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Nonlinear unsteady creep of an ice sheet on a hydraulic foundation. (English. Russian original) Zbl 0921.73152

J. Appl. Math. Mech. 60, No. 4, 677-681 (1996); translation from Prikl. Mat. Mekh. 60, No. 4, 681-686 (1996).
Summary: The problem of the nonlinear unsteady creep of the bending deformation of an ice sheet which partially covers a hydraulic foundation is considered within the framework of the hypothesis of plane sections. In a plan view the sheet is a strip of finite width and length with a single clamped end. This may be shore ice close to the wall of a hydroelectric structure or a plate which has been specially sawn out in an ice sheet for natural experimental investigation. A frequently adopted relationship between the strain, creep and stress which is, to some degree, under the sign of a Volterra-type time operator with a non-difference kernel is used to describe the rheology of the ice. A nonlinear integro-differential equation for the bending moment in a sheet on a hydraulic foundation is obtained which is solved by expansion in a series in a certain small time parameter and, subsequently, numerically along a coordinate by the monotonic sweep method. The deflection of the sheet is also found. Characteristic cases of the change in the bending moment and the deflection along the length of the sheet with time are considered.

MSC:

74Hxx Dynamical problems in solid mechanics
86A40 Glaciology
86A05 Hydrology, hydrography, oceanography
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References:

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