Stability of unfigured and stiffened shells made of fibrous composites

Conclusions Within the known generalizations of the theory of thin shells, formulas were obtained for calculating critical loads of unfigured and stiffened cylindrical shells made of fibrous composite materials under an external pressure and axial compression, taking into account not only the longitudinal (compressive) and flexural rigidity, but also the torsional and shear rigidities. From an analysis of the testing results of unfigured shells made of fiber-glass material, the divergence between the calculated and experimental data has been estimated by introducing into the formulas correction functions 0.181 In + 1.32 and a coefficient 0.697. The values of the safety factor were determined, which with a given reliability guarantee the selection of the geometrical parameters of the shells, amounting to (for a 0.95 reliability) 1.244 and 1.45.Paper presented at the Fourth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, October, 1980).Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 640–646, July–August, 1980.     

Numerical solution of problems in the dynamics of ribbed shells of revolution

We consider dynamic processes in shells of revolution reinforced with discrete ribs. The stress—strain state of the shell is determined in the framework of the linear theory of Timoshenko elastic thin shells. The ribs are described using the theory of curvilinear rods. The system of differential equations is solved by applying the variational principle to nonstationary problems.S. I. Subbotin Institute of Geophysics of the Ukrainian Academy of Sciences. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 74, pp. 45–48, 1992;     

Spatial effects in problems on the deformation of cylindrical shells of anisotropic composites

Mechanics of Composite Materials -     

Some problems of the mechanics of polymeric composites

Work on the mechanics of polymer composite materials and structures carried out in the Moscow Power Engineering Institute during the last 5 years is reviewed. The review covers work on the theory of reinforced media and its application to composite sturctures, the theoretical and experimental investigation of the effect of technological factors on the reliability of composite structure, the theory of hardening viscoelastic media, and the mechanical testing of specimens and models of polymer composites.     

Some mathematical problems related to the nonequilibrium statistical mechanics of infinitely many particles

This review article deals with mathematical problems related to the time evolution of systems of infinitely many particles. The probabilistic aspect of the obtained results is emphasized.Translated from Itogi Nauki i Tekhniki. Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 14, pp. 5–39, 1977.     

Some problems of heat conduction in transversally graded composites

The object of considerations is a two-component layer made of conductors non-periodically distributed in the form of laminas along the layer thickness. It is assumed that the distribution of the macroscopic properties of this laminate is approximated by continuous slowly-varying functions across laminas. Media of this kind can be treated as made of a functionally graded material. The aim of the paper is to apply the tolerance model, [8], to analyse one-directional, non-stationary heat conduction along the axis perpendicular to laminas. Moreover, received results are compared to the solutions obtained in the framework of the higher-order theory, [1]. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some statistical problems in random translations of stochastic point processes

A random translation of a marked point process is considered. The distribution of random translation is assumed to be dependent upon the mark through a certain functionh(·). The main concern is to make inferences about the functionh(·) for different types of data. Complete identification and estimation are not possible in general, but some interesting particular solutions are presented.     

Localization of microfailure in fibrous composites

Conclusion When a fibrous composite is loaded, the process of microfailures becomes localized in consequence of the nonuiformity of internal stresses. The degree of localization can be quantitatively characterized by the magnitude of the parameter of localization whose determination was provided in the present work. The dependence of the parameter of localization on the stress applied to the specimen can be measured experimentally from the data on the location of the coordinates of the sources of AE, and it can be calculated theoretically on the basis of the model of failure of the composite. A comparison of the theoretical model with the experimental data makes it possible to determine the magnitude of the overstresses in the fibers of the composite material and the form of the distribution function of these overstresses.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 437–443, May–June, 1989.     

Modern trends in the development of fibrous composites

The two main trends in the development of high-modulus composites are considered. Improved methods of calculation sensitive to the effects associated with the weak shear and transverse characteristics are reviewed. It is shown that the disadvantages of composites with a traditional arrangement of the reinforcement can be overcome. The properties of boron- and carbon-reinforced plastics with a traditional reinforcement structure are described and compared with those of three-dimensionally structured materials with two- or three-strand reinforcing. Whiskerized fiber reinforcement is also considered. A program of further research on high-modulus composites is outlined.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 541–552, May–June, 1972.     

Some problems in finite dams with an application to insurance risk

Summary This paper considers a finite dam in continuous time fed by inputs, with a negative exponential distribution, whose arrival times form a Poisson process; there is a continuous release at unit rate, and overflow is allowed. Various results have been obtained by appropriate limiting methods from an analogous discrete time process, for which it is possible to find some solutions directly by determinantal methods.First the stationary dam content distribution is found. The distribution of the probability of first emptiness is obtained both when overflow is, and is not allowed. This is followed by the probability the overflow before emptiness, which is then applied to determine the exact solution for an insurance risk problem with claims having a negative exponential distribution. The time-dependent content distribution is found, and the analogy with queueing theory is discussed.     

Traveling-wave solutions and their application to inverse problems of sorption dynamics

Translated from Matematicheskie Modeli i Optimizatsiya Vychislitel'nykh Algoritmov, pp. 67–74, 1994.     

Some isoperimetric inequalities and their application to problems on polynomials

We prove sharp inequalities for the product of the Lebesgue integral of certain power of a positive absolutely continuous and nondecreasing function (or a linear combination of such distinct powers) and the Lebesgue integral of the square of its derivative. These inequalities are related to some problems for polynomials having small Mahler measure. As an application, we give a lower bound for the logarithmic height of a noncyclotomic algebraic number in terms of its degree.