Stress-deformed state of a semi-infinite ice sheet under the action of a moving load

Komsomol'sk on Don. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fiziki, No. 5, pp. 112–117, September–October, 1994.     

Numerical solution of the problem of an ice sheet under a moving load

A method for analyzing the bending of an ice sheet subjected to a moving load is proposed. The problem is solved in a dynamic formulation. The algorithm of solution is based on the finiteelement method and the finite-difference method. The method proposed allows one to determine the stress-strain state of an ice sheet for any law of motion of a load over ice. Two versions of initial conditions are considered. Examples of calculations are given. Komsomol’sk-on-Amur State Technical University, Komsomol’sk-on-Amur 681013. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 243–248, July–August, 1999.     

Oscillations of an ice sheet under a periodically varying load

Translated from Prikiadnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 141–146, September–October, 1992.     

Vibrations of an ice sheet with crack under a time-periodic load

The analytic solution of the problem of vibrations of an ice sheet with a rectilinear crack floating on the surface of an ideal incompressible fluid of shallow depth under the action of a local zone of the time-periodic pressure is obtained. The ice sheet is simulated by two thin viscoelastic semiinfinite plates of different thickness. Various conditions on the crack edges are considered. Far field asymptotics are investigated and it is revealed that the predominant directions of wave propagation at an angle to the crack can be distinguished in the far field in the case of contact of two plates of different thickness. In the case of contact of identical plates, a waveguide mode propagating along the crack is excited. It is shown that the waveguide mode is the same for the plates with the free edges and the free overlap since the part of the solution symmetric about the crack is the same while the difference between the solutions is caused by the antisymmetric part of the solution.     

Stress-strain state of a half-space in the neighborhood of a stiff sphere subjected to a normal load

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Institute of Ultrahard Materials, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 4, pp. 19–25, April, 1988.     

Effect of the viscosity properties of ICE on the deflection of an ICE sheet subjected to a moving load

Steady-state rectilinear motion of a load on an ice sheet modeled by a viscoelastic plate is considered. The viscoelastic properties of ice are described using the linear Maxwell and Kelvin-Voigt models and a generalized Maxwell-Kelvin model. Calculated vertical displacements and strains of the ice plate are compared with available experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 147–157, May–June, 2009.     

FRP约束混凝土快速荷载下应力应变关系初探

在四种不同约束比下FRP(fiberreinforcesplastic)约束混凝土柱静力性能试验的基础上,选定一种约束比,进行了FRP约束混凝土柱在三种应变速率下的快速加载试验,研究其在快速荷载下的力学行为。结果表明,FRP约束混凝土在快速荷载作用下,其强度与极限应变随应变速率的增加而增大并与对数应变速率成较好的线性关系,其应变速率敏感性远高于无约束混凝土,且应力应变关系曲线大致呈一条平滑曲线。根据试验结果拟合了FRP约束混凝土在快速荷载下强度与极限应变的经验公式,并对其应力应变关系进行了初步探索。     

Stress waves in a rod subjected to a moving load

The wave processes in a semi-infinite rod located in an elastic medium and subjected to a point load moving at a constant velocity are considered. The system of two differential equations of motion of Timoshenko beam theory is solved using the Laplace transform in time. The integrals obtained are determined numerically. Variation of the bending moment on the longitudinal coordinate behind the elastic-wave front and the region of action of the point force at various times is shown. The results of the solution are influence functions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 112–122, March–April, 2007.     

Stress-strain state of a parabolic shell of revolution subjected to external magnetic pressure

The paper investigates the stress-strain state of an axisymmetrically loaded shell which arises when a strong electric current flows in it. The shell with current is an element of a system intended for focusing π and K mesons in neutron experiments. The problem is solved by numerical integration on a computer of equations of the theory of shells by the two-sided matrix run-through method, and also by an approximate analytical solution. The algorithm being applied can be used to calculate an arbitrary shell of revolution of variable thickness. The results thus obtained are discussed.     

A half-space saturated poro-elastic medium subjected to a moving point load

In this paper, an analytical solution for the dynamic response of a half-space porous medium subjected to a moving point load is derived. In the model, the displacements of the solid skeleton and the pore pressure are expressed in terms of two scalar potentials and one vectorial potential. Based on Biot’s theory, the frequency domain Holmholtz equations for the potentials are derived through the Fourier transformation with respect to time. The general solutions for the potentials are derived through the Fourier transformation with respect to the horizontal coordinates. Numerical results suggest that moving loads have very complicated effects on the dynamic response of the porous medium. Generally speaking, a moving load with a high speed will generate a larger response in the porous medium than a static or a lower speed load.     

The axially stressed LIM reaction rail subjected to a moving load

A recently developed high speed test track for the Linear Induction Motor (LIM) Vehicle at Pueblo, Colorado consists of a welded railroad track supplemented by a continuous reaction rail. Due to constrained thermal expansions, high axial compressive forces may occur in this rail. Since the reaction rail is a relatively slender plate, high axial forces may affect its lateral stability and dynamic characteristics. In this paper the stability of the reaction rail due to axial compressive force is studied first. Following this, the effect of axial forces upon the critical velocity of a moving lateral load is studied.Included in the analysis are representations of the rail, both as an isotropic and orthotropic entity. The moving lateral load applied to the rail is assumed to be a concentrated force, acting first at the top of the reaction rail, and then at two arbitrary points.     

The stress state of a plate subjected to a piecewise homogeneous load

We consider the stress-strain state of a plate having a doubly connected domain S bounded from the outside by a circle of radius R and from the inside by an ellipse with two rectilinear cuts. The cuts lie symmetrically on the x-axis. The plate is subjected to various forces: the hole contour (the ellipse) is under the action of uniformly distributed forces of intensity q, and the cut shores are free of loads; at the points ±ib of the imaginary axis, the plate is under the action of a lumped force P.The solution of the problem is reduced to determining two analytic functions φ(z) and ψ(z) satisfying certain boundary conditions (depending on the type of the acting loads).We use the Kolosov-Muskhelishvili method to reduce the problem to a system of linear algebraic equations for the coefficients in the expansions of the functions φ(z) and ψ(z). The solution thus obtained is illustrated by numerical examples.     

On dynamics and stability of continuous systems subjected to a distributed moving load

Summary The paper deals with an analysis of different models of continuous systems subjected to a load distributed over a given length and moving at a constant velocity.The general discussion concerns a beam resting on a viscoelastic semi-space. The motion of the body is described by polynomial differential operators. With body forces being disregarded, the motion of the beam lying on a viscoelastic foundation is discussed with either taking into account the effect of shear deflection and the inertia of rotation or with neglecting them. Consideration is also given to the cases of relative motion of two continuous systems and the stability of their interaction. The above cases represent the models of a number of mechanical systems applied in e.g. modern transportation facilities, technology of bonding of layer materials, etc.The analysis is substantially simplified because the equations of motion and the boundary conditions are written in a moving coordinate system related with the load and only stationary solutions are considered. With such an approach, the solutions depend only on the transformed space variable, while the velocity of the load appears as one of the parameters of the system. Interesting conclusions are drawn from the obtained solutions and numerical calculations.

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Zur Dynamik und Stabilität von kontinuierlichen Systemen unter verteilten bewegten Lasten

Übersicht Der vorliegende Beitrag behandelt die Analyse von kontinuierlichen Systemen, die verteilten bewegten Lasten ausgesetzt sind. Es wird zunächst ein Balken auf viskoelastischem Halbraum behandelt. Die Bewegung des Körpers wird beschrieben durch Differentialoperatoren in Polynomform, wobei der Einfluß von Schubverformung und Drehträgheit diskutiert wird. Der Fall der Relativbewegung von zwei kontinuierlichen Systemen und ihre Stabilität wird ebenfalls diskutiert. Die untersuchten Fälle stellen Modelle zahlreicher mechanischer Systeme dar, wie zum Beispiel moderne Schnelltransportsysteme, Fügevorrichtungen von Schichtmaterialien, usw.Die Analyse der Probleme wird wesentlich dadurch vereinfacht, daß die Bewegungsgleichungen und Randbedingungen in einem mitbewegten Koordinatensystem formuliert werden und nur stationäre Lösungen betrachtet werden. Auf diese Weise hängen die Lösungen nur von der transformierten Ortsvariablen ab; die Geschwindigkeit der Belastung tritt als ein Parameter des Systems auf.Aufschlußreiche Schlußfolgerungen werden anhand der erhaltenen Lösungen und numerischen Berechnungen dargestellt.

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This paper was presented at the Second Symposium on Inelastic Solids and Structures, Bad Honnef, September 1981     

Stress-strain state of an inclined elliptical defect in a plate under biaxial loading

A mathematical model for the stress-strain state of a plate with an inclined elliptical defect under biaxial loading is considered. Exact formulas for stresses in polar coordinates, displacements, principal stresses, maximum shear stress, and stress intensity in the case of a plane stress state of the plate were obtained by the Kolosov-Muskhelishvili method. Simulation results are compared with experimental data obtained by holographic interferometry.     

Stress-strain state of ice cover during aircraft takeoff and landing

We consider the linear unsteady motion of an IL-76TD aircraft on ice. Water is treated as an ideal incompressible liquid, and the liquid motion is considered potential. Ice cover is modeled by an initially unstressed uniform isotropic elastic plate, and the load exerted by the aircraft on the ice cover with consideration of the wing lift is modeled by regions of distributed pressure of variable intensity, arranged under the aircraft landing gear. The effect of the thickness and elastic modulus of the ice plate, takeoff and landing regimes on stress-strain state of the ice cover used as a runway.     

Steady state and stability of a beam on a damped tensionless foundation under a moving load

In the first part of this paper we study the effect of damping on the multiple steady state deformations of an infinite beam resting on a tensionless foundation and under a point load moving with a sub-critical speed. Due to the non-linear characteristics of the problem, a guess on the deformed shape has to be made before a numerical search can be initiated. It is found that when the damping is present, all the steady state solutions are asymmetric. As the damping approaches zero, some of the steady state solutions become symmetric, while some others remain asymmetric. In the second part of the paper we propose to test the stability of these steady state deformations by a transient analysis on a long finite beam. Our numerical experiment indicates that among all these multiple steady state solutions only one of them is stable. This stable steady state deformation reduces to a symmetric solution when the damping approaches zero. Furthermore, it is found that this stable solution is also the one among all steady state solutions closest in shape to the linear solution based on a bilateral foundation model.     

Mode II stress intensity factors for a crack parallel to the surface of an elastic half-space subjected to a moving point load

The direction of propagation of rolling contact fatigue cracks is observed to depend upon the direction of motion of the load. In this paper approximate calculations are described of the variation of Mode II stress intensity factors at each tip of a subsurface crack, which lies parallel to the surface of an elastic half-space, due to a load moving over the surface. In particular the effect of frictional locking of the crack faces under the load is investigated. In consequence of frictional locking the range of SIF at the trailing tip ΔK_T is found to be about 30% greater than that of the leading tip ΔK_L, which is consistent with observations that subsurface cracks propagate predominantly in the direction of motion of the load over the surface. The effects on k_t and k_lof crack length, crack face friction, traction forces at the surface and residual shear stresses are also investigated.     

Reaction of an anisotropic cylindrical shell to a moving load

A method is proposed to determine the stress-strain state of inhomogeneous anisotropic viscoelastic cylindrical shells subject to a load moving along the circumference with a given velocity. The effect of localization of the load on the dynamic stress and displacement amplification factors is examined for cylinders of different lengths __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 80–88, April 2007.