Dynamic Uplift Scenarios for Floating Ice

Abstract

Three uplift scenarios in the forced dynamics of floating ice are studied. Linear, quadratic, and square-root uplift forcing functions are considered and the associated uplift displacement functions are computed numerically. In each case, the uplift forcing is known and the displacement at the point of forcing is unknown. This is the so-called “direct” problem. In essence, this study is aimed at learning more about the “indirect” or inverse problem, where the uplift displacement function is known and the forcing is unknown. A model problem, that is able to be solved in closed form for each of the three forcing functions considered, is used to verify the numerical calculations. By curve fitting the relative error between the model problem and the actual uplift problem, a general modus operandi is arrived at for deriving approximate expressions for the otherwise intractable uplift displacement. These approximate expressions satisfy the required initial conditions and are shown to be accurate.