2   5  7   11     16   21
    - --- -- ---- ----- ----- -----
   |X|   |  |LE2D|    3|   12|11112|
    - --- -- ---- ----- ----- -----
       |  |   |     |     |     |
       |  |   |     |     |     |
       |  |   |     |     |     |
       |  |   |     |     |     |_(3) Warning flags and Symmetry forcing (I5)
       |  |   |     |     |           (Default = all warnings issued)
       |  |   |     |     |
       |  |   |     |     |_(2) Number of X/H/V values (I5) 
       |  |   |     |           (Default = 12, Maximum = 40 or 600 divided by (1), whichever is less)
       |  |   |     |
       |  |   |     |_(1) Number of Z coordinates (I5)
       |  |   |           (Default = 5, Maximum = 20 or 600 divided by (2), whichever is less)
       |  |   |
       |  |   |_Compulsory Data Record Keyword (A4)
       |  |
       |  |_Optional User Identifier (A2)
       |
       |_Compulsory END on last data record in Data Category (A3)

(1) The number of values of Z to be input on the ZRNG data record and hence the number of values on each XRNG, HRNG and VRNG data records.

(2) The number of values XRNG, HRNG and VRNG data records making up the load extension curves. This data record together with (1) form a database which is represented by a matrix of values, e.g. for the default size of the database Z(5), X(12,5), H(12,5), V(12,5) would be created.

(Further details may be found in The 2 Dimensional Load Extension Characteristics.)

(3) This parameter indicates whether warnings should be issued when the position of the attachment point of the mooring line relative to the anchor point is outside of the range specified in the ZNRG and XRNG data records. In addition, warnings about the degree of symmetry of the resulting stiffness matrix can also be issued, omitted or the matrix can be forced to be symmetrical. This is explained further below.

The parameter should be thought of as five separate flags which indicate the following:

If flag 1 = 0 or is blank, Warnings are issued when the X position exceeds the range specified

If flag 2 = 0 or is blank, Warnings are issued when the X position is below the range specified

If flag 3 = 0 or is blank, Warnings are issued when the Z position exceeds the range specified

If flag 4 = 0 or is blank, Warnings are issued when the Z position is below the range specified

If flag 5 = 0 or is blank, Warnings are issued when the degree of asymmetry of the stiffness matrix formed from the database is considered unacceptable.

If any flag value is non-zero then warnings are not issued for that flag’s conditions.

For the stiffness asymmetry, if the value is greater than unity, symmetry of the stiffness matrix will be imposed. Clearly in this case no warning asymmetry warning message will be issued. Note that in time history programs (Aqwa-Naut/Drift) the stiffness matrix is not used except for output of information to the user.

Stiffness Matrix Asymmetry

The stiffness matrix which can be formed from the 2-D load/extension is evaluated as follows:

           K =  DH         DH
                --    0    --
                DX         DZ
                      H
                0     -     0
                      X
                DV         DV
                --    0    --
                DX         DZ

where

H = the horizontal force

V = the vertical force

D/DX, D/DZ = differential operators

The values of DH/DZ and DV/DX for a completely elastic mooring line must be equal. It is the responsibility of the user to input values of z, x, H and V which obey this condition. Failure to do so will result in a mooring system which will generate or absorb energy - impossible for a real mooring system.