Mechanics of composite materials with distorted structure (review). continuum theory,fiber composites

Conclusions Investigations of the mechanics of composite materials with structural distortion within the framework of the continuum approach and within the framework of the model of a piecewise-homogeneous body for fibrous composite materials have been reviewed in the present work. On the basis of this review, these investigations must be regarded as in their early stages, In our view, the next stages in this work are to investigate the characteristic static and dynamic problems within the framework of continuum theory [10, 21, 23] and to investigate the stress-strain state in fibrous composite materials with structural distortion taking account of the mutual influence of the fibers.Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaidzhan SSR, Baku. Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No, 5, pp. 3–20, May, 1991.     

Study of thermoviscoelastoplastic processes in the deformation of structural elements

This article surveys a number of studies made at the S.P. Timoshenko Institute of Mechanics on the effect of the history of thermoviscoelastoplastic loading of certain structural elements on their elastoplastic stress-strain state. Paper presented at the General Meeting of the Mechanics Division of the National Academy of Sciences of Ukraine (Kiev, November 30, 1998). S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 3–12, September, 1999.     

Natural vibration of a rectangular plate of composite material with periodically bent structures

The natural vibration of a thin rectangular plate made of a composite material with periodically bent structures is studied. The problem is examined by the finite-element method using the variation principle. The effect of the bending parameters on the natural frequency of the plate is analyzed using the numerical results obtained. Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 68–73, October, 1999.     

Continuum theory in the mechanics of composite materials with small-scale structural distortion

Conclusions In the present work, the continuum theory proposed in [3, 5] has been developed for composite materials with small-scale structures of arbitrary spatial distortion, in the case of both periodic and local distortion. A general method is proposed for the solution of linear problems in the given continuum theory in any approximation, on the basis of the small-parameter method. An example admitting of accurate solution for any form of plane structural distortion of the given composite material is investigated, illustrating the influence of distortion. The accurate solution obtained may serve as a standard solution for problems within the framework of the given theory.Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaidzhan SSR, Baku. Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 2, pp. 3–13, February, 1991.     

Extension of the microstructural theory of two-phase mixtures to composite materials

Studies in the microstructural theory of two-phase elastic, viscoelastic, and piezoelastic mixtures are analyzed with reference to composite materials. It is confirmed that an integral part of the studies in this subject area has been carried out at the S.P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 33–64, May, 2000.     

Natural vibrations of a conical orthotropic shell with small curvatures of the generatrix

The Ostrogradskii-Hamilton principle is used with the variational-difference approach to solving eigenvalue problems as the basis for analyzing the influence of small distortions of the generatrix on the natural frequencies of vibration of free conical shells and conical shells precompressed in the axial direction. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 64–68, March 1999.     

Solution of problems involving the stress state of composite materials with curved layers in the geometrically nonlinear statement

Mechanics Institute, Academy of Sciences of the Ukraine, Kiev. Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaijan Republic, Baku. Translated from Prikladnaya Mekhanika, Vol. 28, No. 6, pp. 3–8, June, 1992.     

Vibrations of shallow shells that are circular in plan and have local supports

The paper deals with vibrations of doubly curved shallow shells that are circular in plan and are reinforced by local rod-type supporting elements or cylindrical shells. The coefficients of the frequency equation are found by using numerical-analytical methods to solve boundary-value problems for fixed values of frequency. The natural frequencies and modes of vibration of a system composed of a shell and elastic supports are determined in the course of solving the problem. It is shown that it is possible to also account for reactive moments and shearing forces, in addition to the normal reactions of an elastic support. The potential of the approach which is developed is illustrated by the solution of specific problems. Special Design Office of the S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 69–75, March, 1999.     

Stability of two noncircular cylinders in an elastic matrix with small subcritical strains

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaidzhan SSR. Baku. Translated from Prikladnaya Mekhanika, Vol. 25, No. 11, pp. 3–9, November, 1989.     

Mechanics of composite materials with curved structures (survey). Composite laminates

Institute of Mathematics and Mechanics of the Academy of Sciences of the Azerbaidzhan SSR, Baku. Institute of Mechanics of the Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 6, pp. 3–22, June, 1991.     

Applied model of the deformation of nonlinearly viscoelastic vibration insulators subject to cyclic deformation

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Institute of Geotechnical Mechanics, National Academy of Sciences of Ukraine, Dnepropetrovsk. Translated from Prikladnaya Mekhanika, Vol. 30, No. 9, pp. 63–68, September, 1994.     

Three-dimensional problems of mechanics of deformable bodies of noncanonical shape

The paper is based on the author's report at the General Jubilee Meeting of the Mechanics Division on the occasion of the 80th anniversary of the National Academy of Sciences of Ukraine. Results obtained in the subject area “mechanics of deformable bodies of noncanonical shape” are discussed. This subject area was formed at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine on the basis of variants of the analytical method of boundary-shape perturbation proposed and developed at the Institute. The objects of investigation and the classification of three-dimensional boundary-value problems for noncanonical areas are analyzed. Tests of the accuracy of approximate solutions obtained using the developed analytical methods are indicated. Presented at General Meeting of Mechanics Division of National Academy of Sciences of Ukraine (Kiev, November 30, 1998). S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 3–20, October, 1999.     

Experimental investigation of the dynamics of shells of revolution (review)

The results of experimental investigations carried out at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine are analyzed in this review. The analysis suggests that experimental investigations of shell dynamics must be contained and developed if the method used to calculate the stressed-strained state and stability of dynamically loaded shells is to be developed further and made more precise. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, 35, No. 7, pp. 3–11, March, 1999.     

Development of analytical methods in three-dimensional problems of the statics of anisotropic bodies (Review)

The main results of scientific research carried out at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine in the field of three-dimensional problems of the statics of anisotropic bodies are stated in a systematic form. The results include the structural method of constructing the exact analytical solutions of equations of the elastic and thermoelastic equilibrium of rectilinearly orthotropic bodies and approximate analytical methods of solving three-dimensional boundary-value problems for curvilinearly orthotropic bodies of canonical and noncanonical form. Results of solution of specific boundary-value problems for orthotropic and transversally isotropic bodies are analyzed. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 3–38, February, 2000.     

Longitudinal nonlinear oscillations of a gas in a closed pipe

Results of an experimental study of longitudinal nonlinear oscillations of a gas in a closed pipe are reported. Pressure waves in a broad range of excitation amplitudes and frequencies are studied. Strong nonlinear oscillations at a frequency thrice as low as the first natural frequency of the gas column are discovered. Institute of Mechanics and Mechanical Engineering, Kazan' Scientific Center, Russian Academy of Sciences, Kazan' 420503. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 60–62, November–December, 1999.     

Calculation of the plane vibration and vibrational heating of plates of variable thicknesses

Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Institute of Electric Welding, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 5, pp. 64–69, May, 1992.     

On the relations governing rayleigh wave propagation in bodies with initial stresses

Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Institute of Electrowelding, Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 11, pp. 47–52, November, 1993.     

Use of rayleigh waves for investigating nonlinear elastic properties of surface layers of structural materials

Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Institute of Electric Welding, Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 7, pp. 33–37, July, 1992.     

Several results and real problems in the theory of periodic motions and nonlinear mechanics (review)

Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev. Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 3, pp. 3–14, March, 1988.     

Refined theory of flexible laminar orthotropic shells

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Institute of Computational Mathematics. Academy of Sciences of the Georgian SSR, Tbilisi. Translated from Prikladnaya Mekhanika, Vol. 25, No. 8, pp. 44–52, August, 1989.