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.     

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.     

Stress-strain state of an ice sheet subjected to a moving load under shallow-water conditions

The following two classes of problems of determining the stress-strain state of an ice sheet under a moving load are considered: determination of the resonant velocity for a load moving over a continuous ice field and calculation of the deflections of an ice field with a bounded ice-free zone subjected to a moving load. The problems are solved in a dynamic formulation. The algorithm of solution is based on the finite-clement method and finite-difference methods. 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 41, No. 4, pp. 206–210, July–August, 2000.     

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.     

Surface wave diffraction at a crack in sheet ice

The time-periodic motions of a liquid layer of finite depth beneath an ice sheet with a straight infinite crack having a periodic dependence on the horizontal coordinate in the direction of the crack are considered. The ice sheet is simulated by a thin elastic plate. It is assumed that the thickness of the plate changes abruptly across the crack. The problems of plane-wave diffraction at a crack, plane-wave diffraction atN cracks in a uniform ice sheet, and plane-wave reflection from a rigid wall are solved. The effect of the pre-existing state of stress of the ice sheet on the properties of the reflected waves is investigated. The condition of nontransmission of fix-frequency waves beneath the edge of the ice is obtained.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 93–102, March–April, 1993.     

Parametric excitation of flexural-gravity edge waves in the fluid beneath an elastic ice sheet with a crack

The properties of elastic-gravity oscillations of deep water beneath a thin elastic plate with a crack are investigated in the paper. The dependence of the reflection and transition coefficients of the waves through the crack on wave frequency and incident angle are found. The shape of the fluid surface deformed by edge waves, propagating along the crack and decreasing exponentially away from the crack, is investigated in the vicinity of the crack. The asymptotic equations describing the parametric excitation of counterpropagating edge waves by flexural-gravity waves which hit the crack at normal incidence are derived.     

The singularity behavior of an interface crack under a dynamic load

The singularity behavior of a crack on the interface of two different media under dynamic load is investigated. By introducing a small region in which the crack faces make frictionless contact and making use of a kind of integral equations with moving boundaries, it is proved that there are only square-root singularities near the interface crack tips in case that a dynamic load acts on it. Numerical results show that the normal stress in the contact region remains negative. The results of the stress intensity factor and the length of the crack face contact region are given to illustrate the dynamic behavior of the interface crack.This work is supported by the National Natural Science Foundation of China.     

Numerical solution of the problem of motion of a load on a cracked ice sheet

A mathematical model is constructed for the motion of a load on a cracked ice sheet. Examples of calculation of ice deflections are given, and the calculation results are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 151–156, May–June, 2008.     

Delayed fracture of a plate made of an orthotropic viscoelastic composite with a central crack under a constant load

Conclusions The results obtained here can also be used for a plate with a central through crack of the normal rupture type when it is subjected to tension by constant fillers and 1) the material of which the plate is composed, having orthotropic viscoelastic strain properties, can be modeled by a uniform orthotropic viscoelastic material; 2) the prefracture region at the edge of an advancing crack in the plate is small in the height direction; 3) the length of the prefracture region is constant during propagation of the crack.Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 11, pp. 77–84, November, 1991.     

Some features of flexural-gravity wave propagation in the presence of a crack in sheet ice

The effect of a crack in an ice sheet on the propagation of surface flexural-gravity waves in a basin of constant depth is analyzed. The ice sheet is simulated by two floating semi-infinite fragments of a thin elastic isotropic plate. As the boundary-contact conditions on the line of contact between the parts of the plate the conditions of continuity of displacements for arbitrary slopes simulating one ice-floe overlying on another and free-edge conditions (crack) are considered. The dependence of the amplitude characteristics of the perturbations on the thickness of the ice, its degree of compression, the incident wave frequency, the depth of the basin, and the form of the boundary-contact conditions is investigated. Problems of wave diffraction on inhomogeneities of an elastic plate were solved in [1, 2], and on a crack in the ice sheet in [3, 4].Sevastopol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 144–150, March–April, 1996.     

Contact interaction between crack edges under a dynamic load

Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Kharlov Automobile and Highway Institute. Translated from Prikladnaya Mekhanika, Vol. 28, No. 7, pp. 3–11, July, 1992.     

Delayed fracture of a transversally isotropic viscoelastic material with a crack under a cyclic load

The delayed fracture of a transversally isotropic viscoelastic material due to slow subcritical growth of a flat circular macrocrack of normal separation under a cyclic load is investigated. The analysis is based on the modified δC of fracture and the hypothesis of the constancy of the prefracture zone. The study is made within the framework of the Boltzmann-Volterra theory for bounded resolvent operators of difference type, which describe the transversal isotropy of the strain properties of the material. To determine the analytic form of the kernel for the irrational function of a linear combination of the above-mentioned integral operators, the method of continued fractions is used. Analytical and numerical calculations are carried out for the bounded resolvent operators of difference type with the kernel in the form of Rabotnov's fractional exponential function. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 1, pp. 123–129, January, 2000.     

Long-term failure of a cylindrically anisotropic viscoelastic material with a crack under a variable load

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 12, pp. 61–68, December, 1994.     

On the elastic-plastic deformation of a sheet containing an edge crack

The solution of the planar tension and bending of an edge-cracked sheet of elastic-plastic material is given when the plastic deformation is represented by a Dugdale model. The analysis assumes conditions of generalized plane stress (for which the model of plastic relaxation is often a suitable one), but the usual transformation of elastic constants may be used to obtain the results also for plane-strain conditions. The method of solution involves the use of a Mellin transform and a Weiner-Hopf technique. Computed results for the size of the plastic zone and the opening at the crack tip are presented, and asymptotic results are obtained for small-scale and large-scale yielding. The results suggest that, when the material is constrained to fracture close to its ultimate tensile stress, the extra severity of a surface flaw compared with a corresponding internal crack is significantly greater than that predicted by linear elastic fracture mechanics.     

Swell wave propagation in an inhomogeneous ice sheet

The propagation of surface waves beneath a periodically inhomogeneous ice sheet is considered. Areas of broken ice and hummock ridges are considered as irregularities. It is shown that waves with frequencies corresponding to wind and swell waves are strongly scattered by the irregularities and are damped exponentially as they propagate beneath the ice.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 162–169, September–October, 1996.