Distribution of self-balanced stresses in a stratified composite material with warped structures

We use the model of a linear, piecewise homogeneous elastic body to study the distribution of selfbalanced normal and tangential stresses for a horizontal deformation of a stratified composite material with warped structures which is under the action at infinity of uniformly distributed normal stresses directed along the stratification.Translated from Matematicheskie Metody i Fiziko-mekhanicheskie Polya, No. 26, pp. 83–89, 1987.     

Viscoelastic deformations of a thick-walled cylinder under prolonged exposure to gravitational stresses

A method is presented for the calculation of the stress-deformed state of an infinitely long viscoelastic thick-walled cylinder, enclosed in an elastic casing and exposed to gravitational stress in equilibrium with a system of concentrated forces, applied to the casing. The problem is solved by analyzing the flat deformation of the annular region under the influence of mass forces and unknown reactions on the outer surface, and by determining the stress-deformed state of the casing ring exposed to distributed normal and tangential loads, and to a system of concentrated forces. The solutions are then compared on the basis of compatibility of the deformations and equality of the stresses. Integral transformations are used in the calculations and an example is cited.S. Ordzhonikidze Aviation Institute, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 846–853, September–October, 1972.     

Deformation of polymers under friction loading

A study has been made of the laws of distribution of elastic and residual deformations in the surface layers of polymers subjected to friction. The dependence of these deformations on normal pressure, sliding velocity, and duration of loading has been determined. A relation between deformation and antifriction characteristics has been established, and the relative effect of normal and tangential loads on surface-layer deformation determined.Mekhanika Polimerov, Vol. 3, No. 3, pp. 539–543, 1967     

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.     

Stress concentrations around openings in transversely isotropic shells

A method of investigating stress concentrations around openings in shells made of a transversely isotropic material (oriented glass-reinforced plastic [5]) is described. The use of a Timoshenko-type theory makes it possible to take into account the effect of tangential shearing stresses and the anisotropy of the elastic properties of the shell in a direction normal to the middle surface. A complex form of the resolvents of this theory, constructed in [6], is employed.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. L'vov Franko State University. Translated from Mekhanika Polimerov, No. 6, pp. 1076–1081, November–December, 1970.     

Elastic and Sorption Characteristics of an Epoxy Binder in a Composite During Its Moistening

Results of an experimental investigation into the elastic and sorption characteristics of a model composite material (CM) — epoxy resin filled with LiF crystals — during its moistening are presented. Properties of the binder in the CM with different filler contents (v _f = 0, 0.05, 0.11, 0.23, 0.28, 0.33, 0.38, and 0.46) were evaluated indirectly by using known micromechanical models of CMs. It was revealed that, for the CM in a conditionally initial state, the elastic modulus of the binder in it and the filler microstrain (change in the interplanar distance in the crystals, measured by the X-ray method) as functions of filler content had the same character. The elastic modulus of the binder in the CM with a low filler content was equal to that for the binder in a block; the elastic modulus of the binder in the CM decreased with increasing filler content. The maximum (corresponding to water saturation of the CM) stresses in the binder and the filler microstresses as functions of filler content were of the same character. Moreover, the absolute values of maximum stresses in the binder and of filler microstresses coincided for high and low contents of the filler. At v _f = 0.2–0. 3, the filler microstrains exceeded the stresses in the binder. The effect of moisture on the epoxy binder in the CM with a high filler content was not entirely reversible: the elastic characteristics of the binder increased, the diffusivity decreased, and the ultimate water content increased after a moistening-drying cycle.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 499–511, July–August, 2005.     

Calculation for thin-walled closed contours of composite materials in torsion

We consider the torsion of closed torsion-box structures made of composite materials (such as airplane wings) under mechanical loads inducing only torsion of the construction without bending. The problem is solved by an energy method and using a conforming displacement method. The derived distribution law for the tangential stresses contains two terms and gives the Bredt formula for the special case of pure torsion. Since in solving the problem by a conforming displacement method the axial warping distribution law for torsion of a simple closed contour is obtained automatically, this method may be considered to be ecact in the sense of satisfying the continuity condition for the structural material.Deceased.Moscow State Aviation Institute (Technical University), Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 235–241, March–April, 1997.     

Plane strain deformation of an initially unstressed elastic medium

Selim and Ahmed [1] used the eigenvalue approach by assuming distinct eigenvalues to calculate the elastic deformation due to an inclined load at any point as a result of an inclined line load of initially stressed orthotropic elastic medium. They studied the plane strain problem and obtained the corresponding results for an unstressed orthotropic medium as a particular case. In the present paper, it is shown that all the eigenvalues do not remain distinct, but become repeated when the elastic medium is free from the initial compressive stresses. Further, the displacements and stresses for an unstressed elastic medium have been independently obtained. The variation of the displacements and stresses due to normal and tangential line load are also shown graphically.     

Stress-strain state and stability of composite sandwich shells with a scaling zone between the core and facings

A finite element model is presented for analyzing the strength and stability of sandwich shells of arbitrary configuration with an adhesion failure zone between the core and one of the facings. The model is based on the assumptions that both facings are laminated Timoshenko-type composite shells, only transverse shear stresses in the core and normal stresses in the thickness direction have nonzero values, a free slip in the tangential plane in the adhesion failure zone and unilateral contact along the normal are possible, and the prebuckling state in the stability problem is linear. Biquadratic nine-node approximations for all functions and numerical integration were used. The displacements and rotation angles of the normals toward the facings as well as stresses in the core are taken as global degrees of freedom. The algebraic problem is solved using a special step-by-step procedure of determining the contact area in the scaling zone and employing unilateral constraints for some of the unknowns. Numerical examples are also given.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 640–652, September–October, 1993.     

Linear Viscoelasticity of Liquid-Crystalline Polymers

A linear (small-amplitude) periodic shear deformation of anisotropic viscoelastic liquids obeying the Akay–Leslie rheological model is considered. The frequency dependences of the real and imaginary components of the complex shear modulus and complex normal-stress coefficient are determined. A comparison between calculation results and test data on the shear flow of poly(-benzylglutamate) in m-cresol is carried out. It is stated that, if the material is characterized by some initial orientation, both components of the complex shear modulus contain a multiplier which depends on the degree of the initial orientation and increases the values of the components compared with those for an initially isotropic material. The model predicts that, in a periodic shear flow, the components of shear and normal stresses are constant and, like the components of shear modulus, are independent of deformation frequency. If the parameter d ₀ of the Akay–Leslie model is equal to zero, the values of its other parameters can be determined from experimental results on periodic shear flow.     

Model of a layered plate considering nonideal contact between layers

We propose a mathematical model for doing calculations for layered plates, allowing for both rigid and sliding contact in the presence of frictional forces between the sliding layers. The model takes into account the distribution of tangential and normal displacements across the thickness of the sliding layered stack, and also the distribution of transverse normal stresses. The strain tensor is obtained using the Cauchy relations; the stress tensor is obtained based on Hooke's law. Tne Lagrange variational principle allows us to obtain the resolvent system of differential equations and the corresponding boundary conditions. The spatial model for deformation of a layered plate has a number of special features compared with familiar models. The system of differential equations has operators no higher than second order. It is described relative to displacements on the faces of the stack. This is convenient in solving problems involving sliding of layers with and without friction.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 671–676, September–October 1995.     

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.     

Effect of tensile stresses on the strength of heat-treated glass fibers

Possibilities of controlling the internal stresses developing during production of glass reinforced plastics were investigated. A favorable effect can be obtained by prestressing the glass fiber reinforcement during molding. Prestressing during heat treatment was found to increase the strength of the fibers. The strengthening is due to a reduction in stress concentration around microcracks as a result of forced elastic and plastic deformation.Mekhanika polimerov, Vol. 1, No. 1, pp. 89–92, 1965     

Study of prefracture states of rigid polymers. 2. Elastic limit and strength

An explanation is offered for the relation between the magnitude of stresses at the elastic limit (strength) and the strains in rigid polymers. The possibility of high-elastic deformation and orienting processes, which have been considered in [1], is also explained here. Expressions are derived that relate the elastic limit to the strain, the modulus of elasticity, the coefficient of thermal expansion, and the Poisson ratio.For communication 1, see [1].A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 195–201, March–April, 1976.     

Friction method of measuring elastic deformations occurring during the testing of polymers under conditions of reversible slippage

A method of determining the elastic deformation and the magnitude of the relative slipping of parts, during the testing of polymers under conditions of reversible slippage is examined. A significant reduction in the amplitude of slippage is noted. The magnitude of the actual amplitude of reversal can be determined if the variation in the moment of friction and the displacement in time of the moving part are known.Ya. Alksnisa Riga Upper Military Aeronautical Engineering Academy. Translated from Mekhanika Polimerov, No. 6, pp. 1125–1127, November–December, 1975.     

Thermodynamic constraints on the relation between the stresses and the time derivatives of the strains and temperature for reversible processes

It is assumed that the free energy and entropy are functions of time and time derivatives of the temperature and strain of any order. The laws of thermodynamics of reversible processes are employed to obtain constraints on the relation between the stresses and the time derivatives of the strains and temperature and, moreover, the relation between the free energy and the part of the entropy that does not depend on the first derivative of the strains with respect to time.Moscow Lomonosov State University. Translated from Mekhanika Polimerov, No. 6, pp. 1001–1008, November–December, 1970.     

A refined model for three-point bending of sandwich panels 2. Transverse stresses

According to the relationships derived in [1], transverse normal and tangential stresses in a sandwich panel have been analyzed. Asymptotic formulas for the stress concentration area in the vicinity of point forces are derived. Analytical estimates of a normal stress at the central and end sections of the panel are deduced. The Saint-Venant effect of the degeneration of a panel of finite length into an infinite strip is studied. For the estimation of the concentration of the transverse tangential stress, the possibility of a superposition of the solution of the slippage problem of the face layers and the classical solution allowing for shear is substantiated. It is shown that the local Reissner-type effects are specified by reducing the concentration of the tangential stress in the face layers along the longitudinal coordinate and transition to the steady tangential stress state in the filler layer. The concentration coefficients of the tangential stress are derived as functions of the dimensional parameters of the panel section.Institute of Polymer Mechanics. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 1, pp. 66–93, January–February, 1998.     

Stresses in plastics reinforced with anisotropic fibers and subjected to transverse normal loading

The question of the stress distribution in plastics reinforced with anisotropic fibers and subjected to transverse normal loading is considered. The stresses in the components are determined by the methods of the theory of elasticity using stress functions. The theoretical relations obtained are used to construct diagrams showing the distribution of the tangential, radial, and shear stresses in the composite and the isoclines of the concentration coefficient for a carbon-reinforced plastic. The results obtained for the carbon-reinforced plastic are compared with the analogous results for a glass-reinforced plastic.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 244–252, March–April, 1973.     

Resultant forces and moments in mixed-mixed problems of the theory of elasticity

A problem is called mixed-mixed, when both normal and tangential displacements are prescribed on a part of the boundary, while the normal and tangential stresses are prescribed at the rest of the boundary. Exact closed form expressions have been derived for the resultant normal and tangential forces, tilting moment and torque, directly through the prescribed displacements, thus eliminating the need for determination of stresses. The problem solved treats a transversely isotropic elastic half-space, with arbitrary normal and tangential displacements prescribed inside a circle, and the rest of the boundary being stress-free. The interaction between an arbitrary force inside the half-space and a bonded punch is considered as an example. No similar result has ever been reported, even in the case of isotropy.     

Investigation of the energy effects accompanying the elastic deformation of uniaxially oriented crystalline polymers

The energy (thermal and mechanical) effects accompanying the elastic deformation of uniaxially oriented crystalline polymers have been investigated; it has been established that, when these polymers are stretched, heat is released. It is shown that the heat release in uniaxial tension is a consequence of localization of the elastic deformation in the poorly ordered regions of the polymer. The relation between the thermoelasticity of uniaxially oriented crystalline polymers and their supermolecular structure is examined.Institute of Heteroorganic Compounds, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 785–798, September–October, 1970.