have been investigated theoretically and experimentally in short-time tests with concentrated loads applied in the plane of the specimen. It is shown that the low shear resistance and the geometric nonlinearity must be taken into account in testing thick- and thin-walled specimens, respectively. The equations and graphs presented make it possible to allow for these effects in analyzing the test results or in design calculations. Experiments on unidirectional glass-reinforced plastics indicate good agreement with the proposed theoretical equations.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 719–727, July–August, 1969.