Application of asymptotic methods to the investigation of one-frequency nonlinear oscillations of cylindrical shells interacting with moving fluid

We demonstrate the applicability of the Bogolyubov-Mitropol’skii asymptotic method to the construction of one-frequency solutions of a system of nonlinear equations used to describe the multimode free, forced, and parametrically excited vibrations of cylindrical shells interacting with moving fluid. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 476–487, April, 2007.     

Flexural transient waves in shells of revolution: An asymptotic approach

The transverse asymptotic approximation for flexural waves initiated by edge bending shock loading in thin walled shells of revolution is considered. Methods for solving boundary value problems for this component are constructed with the help of the Laplace transform, the method of expanding the transform in negative powers of the square root from the transform parameter, the saddle point method and other one being utilised. The methods obtained describe solutions for all values of time and tend to the static ones with growth of time.     

Application of asymptotic methods to the investigation of synchrotron radiation properties with regard to betatron oscillations

Dynamics and magnetobremsstrahlung of electrons in periodic magnetic systems with straight sections are considered. Methods to solve the corresponding differential equations with periodic coefficients are proposed. It is shown that the angular characteristics of synchrotron radiation depend on the parameters of the structure of the accelerator magnet.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 2, pp. 285–299, February, 1996.     

An avoidance principle with an application to the asymptotic behaviour of graded local cohomology

We present an avoidance principle for certain graded rings. As an application we fill a gap in the proof of a result of Brodmann, Rohrer and Sazeedeh about the antipolynomiality of the Hilbert–Samuel multiplicity of the graded components of the local cohomology modules of a finitely generated module over a Noetherian homogeneous ring with two-dimensional local base ring.     

An asymptotic expansion for perturbations in the displacement field due to the presence of thin interfaces

We rigorously derive an asymptotic expansion for two-dimensional displacement field associated with thin elastic inclusion having no uniform thickness. Our approach is based on layer potential techniques through integral representation formulas of the fields. We extend these techniques to determine a relationship between traction–displacement measurements and the shape of the thin inclusion.     

An investigation of the asymptotic decomposition method for nonlinear equations in physics

This paper considers an interesting variation of the author's decomposition method, first proposed in 1983, which permits determination of the behavior of the solution of a differential equation as the independent variable approaches infinity. Extensions to partial differential equations are also considered.     

An investigation of the complete post-buckling behavior of axisymmetric spherical shells

Summary The post-buckling behavior of an elastic spherical shell is studied for large axisymmetric deformations. The complete post-buckling path is given for the experimentally confirmed single dimple solution in a load-deformation diagram, making use of the methods of local bifurcation theory, singular perturbation analysis and numerical analysis. From the specific form of the post-buckling path with its predominating unstable part follows the strong imperfection sensitivity of the shell structure.

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Zusammenfassung Es wird das Nachbeulverhalten einer elastischen Kugelschale für große achsensymmetrische Deformationen untersucht. Der gesamte Nachbeulpfad wird für die experimentell bestätigte single dimple Lösung, die eine starke lokale Eindellung darstellt, angegeben, wobei Methoden der lokalen Verzweigungstheorie, der singulären Störungsrechnung und der numerischen Analysis verwendet wurden. Aus der besonderen Form des Nachbeulpfades mit seinem überwiegend instabilen Teil ist die starke Imperfektionsempfindlichkeit dieser Konstruktion deutlich erkennbar.

     

Determination of the thermal stresses in anisotropic shells of revolution

Using the relations of the improved model of layered anisotropic shells based on the straight line assumption taking account of the thermal compression over the thickness we obtain a resolvent system of equations for shells whose properties depend on temperature. We carry out a study of the stresses in a two-layer cylindrical shell formed by winding as a function of the winding angle. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 82–85.     

An optimization procedure for maximizing the energy absorption capability of composite shells

Composite cylindrical shells are being used more extensively for structural applications in both rotary- and fixed-wing aircraft where low weight and high strength are important design issues. This paper addresses the energy absorption capability of such shells, under axial compressive loading. A design optimization procedure is developed to improve the energy absorption by maximizing the buckling and postbuckling characteristics of the shells. The sensitivity of both geometric and material properties is investigated by studying thin-walled shells of several thicknesses, made of different types of orthotropic laminates. Constraints are imposed on the longitudinal, normal, and in-plane shear stresses of each ply by utilizing a failure criteria. Design variables include shell diameter and ply orientations. The optimization is performed using the nonlinear programming method of feasible directions. A two-point exponential approximation is also used to reduce computational effort. Results are presented for Graphite/Epoxy, Glass/Epoxy, and Kevlar/Epoxy composite cylindrical shells with symmetric ply arrangements.     

Effect of cooling regime on the shrinkage stresses in glass-reinforced plastic cylindrical shells

Approximate stepwise cooling of the product is proposed as a means of taking into account the effect of the inelastic properties of the resin at high temperatures on the macroscopic shrinkage stresses in glass-reinforced plastic cylindrical shells.     

An improved closed-form solution to interfacial stresses in rc beams strengthened with a composite plate

The strengthening of concrete structures in situ with externally bonded fiber-reinforced plastic (FRP) composite sheets is increasingly being used for the repair and rehabilitation of existing structures. However, debonding along the FRP-concrete interface can lead to premature failure of the structures. The interfacial stresses have played a significant role in understanding this premature debonding failure of such repaired structures. In this paper, an improved theoretical analysis of the interfacial stresses is presented for a simply supported concrete beam bonded with a FRP plate. The shear strains of the adherends have been included in the present theoretical analysis by assuming a parabolic distribution of shear stress across their thickness. Contrary to some existing studies, the assumption that both adherends have the same curvature is not used in the present investigation. The results of this numerical study are beneficial for understanding the mechanical behavior of material interfaces and for the design of hybrid FRP-reinforced concrete structures.     

Multiscale hygroviscoelastic approach to predicting the internal stresses in composite materials

A self-consistent approach is used to estimate the internal stresses induced by moisture absorption in composite materials with a viscoelastic matrix and linear elastic fibers. A strong influence of the behavior of the viscoelastic matrix and humidity on the internal stresses in the structures at macroscopic and local scales is found to exist.