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# Mechanics of Composite Materials (v.33, #2)

Analysis of contact stresses due to combined bending and sliding of high-performance fibers by C. -H. Andersson (

*pp. 101-106*).

Analytical formulas for the estimation of pressure and shear stresses due to friction on bent surfaces during the handling of fibers in the manufacture of industrial textiles and composites have been derived using the drive belt formula and Hertz contact stress relations. Experimentally measured at low speed, the forces and coefficients of friction give shear stresses in the same range as for the debonding in composites. This supports a partially adhesion view of the friction processes.

Determination of rational structure for spherofibrous plastics by G. A. Vanin; Nguyen Dinh Duc (

*pp. 107-111*).

A complete set of elastic constants for various structures of triorthogonally reinforced plastics with a matrix dispersely reinforced by spherical particles has been determined on the basis of the proposed algorithm. Approximate equations are obtained for determination of all integral parameters from data on the components and structure geometry. It is established that for the reinforcement schemes investigated, the shear moduli of the composites have the lowest possible values and are calculated with a higher accuracy than the other elastic constants.

Generalized self-adjustment method for statistical mechanics of composite materials by A. A. Pan'kov (

*pp. 112-118*).

A new method is developed for the statistical mechanics of composite materials — the generalized selfadjustment method — which makes it possible to reduce the problem of predicting effective elastic properties of composites with random structures to the solution of two simpler “averaged” problems of an inclusion with transitional layers in a medium with the desired effective elastic properties. The inhomogeneous elastic properties and dimensions of the transitional layers take into account both the “approximate” order of mutual positioning, and also the variation in the dimensions and elastics properties of inclusions through appropriate special averaged indicator functions of the random structure of the composite. A numerical calculation of averaged indicator functions and effective elastic characteristics is performed by the generalized self-adjustment method for a unidirectional fiberglass on the basis of various models of actual random structures in the plane of isotropy.

Smooth convex limit surfaces in the space of symmetric second-rank tensors by A. Lagzdin' (

*pp. 119-127*).

Equations are proposed to describe smooth (regular) convex hexagonal and triangular curves in the deviatoric plane. The equations are used to construct smooth convex limit surfaces for media whose properties are arbitrarily anisotropic. The results supplement the findings in [

*A. Lagzdin' and A. Zilauts, Mekh. Kompozitn. Mater.*,*32*, No. 3, 339–349 (1996)], where the third invariant of a tensor was introduced into the limit-surface equation by means of singular deviatoric curves.Elastic characteristics of ferrocement reinforced by hexagonal grids by A. A. Skudra; A. M. Skudra (

*pp. 128-131*).

The methods of the structural mechanics of composite materials are used to develop a method for predicting the elastic modulus and shear modulus of ferrocement reinforced with hexagonal woven and stamped grids. The method takes into account the elastic properties of the components and the geometry of the reinforcement.

Elastic properties of honeycomb sandwich plates with nontraditional cell forms by V. E. Kryutchenko (

*pp. 132-135*).

A method for correcting the elastic properties of honeycomb sandwich plates by changing the cell shape is described. Compact and convenient analytical expressions (1) are proposed for calculating the reduced elastic parameters of the honeycomb sandwich plates. The acceptable range of changes in the size of the honeycombs is restricted by the cell elongation region β∈[0.5;2] and the region of variation of the angle between cell walls α∈[π/6; 5π/6]. The results of the calculation experiment showed that the traditional cell shape (α=π/3, β=1) is not effective as an optimum structure (Table 1).

Consideration of friction between layers in determining the stress-strain state of structures with nonideal layer contact by A. V. Marchuk (

*pp. 136-141*).

A mathematical model for calculation of structures in a three-dimensional installation allowing for layer slippage with friction was constructed. The examples examined show that consideration of friction in problems of calculating laminated structures with nonideal layer contact can introduce an essential correction in the stress—strain state of the structure. In slabs with a freely sagging lower surface, friction is perceived for important friction coefficients and increases when the slippage surface approaches the loaded surface. In masses with a rigidly attached lower surface, even insignificant friction coefficients lead to essential redistribution of the stress—strain state.

The effect of interphase on residual thermal stresses. 2. Unidirectional fiber composite materials by V. Kushnevsky; A. K. Bledzki (

*pp. 142-152*).

In real composite materials an additional phase may exist between the fiber and the matrix. This phase, commonly known as the interphase, is a local region that results from the matrix bonds with the fiber surface or the fiber sizing. The differing thermal expansions or contractions of the fiber and matrix cause thermally induced stresses in composite materials. In the present study, a four-cylinder model is proposed for the determination of residual thermal stresses in unidirectional composite materials. The elastic modulus of the interphase is a function of the interphase radius and thickness. The governing equations in terms of displacements are solved in the form of expansion into a series [1]. The effective elastic characteristics are obtained using the finite element approach. The effect of the interphase thickness and different distributions of the interphase Young's modulus on the thermal residual stress field in unidirectional composite materials is investigated.

Various methods of determining the natural frequencies and damping of composite cantilever plates. 3. The Ritz method by V. S. Ekel'chik; V. M. Ryabov (

*pp. 153-159*).

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°<φ<70°.

Frequency response and damping analyses of structures with different damping models by E. Barkanov (

*pp. 160-165*).

The behavior of structures with different damping models has been investigated using finite element and frequency response analyses. As an example, systems with hysteretic and viscous damping were examined. The damped eigenfrequencies and the corresponding loss factors were computed based on frequency response analysis and then compared to the results obtained from free vibration analysis using the method of complex eigenvalues. Recommendations are given for a more effective employment of frequency response and damping analyses in the structures considered.

Calculation for thin-walled closed contours of composite materials in torsion by A. N. Elpat'evskii; N. N. Kurdyumov (

*pp. 166-171*).

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.

Buckling of a sandwich composite cylindrical shell stiffened by rings under external pressure by A. V. Lopatin (

*pp. 172-178*).

A solution is presented for the problem of buckling of a sandwich composite cylindrical shell stiffened by rings and subjected to external pressure. The solution is obtained on the basis of the theory of stiffened composite shells taking into account the discrete position of the rings, the transverse shear deformation in the shell and rings, the laminated structure, and the orthotropy of the facing materials. The perturbed state of the stiffened shell is described by a semimembrane model. The prebuckling state of the structure is considered to be axisymmetric with allowance for prebuckling bending moments. It is assumed that the rings are deformed in their planes only and that the contact load between the rings and the shell is applied along the axis lying at the midsurface of the shell. The Dirac delta-function is used for the description of the distribution of contact forces acting between the shell and the rings. As an example, the critical external pressure has been obtained for a glass-epoxy structure of 5 m length, 1.25 m radius, and 0.12 m thickness stiffened by various numbers of rings.

Thermoelastic expansion of spherical fiber composites by Nguyen Dinh Duc (

*pp. 179-184*).

A refined solution is constructed for thermoelastic expansion of spherical fiber composites with a three-dimensional structure on the basis of existing hypotheses about the longitudinal state of fibers in a matrix strengthened with spherical inclusions. Relationships defining the dependence in explicit form of thermoelastic coefficients on structural parameters are obtained in analytical form. Thermal expansion coefficients for composites with cubic symmetry are discussed in detail.

Prediction of the short-term strength of polymer materials based on equations of state by O. F. Shlenskii; N. N. Lyasnikova; M. A. Sheryshev (

*pp. 185-188*).

The possibility is analyzed of using equations of state for predicting the mechanical properties of linear amorphous polymers with short-term loading from data for their compressibility.

Averaging of electrical properties of anisotropic fiber-metal composites by D. Bardzokas; M. L. Fil'shtinskii; L. A. Fil'shtinskii (

*pp. 189-193*).

The electrical properties of fiber-metal composites with anisotropic components were averaged within the framework of a regular structure model. The corresponding current problem was reduced to a system of two integral equations with elliptical kernels. The effective electrical conductivity tensor of such materials was defined as several functionals based on integral equation solutions for the boundary problem. The calculation results are given.

Thermal conductivity of organoplastics by S. N. Negreeva (

*pp. 194-200*).

The dependence of the thermal conductivity of a unidirectional reinforced organoplastic on the fiber volume fraction as well as thermal conductivity and structural porosity of the components was studied experimentally and using mathematical models. These results may be used to develop new methods for the manufacture of plastic items and the nondestructive thermal monitoring of the structural parameters of these items.