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Abstract
Deflection of a free, thin, square, elastic, pointloaded ice sheet is studied. A threedimensional, combined finite elementdiscrete element method (FEMDEM) is applied. Examined is a set of square, selfsimilar (plan view) ice sheet samples with the side lengths of L=20, 40, 80, and 160 m; thicknesses of h=0.5, 1.0, and 1.5 m; and the average discrete element sizes of l=2h and 3h. The samples are generated and meshed via a centroidal Voronoi tessellation procedure. Each mesh is unstructured and consists of convex polyhedra as the discrete elements and a Delaunaytriangulated, inplane beam lattice of corotational, viscously damped Timoshenko beam finite elements. Two load cases are considered: a sheet sample subjected to i) a vertical, centrally applied point load; and ii) a vertical point load on an edge. In both load cases, a good agreement is found between the deflections computed with the FEMDEM approach and with FEM. Maximum, nondimensionalized deflections w¯_{max} (w¯_{max}=q/F_{z}, where q=q(w_{max}) is an approximate, resultant reaction force due to the buoyancy, w_{max} the computed maximum deflection, and F_{z} the applied point load) scale, in each load case, either by a powerlaw, w¯_{max}∝h^{m1(L)}, or exponentially, w¯_{max}∝10^{m2(h)L}, depending on whether computed over h (for each L) or vice versa. The exponents m_{1} and m_{2} are not constants, but functions of L and h, respectively, and approximately equal in either load case. Inplane size estimates are sought for an FEMDEM sheet sample to represent either a) an infinite, elastic, pointloaded ice sheet; or b) a semiinfinite, elastic, pointloaded (with the load on the free edge) ice sheet with a free edge. A free, square, pointloaded FEMDEM sheet sample well approximates both a) and b), if L/2>≈5l_{ch}, where l_{ch} denotes a characteristic length.
Original language  English 

Article number  102644 
Number of pages  31 
Journal  Marine Structures 
Volume  68 
Early online date  19 Aug 2019 
DOIs  
Publication status  Published  Nov 2019 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Beam lattice network
 Centroidal Voronoi tessellation
 Finite elementdiscrete element method
 Ice
 Plate on a Winkler foundation
 Size effect
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Projects
 2 Finished

ICESCALE: Scaling of Ice Strength: Measurements and Modeling
Kantola, K., Forsström, A. & Polojärvi, A.
03/11/2015 → 31/12/2018
Project: Business Finland: Other research funding

ARAJÄÄ: Arktisten rakenteiden jääkuormat: mallikokeista teollisuuden mittakaavaan (ARAJÄÄ)
El Gharamti, I., Forsström, A., Taimuri, G., Kulovesi, J., Polojärvi, A. & Lemström, I.
01/09/2015 → 31/03/2019
Project: Business Finland: Other research funding