Natural vibration of the beam-strip fabricated from a composite material with small-scale curvings in the structure

The frequency and forms of natural vibrations of a hinged beam-strip fabricated from a composite material with small-scale curved structures have been investigated using the plate theory in the framework of the Timoshenko hypothesis. The mechanical relationships of the composites are described by the Akbarov and Guz continuum theory. Using the corresponding variational principle, a method of solution of the considered problem is presented. Specific numerical investigations have been carried out for the case when the strip material consists of alternating equidistantly located and curved isotropic layers. The effect of existence of the curving in the beam-strip structure on its frequencies and forms of natural vibrations is studied. Cases of periodic and local curvings in the beam-strip material structure are considered separately.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Yilziz Technical University, Civil Engineering Faculty, 80750 Yildiz-Istanbul, Turkey. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 502–512, July–August, 1996.     

On the stress distribution in a rectangular thick plate of a composite material with curved structure under forced vibration

The stress distribution in a rectangular plate of a multilayer composite material with a periodically curved structure under forced vibration is studied. It is assumed that the plate is hinge supported at opposite sides. The investigation is carried out within the exact three-dimensional linear theory of elasticity. The mechanical relationships of the plate material are described by the continuum theory of Akbarov and Guz'. The numerical results obtained by the finite element method show that even in low-frequency dynamic loading of the plate the extreme values of stresses, which appear as a result of the curving in the plate structure, considerably exceed those in the corresponding static loading.Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 447–454, July–August, 1999.     

Stress analysis for a rectangular thick plate of a composite material with a spatially locally curved structure under forced vibration

Natural and forced vibrations of a thick rectangular plate fabricated from a composite material with a spatially locally curved structure are investigated with the use of exact three-dimensional equations of motion of the theory of elastic anisotropic bodies. The investigations are carried out within the framework of the continuum approach developed by Akbarov and Guz. It is supposed that the plate is clamped at all its edges and is loaded on the upper face with uniformly distributed normal forces periodically changing with time. The influence of the parameters of local curving on the fundamental frequency of the plate and on the distribution of the normal stress acting in the thickness direction under forced vibration is studied. The corresponding boundary-value problems are solved numerically by employing the three-dimensional FEM modelling.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 779–790, November–December, 2004.     

The eigenfrequencies of a slightly curved isotropic strip clamped between absolutely rigid profiles

The propagation of elastic waves along an isotropic homogeneous strip, distorted on a finite part and clamped without friction and detachment between two absolutely rigid profiles, is investigated. It is established that, by choosing the shape of the curved sides one can obtain eigenfrequencies, accompanied by trapping of the elastic wave. The result is based on an asymptotic analysis of an auxiliary object – an augmented scattering matrix, which was previously constructed exclusively for scalar problems.     

Bending of a Composite Material Strip with Curved Structure in the Geometrically Nonlinear Statement

To date, bending problems for strips or plates made of composite materials with curved structure have been investigated only in the linear statement. However, in many cases, the necessity arises to investigate the corresponding bending problems in the geometrically nonlinear statement. Therefore, in the present paper, some bending problems for a composite strip with a periodically curved structure is investigated in such a statement using the exact nonlinear equations of elasticity theory in Lagrangian coordinates. The numerical results are obtained by employing the FEM with the use of the Newton-Raphson and the Modified Newton-Raphson algorithms.     

Three-dimensional analysis of stress fields in the plates fabricated from composite materials with small-scale structural curving

The stress distribution in plates fabricated from the multilayered composite materials with periodical smallscale curved structures has been studied. It is supposed that the continuously distributed normal forces act on the upper plane of the plate. Moreover, it is assumed that the plate is simply and rigidly supported at opposite sides. The investigation has been carried out in terms of the three-dimensional theory of elasticity, while the mechanical relationships of the given plate material have been described by the Akbarov and Guz' continuum approach. The numerical results obtained with the use of the seminalytical FEM show that the curving in the plate material structure affects the stress distributions in this plate.Chemical and Metallurgy Faculty, Department of Mechanical Engineering, Yildiz Technical University, 80750 Yildiz-Istanbul, Turkey. Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 340–348, May–June, 1997.     

Low-cycle fatigue of a composite substance containing a dispersed filler in cyclic compression

Conclusions 1. The lifetime of a composite material having a dispersed filler has been examined under conditions of low-cycle compression.2. It has been shown that, in distinction from materials of fibrous structure, the lifetime of this material is determined, not by a breakdown in the continuity of structure, but the deformability of the polymer matrix.3. The absence of a correlation between the static and fatigue strengths of composite mateials from cold and hot curing is caused by the different effect of the structure of the cured binder as a component of the material on the ultimate static characteristics and creep, whose relaxation character is more clearly expressed.4. Creep of the binder and the strength of the microspheres are the main factors which determine the lifetime of the material in question in cyclic compression.All-Union Scientific-Research Institute of Synthetic Resins, Vladimir. Translated from Mekhanika Polimerov, No. 4, pp. 653–657, July–August, 1978.     

Nonlinear moisture deformation of a composite with a densified reinforcement

Conclusion An analytical method is presented for estimation moisture deformation of densified in technological pressing wood-based composite material with nonlinear swelling properties. This includes modelling of the processing effects as well as interfacial bonding. By using the multilayer model supported on the laminate analogy the optimum particle alignment has been estimated for a real composite production process.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 3, pp. 314–320, May–June, 1994.     

Hygromechanics of composites with unsymmetric structure

Conclusions An analytical method is presented for estimation of midplane strains and curvatures of a 3D general composite. By using the multilayer model based on the laminate analogy, the effect of an unsymmetric distribution of moisture content and material structure on swelling and wrap as well as the stability in compression of a densified technological pressing wooden composite board has been estimated for a real composite production process.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 6, pp. 831–838, November–December, 1994.     

Stress state of a composite shell with a sizable opening

The stress-strain state of a nonshallow cylindrical shell of a composite material is investigated. The shell is weakened by a circular hole and loaded with internal pressure. For solving the problem, the variational-difference method is used. The calculations are carried out for an orthotropic shell with a sizable hole, with account of the reduced shear stiffness of the material.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 49–56, January–February, 2005.     

Minimizing the mass of cylindrical shells formed from a composite material with an elastic filler and designed for strength and stability under a combined loading

The mass of a multilayer cylindrical shell, formed from a composite material with an elastic filler and designed for strength and stability under the combined action of axial compression and external pressure, is minimized. The problem is formulated as one of nonlinear programming and is solved by Rossen's method of projection gradients. The strength of the material is established from analysis of the strength of the layers making up the entire bundle. Failure of an individual layer is determined from Malmeister's criterion. The structure of a shell with different external loads and the dependence of minimal mass on the stiffness of the filler and on the volume coefficient of reinforcement are investigated in numerous examples.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. K. Preikshas Shyaulyaisk Pedagogical Institute. Translated from Mekhanika Polimerov, No. 2, pp. 289–297, March–April, 1976.     

Buckling Instability of a Thick Rectangular Plate of a Composite Material with a Spatially Periodically Curved Structure

Within the framework of the continuum approach for composite materials with a spatially curved structure developed by Akbarov and Guz', with the use of the three-dimensional linearized theory of stability, the buckling instability of a rectangular plate made of a composite material is investigated. Various edge conditions are considered, and, for obtaining a numerical result, a three-dimensional FEM modelling is developed. Uniaxial and biaxial precritical compression of the plate is analyzed. The numerical results presented illustrate the influence of problem parameters on the critical relative shortening of the plate.     

On the three-dimensional stability loss problems of elements of structures of viscoelastic composite materials

Up to now, numerous problems of the stability loss for elements of structures made from composite materials have been investigated in the framework of the three-dimensional linearized theory of stability (TDLTS). It follows from the analysis of these investigations that the TDLTS was mainly applied to the design of elements of structures made from time-independent materials. For the solution of these problems for viscoelastic materials in the framework of the TDLTS, the dynamic investigation method and the critical deformation method are recommended in many references. However, it is known that a very reliable and frequently used approach for viscoelastic materials is the approach based on the study of the growth of insignificant initial imperfections in elements of structures with time. Taking into account the above-mentioned, an approach based on the growth of the initial imperfection for the investigation of the stability loss problems of elements of structures made from viscoelastic composite materials in the framework of TDLTS is proposed in the present paper. The composite material is modeled as an anisotropic, viscoelastic solid with averaged mechanical properties and all investigations are made on the strip simply supported at the ends.Yildiz Technical University, Dept. Math. Eng., 80750, Besiktas-Yildiz, Istanbul, Turkey. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 761–770, November–December, 1998.     

Identification of mechanical properties of composites based on design of experiments

A numerical-experimental method for the identification of mechanical properties of laminated polymeric composites from the experimental results is being developed. For the first time, it is proposed to use the method of experiment planning to solve the identification (inverse) problems. The basic idea of the approach is that simple mathematical models are determined only from information on the response of a structure in reference points of the design. Therefore, a significant reduction in the calculation of the identification functional (about 50–100 times) can be achieved in comparison with the conventional methods of minimization. Examples of the numerical identification of the elastic properties of the laminated composites from the measured eigenfrequencies of plates are discussed.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998, Riga, Latvia.Institute of Computer Analysis of Structures, Riga Technical University, Riga LV-1058 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 1, pp. 3–16, January–February, 1998.     

Natural and parametric vibrations of a cylindrical shell-filler system with tangential interaction taken into account

Conclusions 1. The spectrum of the eigenfrequencies and dynamical instability regions of a shell-filler system breaks up into two infinite spectra for each mode of wave formation; the first of them is determined by the shear modulus of the filler material, and the second — by the volume deformation modulus. The second spectrum is absent for incompressible fillers.2. It has been shown that taking tangential interactions into account has a strong effect on the arrangement and width of the dynamical instability regions belonging to the first spectrum and hardly changes the arrangement and widths of the regions of the second spectrum.3. As a result of the limiting transition as the frequency of the driving force tends to zero, expressions are obtained from the formulas of this paper for calculating the static stability of a shell with an incompressible filler. The numerical results obtained for this case correspond to results given in the literature.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. P. Stuchki Latvian State University, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 503–509, May–June, 1977.     

One dynamic model of a composite material

A model has been constructed for the propagation of waves orthogonally to the layers or fibers of a composite material and based on the Voltaire equation of state with oscillating kernels. The results of treatment of experimental data are presented.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 2, pp. 364–367, March–April, 1976.     

Evaluating the effect of whiskerization of the fibers of composites on the fundamental frequency of a laminated cylindrical shell

Conclusion The calculations showed that whiskerization of the reinforcement of the structural material of multilaminate shells makes it possible in some cases to increase the fundamental vibration frequency of the structure up to 15–20%. In combination with the well-known [1] effect of improved strength characteristics for a whiskerized composite in the transverse and shear directions, this finding allows us to conclude that whiskerized structural materials are more efficient than ordinary laminated composites in shell-type load-bearing structures. Here, the greatest benefit can be expected in the case of whiskers which have higher elastic moduli than the main reinforcement. Since considerably higher reinforcement intensities can be achieved in whiskerized laminated composites than in composites with a reinforcement characterized by an arbitrary three-dimensional structure, it can be concluded on the basis of the results obtained here that, at least for shells of moderate thickness (10 < R/h 50), whiskerized composites are the optimum structural material for load-bearing shells.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1022–1027, November–December, 1987.     

Strain distribution in composites

The strains in specimens of epoxy-furan resin and rubber simulating the structure of a composite material have been experimentally investigated by the network method. The strains in the components are distributed in accordance with an almost normal Iaw.Gomel's State University. Translated from Mekhanika Polimerov, No. 4, pp. 731–734, July–August, 1974.     

Stress Distribution in an Infinite Elastic Body with a Locally Curved Fiber in a Geometrically Nonlinear Statement

Within the framework of a piecewise homogeneous body model, with the use of three-dimensional geometrically nonlinear exact equations of elasticity theory, a method for determining the stress—strain state in unidirectional fibrous composites with locally curved fibers is developed for the case where the interaction between the fibers is neglected. All the investigations are carried out for an infinite elastic body containing a single locally curved fiber. Numerical results illustrating the effect of geometrical nonlinearity on the distribution of the self-balanced normal and shear stresses acting on the interface and arising as a result of local curving of the fiber are presented.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 433–448, July–August, 2005.     

Thermal stresses in a granular composite of regular structure

The problem is considered of thermal stresses in a composite material which is an elastic isotropic matrix with uniform spherical inclusions placed regularly within it. A solution is presented in the form of series for a system of double-periodic solutions of the equilibrium equation built up in a special way. An infinite set of linear algebraic equations of the normal type is obtained from the boundary conditions. Numerical studies are carried out for the stress distribution at the matrix-grain contact surface, and their nature in relation to the volume content of dispersed phase and geometric structure parameters of the composite is determined.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 90–93, 1988.