NONLINEAR UNSTEADY CREEP OF AN ICE-SHEET ON A HYDRAULIC FOUNDATION

The problem of the non-linear unsteady creep of the bending deformatio n of an ice sheet which partially covers a hydraulic foundation is con sidered 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 sing le clamped end. This may be shore ice close to the wall of a hydroelec tric structure or a plate which has been specially sawn out in an ice sheet for natural experimental investigation. A frequently adopted rel ationship [1, 2] between the strain, creep and stress which is, to som e degree, under the sign of a Volterra-type time operator with a non-d ifference kernel is used to describe the rheology of the ice. A non-li near integro-differential equation for the bending moment in a sheet o n a hydraulic foundation is obtained which is solved by expansion in a series in a certain small time parameter and, subsequently, numerical ly along a coordinate by the monotonic sweep method. The deflection of the sheet is also found. Characteristic cases of the change in the be nding moment and the deflection along the length of the sheet with tim e are considered. Copyright (C) 1996 EIsevier Science Ltd.