INRODUCTION TO THE ‘FLOE’ MATLAB PROGRAM

 

The 'FLOE' Matlab program will calculate horizontal and vertical global loads on a conical structure that are caused by semi-infinite ice sheet of constant thickness using Plastic Limit State Analysis which has been proposed by Ralston (1977).

Despite some restrictions, Ralston’s technique is favored by most design codes.

He considered the failure of an advancing ice sheet against a conical structure and used 3-D plate theory instead of simple beam bending theory. In order to compute the forces, Plastic Limit State was employed where the work done by external forces is equated to the rate of energy dissipation. The horizontal and vertical forces HF and VF, respectively, exerted by ice failing in bending can be determined by the equations:

 

 

 

(1)

 

 

 

 

(2)

 

 

 

(3)

 

 

 

(4)

 

 

where

 

HFI is the ice force due to icebreaking.

HFC is the ice force due to clearance.

HF is the total Horizontal force.

VF is the total Vertical force.

r w is density of sea water.

s f is the flexure strength of ice.

D is the waterline diameter of the structure,

DT- is the top diameter of the structure (throat).

T is the thickness of ice.

s f is the friction coefficient for ice and structure.

A1, A2, A3, A4, B1 and B2 are coefficients.

 

Normally, Ralston’s technique requires a number of these coefficients to be determined from graphs; these are functions of complete elliptic integrals of the first and second kind. The program calculates the integrals using series of approximations. Ralston’s method also requires the solution of a complex equation, the roots of which are calculated using secant method (available from most texts on numerical methods).

 

Ralston reports reasonably good agreement between his predictions of load and the results of model tests of upward breaking cones, due to Afanasev, Dolgopolov and Shrainstein (1971) and Edwards and Croasdale (1976).

  

INPUT

 

The following input parameters are required for the structure:

 

 

OUTPUT

 

An output option includes the constant A1 through B1 used for analysis (see above). The principal output parameters include the horizontal loads (both icebreaking and clearing components) and vertical loads.

 

 

 

GETTING STARTED

First, copy the FLOE directory to on of your disk. Then you have to set path for the program. Follow by instructions as shown below:

1) Go to File/Set Path in MATLAB Command Window Panel

 

 

 

 

 

 

  2) Press button to choose the path to folder Floe, which you have already copied to you PC or network disk

3) Now, choose you local or network drive where Floe folder is. Then press

 

 

 

 

 

 

 

 

 

 

  

 

4) For example Floe folder is on E:\ drive, you choose E:\ drive, then single click on Floe icon, then press

 

 

 

 

 

 

 

 

5) After you chose path to Floe folder, press button in MATLAB Path Window

 

 

 

 

 

 

 6) Now we can start program. Launch MATLAB 5.0 program and type ‘Start’

7) The first window will appear. Just enter how many computations you want to have. For example if you want to calculate ice loads for five different angles 20, 30, 45, 60,70 degree, you should enter 5. Then press to continue.

8) Now you are in other window. Here you ca n change cone angle and cone waterline diameter. Then press to find ice forces or to return to the previous window.

 

 

 

9) In the main working window of Matlab program you will find calculated forces. Write them down, you can need it to draw a graph. By default, ice flexural strength is equal to 900 kN/m2, friction coefficient – 0,2, ice thickness –2 m, cone freeboard – 6 m and unit weight of sea water – 10.06 kN/m3 They can be changed in the latest version of this program.

 

 

10) You can use data to make drawings. Here are Cone angle vs. Ice force (horizontal and vertical) and Cone top diameter vs. Ice force graphs as example.

 

11) To start program again just type ‘start’ again in main working window of MATLAB program.