Dependence of elastic and strength characteristics of high-modulus composites on schemes of reinforcement

The elastic and strength characteristics of high-modulus composites with 12 different reinforcement schemes have been studied thoroughly. The effect of reinforcement schemes on change in elastic and strength characteristics of composites has been evaluated. A calculation of the elastic characteristics of high-modulus composites has been performed from the properties of the reinforcement and binder, and a comparison of the results with experimental data is given. Diagrams of deformation upon extension of the composites studied are given.All-Union Scientific-Research Institute of Aviation Materials, Moscow. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1019–1027, November–December, 1974.     

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.     

Experimental-theoretical study of thermal deformations of the KMU-8 structural CFRP

Conclusion The prediction techniques used herein make it possible to calculate with high accuracy the thermal characteristics of the material with the examined reinforcement schemes and make it possible to select the required reinforcement schemes in the design of articles made of a CM of the KMU-8 type. The use of particular reinforcement schemes makes it possible to obtain the desired values of the CLTE of the material in the required direction, and increase of the temperature in the CFRP working range does not lead to qualitative changes of these parameters.Translated from Meknanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 608–612, September–October, 1993.     

Experimental investigation of the anisotropy of strength of bolted joints of laminated composites upon variation of geometric and design parameters

Conclusion In the present work we investigated the anisotropy of the characteristics of tensile (buckling) strength and elasticity of plates made of KMU-4L in a bolted joint in a wide range of parameters of the material (stacking, number of layers), geometric parameters of the joint, parameters of the fastening element and of design parameters. An analysis of the results showed that the strength of the bolted joint under static loading can be increased for thin plates with h = 1–2 mm by local reinforcement of the zone of the hole by layers with = ±45 °, and also by increasing the moment of preliminary tightening; for plates with h = 3–4 mm the only feasible measure is increasing the moment of preliminary tightening to 20–40 Nm. All the results of the experiment were graphically generalized in the form of surfaces of maximal stress; this made it possible to predict the load bearing capacity of a joint for intermediate values of the parameters by calculating the safety factors.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 268–272, March–April, 1990.     

Propagation of elastic waves in certain composites

Conclusions 1. Relationships have been obtained for determining nine elastic characteristics of orthotropic composite materials from the properties of the starting components and the assigned reinforcement scheme.2. Formulas are given for calculating the propagation velocity of three types of elastic flat waves for an arbitrary direction in one of the planes of elastic symmetry of a uniform orthotropic material.3. It has been shown that the velocity of the first arrival of a packet of ultrasonic vibrations which is recorded in an experiment is equal to the velocity of motion of the wave front in a limitless medium even for rather thin (5–10 mm) fiberglass-plastic specimens with unidirectional or cross-reinforced schemes.4. The dependences of elastic properties and rates of propagation of elastic vibrations on direction which are calculated theoretically from the properties of the starting components and the reinforcement scheme agree satisfactorily with experimental results.Translated from Mekhanika Polimerov, No. 3, pp. 531–536, May–June, 1978.     

Various methods of determining the natural frequencies and damping of composite cantilever plates. 3. The Ritz method

The Ritz method was used to determine the frequencies and forms of free vibrations of rectangular cantilever plates made of anisotropic laminated composites. Orthogonal Jacobi and Legendre polynomials were used as coordinate functions. The results of the calculations are in good agreement with the published experimental and calculated data of other authors for plates made of boron and carbon fiber reinforced plastics with different angles of reinforcement of unidirectional layers and different sequence of placing the layers, and also of isotropic plates. The dissipative characteristics in vibrations were determined on the basis of the concept of complex moduli. The solution of the frequency equation with complex coefficients yields a complex frequency; the loss factors are determined from the ratio of the imaginary component of the complex frequency to the real component. For plates of unidirectionally reinforced carbon fiber plastic with different relative length a detailed analysis of the influence of the angle of reinforcement on the interaction and frequency transformation and on the loss factor was carried out. The article shows that the loss factor of a plate depends substantially on the type of vibration mode: bending or torsional. It also examines the asymptotics of the loss factors of plates when their length is increased, and it notes that the binomial model of deformation leads to a noticeable error in the calculation of the loss factor of long plates when the angle of reinforcement lies in the range 20°<<70°.For Communication 2, see [1].Institute of Engineering Science of the Russian Academy of Sciences, St. Petersburg, Russia. St. Petersburg State University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 215–225, March–April, 1997.     

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.     

A Technique for Determining the Elastic and Dissipative Properties of Orthotropic Composites in Shear

A new method is presented for the characterization of three principal complex shear moduli of linear viscoelastic orthotropic materials, which is based on the measurement of complex torsional vibration frequencies of three rods of rectangular cross section. The rod-type test specimens are cut out from a composite plate along the principal material axes in the reinforcement plane. It is shown that the torsional stiffness of an elastic rod can be calculated not only by means of the Saint-Venant torsion theory, but also using a relationship obtained from the Reissner-Mindlin theory of plates. The transfer to a viscoelastic model of the material with complex moduli is realized with the help of the correspondence principle. By applying a numerical sensitivity analysis of natural frequencies to the shear moduli, the advisable width-to-thickness ratios of the specimens are found. As an illustration of data processing, the dynamic shear moduli and the loss factors for a GFRP fabric with an epoxy matrix are calculated. A comparison of the method offered with some known static and dynamic methods for determining the shear moduli of orthotropic materials is given.     

Temperature stresses in plates made of reinforced laminated material

The heat conduction equations and the basic equations of the quasi-static axisymmetric problem of thermoelasticity are obtained for thin plates with heat transfer and cylindrical anisotropy. The nonsteady temperature stresses are determined for an infinite plate with a circular opening and an annular plate, both made of reinforced laminated material.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Translated from Mekhanika Polimerov, No. 4, pp. 721–726, July–August, 1970.     

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.     

A class of contact problems for thin anisotropic reinforced-plastic plates

Certain problems of the interaction of perfectly rigid smooth bodies and elastic reinforced-plastic plates are considered. The state of stress of the plate is described by the equations of orthotropic plates resisting interlaminar shear. Solutions are obtained in the case of a stamp in the shape of a rigid paraboloid of revolution indenting a circular plate with ring reinforcement and in the case of a parabolic cylinder indenting a unidirectionally reinforced plate in cylindrical bending. The expressions obtained for the contact pressure and the relation between the load P, the size of the contact region, and the settlement of the stamp are investigated with respect to their dependence on the orthotropy, wall thickness, and shear compliance parameters.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Ivano-Frankovskii Institute of Petroleum and Gas. Translated from Mekhanika Polimerov, No. 2, pp. 346–350, March–April, 1972.     

Deformability and load-carrying capacity of netted composite rod assemblies with metal fittings

A technology is proposed for making netted rod assemblies with metal joints 3–5 times lighter than existing comparable structures. A procedure was developed for winding assemblies out of carbon-fiber-reinforced plastic (UKN-5000 and binder EKhD-MK). Results are presented from a study of the strain characteristics and load-carrying capacity of assemblies with different reinforcement schemes for different conditions of static damage. It is shown that the design of netted rod assembly proposed here is significantly superior to all known analogs with respect to specific stiffness characteristics and provides great dimensional stability in the case of unilateral heating of the product. The method is most effective if used to develop framework-type structures for use in space — platforms, telescope and antenna supports, and masts.Paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 387–392, May–June, 1995.     

Photoelastic investigation of stress concentrations in model glass-reinforced plastics under static load

The title investigation was carried out using a double-beam polarimeter for studying the stress patterns in "sandwich" models of glass-reinforced plastics. The same experimental technique can be adapted to a wide range of reinforced materials. A comparison of the experimental results with calculations based on the theory for quasi-homogeneous anisotropic plates shows that it is not always permissible to assume that the laminated material has a quasi-homogeneous structure.Translated from Mekhanika Polimerov, No. 4, pp. 711–718, July–August, 1969.     

Stability loss of reinforced cylindrical shells under isotropic external pressure

Conclusions 1. Upon the loading of a composite shell having a metallic matrix the shear effects are insignificant even in the case of comparatively large volume reinforcement contents and wall thicknesses.2. The principal modulus of a material which determines the stability of a reinforced shell upon isotropic external pressure is the secant modulus in the circumferential direction.3. In the case of complex reinforcement schemes some decrease in the stability of the shell is possible, probably due to an imperfection in reinforcement technology.Institute of Solid State Physics, Academy of Sciences of the USSR, Moscow Region. Translated from Mekhanika Polimerov, No. 1, pp. 90–95, January–February, 1977.     

Axisymmetric deformation of a thick circular glass-reinforced plastic cylinder with stiffening ribs

The state of stress of a circular glass-reinforced cylinder strengthened with equally spaced stiffening ribs has been investigated for uniform axisymmetric and longitudinal loads of intensity p. A system of equilibrium equations is obtained for the shell on the assumption that Hooke's law is valid and that the angles of rotation and shear are commensurable for deformation of an element of the structure. A solution of this system is given for boundary conditions that take into account the compatibility of strains of shell and ribs. As a result of an analysis of the solution the limits of applicability of the theory of thin shells to this type of structure are determined, the effect of anisotropy of the material is estimated, and recommendations are made regarding the choice of optimal reinforcing schemes for cylindrical shells.Mekhanika Polimerov, Vol. 2, No. 1, pp. 108–115, 1966     

Radiation and Scattering by Complex Conformal Antennas on a Circular Cylinder

A technique for characterizing and designing complex conformal antennas flush-mounted on a singly-curved surface is presented. This approach is based on the hybrid finite element–boundary integral (FE–BI) method. A related method was proposed in the past utilizing cylindrical-shell finite element and roof-top rectangular basis functions for the boundary integral. Although that method proved very powerful for analyzing cylindrical–rectangular patch arrays flush-mounted to a circular cylinder, the requirement for uniform meshing in the aperture ultimately limited its usefulness. In this present formulation, tetrahedral elements are used to expand the volumetric electric fields while similar basis functions are used for the boundary integral. The curvature of the aperture is explicitly included via the use of the circular cylinder dyadic Green's function. After presentation of the formulation and validation using several well-understood examples, an example is presented that illustrates the capabilities of this method for modeling complex conformal antennas heretofore not examined by rigorous methods due to inherent limitations of the various published methods.     

Experimental study of thermal expansion of layered carbon-reinforced plastics

Conclusion The nonlinear dependence of the thermal deformations on the temperature for a wide class of layered carbon-reinforced plastics was experimentally demonstrated and the use of the thermal expansion function of the material instead of the corresponding characteristic: the thermal expansion coefficient, was substantiated in the present study. A method for determining the parameters of the thermal expansion functions was developed in consideration of their nonlinear dependence on the temperature and the numerical values were reported for layered carbon-reinforced plastics of two types with typical reinforcement schemes. In addition, the significant dependence of the thermal expansion functions on the geometry of the structure of the carbon-reinforced plastics was observed, and the major possibility of optimum planning of the structure of the material from considerations of geometric stability was demonstrated. The study of thermal deformations of reinforced plastics in consideration of their random character is promising as a result of the significant variance of the experimental data.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 32–36, January–February, 1990.     

Solution of two-dimensional boundary-value problems of the theory of thin composite shells

Discrete analogues of the boundary-value problems of a two-dimensional refined theory of anisotropic shells taking into account the transverse shear deformation are presented. The systems of resolving equations in the general form are obtained for arbitrary nonshallow shells of variable curvature whose coordinate lines of the reduction surface may not coincide with the lines of principal curvatures. The algebraic problems of determining the stress-strain state in shells made of composite materials with stress concentrators under various kinds of loads are obtained as particular cases of the schemes presented. The results of calculating the stress concentration near a nonsmall circular hole in a transversely isotropic nonshallow spherical shell under internal pressure are presented. The dependences of stress concentration factors on the hole dimension and on a change in the shear stiffness of the shells are studied. A comparison between the calculation results obtained within the framework of the theories of shallow and nonshallow shells is given.Presented at the 11th International Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).Timoshenko Institute of Mechanics, Ukranian National Academy of Sciences, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 465–472, July–August, 2000.     

Application of the finite-element method to improve the quasi-exact reinforcement theory of fibrous polymeric composites

In the paper, the WL quasi-exact reinforcement theory of fibrous polymeric composites is improved. An optimum compatibility condition related to the transverse shear problem for a unit cell, which brings solutions closest to reality, is derived. This condition is formulated in the form of a linear combination of maximum radial and circumferential displacements. Optimum coefficients of this combination are determined by comparing analytical and numerical solutions for a test specimen in the form of a rectangular thin plate, which is in a plane strain state and is subject to selected loading schemes. The analytic solutions are obtained for a homogenized material by using the WL reinforcement theory. The numerical solutions are found for an actual heterogeneous composite material by using the finite-element method, and they verify the WL reinforcement theory, in particular, the admissibility of Hills assumption. An analysis performed for two composite materials shows that the improved WL reinforcement theory gives adequate displacement fields.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 79–92, January–Febrauary, 2005.     

Fracture of plates,the compression of which is accompanied by cracking

The appearance of fracture shapes, analogous to fractures in the shape of a "Chinese lantern" in rectangular plates has been discussed, the compression of which is accompanied by cracking. It has been shown that one or two cracks can appear when rectangular hinged plates are subjected to compression. An arbitrary number of cracks can be formed when a cylindrical shell is subjected to compression.Paper presented at the 9th International Conference on the Mechanics of Composite Materials, Riga, October (1994).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 326–329, May–June, 1995.