Initial imperfections and buckling modes of polymeric cylindrical shells under long-term loading

The problem of buckling of polymeric cylindrical shells under long-term loading is considered. The results of compressive and external-pressure tests on shells [10, 11, 12, 17] are discussed and their carrying capacity is estimated [16]. The buckling problem is solved theoretically on the basis of an investigation of the development of axisymmetric modes and their conversion to nonaxisymmetric modes [15]. The equations of the nonlinear theory of viscoelasticity are used as the physical relations. The theoretical model gives qualitative agreement with the experimental behavior of the shell under load.     

Nonlinear multivariable modeling and stability analysis of vibrations in horizontal drill string

Nowadays, economical extraction of the oil and gas, and their products is an important problem. Up to now, vertical wells have been used for oil extraction but some wells exist that they cannot be reached by using the vertical drilling. Horizontal and directional drillings are some techniques to reach these wells. In this article, dynamics of the horizontal drill string is studied. According to the forces that affect the dynamics of drilling, its longitudinal vibration is analyzed. After determination of the boundary conditions and normal modes of the system with using mode summation method, displacement of the bit is obtained. Finally, dynamics of the horizontal drill string is simulated and the effect of increasing the number of modes and the mode convergence phenomenon is discussed. Through this study, while it is shown that four modes are sufficient for a reliable prediction of the stable and unstable conditions; five modes are included for the system analysis. Then, the effects of other parameters such as the mud frequency and constants of bit/rock interaction model are studied. Through the proposed parametric study, the stability of the system is investigated. Moreover, the dominant modes which cause the instability of the horizontal drilling process are determined.     

Investigation of the initial imperfections and buckling modes of glass-reinforced plastic shells under hydrostatic pressure

The results of testing the stability of glass-reinforced plastic cylindrical shells under hydrostatic pressure are examined. The initial imperfections and deflections of the shells were directly measured. It is found that during loading or in the course of time (under load) the shape of the initial imperfections is transformed. An algorithm (see [11]) based on the approximation of the experimental deflection function by a Fourier series is used to establish the characteristic coefficients of the series important in connection with the elastic loss of stability and progressive buckling of the shell.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1057–1063, November–December, 1971.     

Nonlinear buckling and postbuckling of a shear-deformable anisotropic laminated cylindrical panel under axial compression

The nonlinear buckling and postbuckling of a shear-deformable anisotropic laminated cylindrical panel of finite length is investigated based on a boundary-layer theory for buckling. The layers of the panel are assumed to be linearly elastic. The governing equations are based on Reddy’s higher-order shear deformation theory of shells and include the von Karman-type kinematic nonlinearity and extension/twist, extension/flexure, and flexure/twist couplings. The nonlinear prebuckling deformations and the initial geometric imperfections of the panel are both taken into account. The postbuckling behavior of the panel under axial compression is analyzed. A singular perturbation technique is employed to determine its buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect moderately thick anisotropic laminated cylindrical panels with different geometric parameters and stacking sequences. The new finding reveals that there arises a compressive stress along with an associate shear stress and twisting when a moderately thick anisotropic laminated cylindrical panel is subjected to axial compression.     

The velocities of long waves in composites with interphase imperfections

We develop a model of elastic strain of a composite material with interphase imperfections. In the context of this model we construct a continuous model of first order (theory of effective models) for stratified and unidirectional fibrous compounds. We determine the velocities of propagation of long (compared with the size of the structure) waves in any direction. We exhibit the possible characteristic regularities of the influence of interphase imperfections on the value of the velocities. Bibliography: 6 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 100–105.     

The deflection and buckling of a beam-column with a one-sided constraint

Zusammenfassung Das Problem eines horizontalen, gelenkig gelagerten Stabes mit VertikalkraftQ am Mittelpunkt und mit axialer DurchlastP wird behandelt. Eine Durchbiegung infolgeQ wird jedoch durch eine Bodenebene verhindert. Die gekrümmten Formen des Stabes werden durch die lineare Stabtheorie und durch die Theorie der Elastika bestimmt. Die letztere ergibt eine Vergabelung der Gleichgewichtslagen, die in der linearen Theorie nicht erscheint. Schliesslich wird die Stabilität des geraden Stabes behandelt. Das kinetische Kriterium, das Energiekriterium und das klassische, auf nichttrivialen benachbarten Gleichgewichtslagen sich beziehende Kriterium werden alle in Betracht gezogen. Alle zeigen, dass eine beliebig kleine VertikalkraftQ die kritische DurchlastP um mehr als das Achtfache erhöht. Das heisst,P geht von der Knicklast für den gelenkig gelagerten Stab über auf die Knicklast für den halblangen, einerseits eingebauten Stab. Es wird gezeigt, dass die klassischen Kriterien in diesem Falle irreführend sind. Nicht nur die Grösse vonQ, sondern auch die der erwarteten Störung muss berücksichtigt werden.     

Interaction of elastic waves with a curvilinear crack in a half-plane

We consider the problem of the interaction of monochromatic displacement waves with a curvilinear crack-cut in a half-plane. We find integral representations of the solution. The boundary-value problem is reduced to a system of singular integral equations. A parametric investigation is carried out for the effect of the form of the load, the fastening conditions on the boundary of the half-plane, and the curvature of the crack on the dynamic coefficients of the stress intensity.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 77–82, 1988.     

A contribution to efficient calculation of complex drill string dynamics for deep hole drilling

This paper presents a hybrid model to describe drill string dynamics for deep hole drilling. Generally, a typical rotary drill string has a length of several kilometers, but the diameter is less than half a meter. Due to the large ratio of length to diameter, a drill string is a very flexible system. Consequently, an operating drill string is always affected by axial, torsional and lateral vibrations, which potentially induce serious failures. In order to avoid fatal defects, simulations to forecast vibrations are necessary. The simulation should be capable to exhibit the complex dynamical phenomena, e.g. sick-slip, forward whirl and backward whirl, and interactions between drill string and borehole. Usually, these simulations are very time-consuming. In this work, a hybrid model consisting of lumped masses connected with weightless beam elements representing the drill string is developed. The interaction between the drill string and the borehole is implemented by unilateral constraints to describe the nonlinear contact behavior. It was shown that accuracy and simulating time were improved by this model with respect to classical finite-element models. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Waves in periodic structures with imperfections

The study of wave propagation in structures and media has a significant history which follows from the examination of the dynamics of atomic and molecular lattices. Relatively recently, some of these ideas have been transferred and applied to the dynamic behavior of engineered structures. In particular, structures with periodic and almost periodic topologies and material properties have been extensively studied and important conclusions drawn regarding their energy-transmission properties. The attraction to wave propagation models is due to the efficient nature of the analytical tools available to study how energies of different frequency content are propagated or filtered by the structure. Such properties of a structure are profoundly affected by any imperfections or “near-periodicities”. It has been found that imperfections will have the effect of localizing energies about them, thus not allowing the development of normal modes of vibration as would be observed when assuming a perfect structure. It is envisioned that such understanding will permit the analyst to take advantage of localization effects to isolate locations experiencing loading. Additional applications possibly include the modeling of composite and layered structures and cracks. Also, one expects that structures with periodic boundary conditions will experience some sort of localization of energies in certain frequency ranges.     

Conformal-mapping construction of a difference grid in a region with curvilinear boundaries

Translated from Aktual'nye Voprosy Prikladnoi Matematiki, pp. 88–93, 1989.     

Resonance phenomena in a semi-infinite string with a periodic end

We study the propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in a semi-infinite string under the assumption that the material properties depend p-period-ically on the space variable outside a sufficiently large interval [0, a]. The spectrum of the self-adjoint extension A of the spatial part of the differential operator consists of a finite or countable number of bands and a (possibly empty) discrete set of eigenvalues located in the gaps of the continuous spectrum. We show that resonances of order t or t^½, respectively, occur if either ω² is an eigenvalue of A or (i) ω² is a boundary point of the continuous spectrum of A and (ii) the corresponding time-independent homogeneous problem has a non-trivial solution which is p-periodic or p-semiperiodic for x > a (‘standing wave’).     

The motion of a point mass along a string

An equation for the trajectory of a point mass (a particle) when it moves (slides) in a plane by inertia along a weightless elastic thread (string), stretched between two fixed points is obtained. The time dependence of the trajectory parameter is established. An equation of the trajectory of the particle when it suddenly decelerates is obtained. Forced motion of the particle along a straight string (as a model of the swinging of a lift on an elastic tether in zero gravity) is considered.     

The motion of a point mass along a string

As a supplement to results obtained earlier [1], the general integral of motion of a point mass along a string is determined, and the influence of friction is evaluated.     

Dynamic stability and sensitivity to geometric imperfections of strongly compressed circular cylindrical shells under dynamic axial loads

In the present paper, the dynamic stability of circular cylindrical shells is investigated; the combined effect of compressive static and periodic axial loads is considered. The Sanders–Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differential equations to a set of ordinary differential equations. The dynamic stability is investigated using direct numerical simulation and a dichotomic algorithm to find the instability boundaries as the excitation frequency is varied; the effect of geometric imperfections is investigated in detail. The accuracy of the approach is checked by means of comparisons with the literature.     

Antiplane deformation of an isotropic massif with a curvilinear cavity

We solve the problem of antiplane deformation for an infinite isotropic massif with a curvilinear cavity in which a harmonic shear wave is propagating. The solution of the problem, which is based on the application of the theory of functions of a complex variable, is reduced to finding unknown constants from a system of linear algebraic equations. Numerical results are given for a circular cavity. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 115–119.