11. Wave Frequency Dependent Parameters and Stiffness Matrix WFS* (Data Category 7)
11.3. Hydrostatic Stiffness
11.3.1. The LSTF Data Record - Linear Hydrostatic Stiffness Matrix 11.3.2. The ASTF Data Record - Additional Hydrostatic Stiffness Matrix 11.3.3. The BFEQ Data Record - Buoyancy Force at Equilibrium
11.3.4. The GMXX/GMYY Data Record - User-Specified Metacentric Height
11.3.1. The LSTF Data Record - Linear Hydrostatic Stiffness Matrix
These data records may be used to input a linear hydrostatic stiffness matrix. If the matrix has been read from the backing file, the LSTF data record will replace (i.e. overwrite) the existing values within that matrix. If you wish to add TO the existing values, use the ASTF data record (The ASTF Data Record - Additional Hydrostatic Stiffness Matrix (p. 83)).
Note
• LSTF data records must be used to define the whole hydrostatic stiffness matrix for a particular structure. If any LSTF data records are used, undefined rows will be re-set to zero.
• The Z coordinate of the center of gravity and the buoyancy force at equilibrium must always be defined when using LSTF data records to specify the stiffness matrix.
See the notes at the end of this section about the effects of the LSTF data record on the calculations.
2 5 7 11 16 21 31 41 - --- -- ---- --- --- --- --- --- |X| | |LSTF|XXXXX| | | | ... - --- -- ---- --- --- --- --- --- | | | | | | | | | | | |--- | | | | | | | | | |_(2)-(7)6 Stiffness Values
| | | | (6E10.0)(Units for freedoms | | | | 1-3 = force/length, | | | | 4-6 = force*length/RADIAN) | | | |
| | | |_(1)Row Number of Stiffness Matrix(I5) | | |
| | |_Compulsory Data Record Keyword(A4) | |
| |_Optional User Identifier(A2) |
|_Compulsory END on Last data record in data category(A3)
(1) This number indicates which row of the stiffness matrix the values input in columns 21-80 relate to.
(2)-(7) These are the values which replace the row (1) in the hydrostatic stiffness matrix.
Note
• Stiffness related forces acting on the structure
Wave Frequency Dependent Parameters and Stiffness Matrix - WFS* (Data Category 7)
The linear hydrostatic stiffness matrix relates to the hydrostatic forces contributing to the equations of static equilibrium of a structure. Specifically, the net linear hydrostatic forces F(s), acting at the center of gravity of a structure, when the structure is at an arbitrary position X, is given by:
F(s) = K ( X(e) - X ) + B(e)
where
K = stiffness matrix
X(e) = equilibrium position
B(e) = buoyancy force at equilibrium
At equilibrium, all forces act in the Z direction of the Fixed Reference Axis (FRA), where X(e)=X, and B(e) = F(s). Thus, the Z coordinate of the center of gravity and the buoyancy force at equilibrium must always be defined, when using the LSTF data record to specify the stiffness matrix, in order to fully describe the hydrostatic forces acting on the structure. These parameters must be input using the ZCGE and BFEQ data records which are described in The ZCGE Data Record - Z Coordinate of the Center of Gravity at Equilibrium (p. 85)
and The BFEQ Data Record - Buoyancy Force at Equilibrium (p. 84).
• Effect of the LSTF data record when running Aqwa-Line
Normally Aqwa-Line calculates the hydrostatic stiffness matrix from the element description in Data Category 2. Input of 1 or more LSTF data records indicates that this calculation is to be omitted for the specified structure, and the hydrostatic stiffness matrix will use the specified values. Data Records must be used in sets of 6 to define the full hydrostatic stiffness matrix; undefined values will default to zero.
The hydrostatic stiffness matrix is used in the calculation of the 2nd order drift coefficients. For this purpose it should only represent the hydrostatic stiffness of the outer wetted hull itself; LSTF should not be increased to add in the effect of (e.g.) moorings.
11.3.2. The ASTF Data Record - Additional Hydrostatic Stiffness Matrix
The ASTF data record may be used to add TO the existing values within the hydrostatic stiffness matrix.Note
If the analysis includes stage 2 any additional stiffness already in the database will be re-set to zero and must be re-defined.
See the notes at the end of this section about the effects of this data record when using different pro- grams. 2 5 7 11 16 21 31 41 - --- -- ---- --- --- --- --- --- |X| | |ASTF|XXXXX| | | | ... - --- -- ---- --- --- --- --- --- | | | | | | | | | | | |--- Hydrostatic Stiffness
| | | | |
| | | | |_(2)-(7)6 Stiffness Values
| | | | (6E10.0)(Units for freedoms | | | | 1-3 = force/length, | | | | 4-6 = force*length/RADIAN) | | | |
| | | |_(1)Row Number of Stiffness Matrix(I5) | | |
| | |_Compulsory Data Record Keyword(A4) | |
| |_Optional User Identifier(A2) |
|_Compulsory END on Last data record in data category(A3)
(1) This number indicates which row of the stiffness matrix the values input in columns 21-80 relate to.
(2)-(7) These are the values which add TO the row (1) in the hydrostatic stiffness matrix.
• Stiffness related forces acting on the structure
The linear stiffness matrix relates to the hydrostatic forces contributing to the equations of static equilibrium of a structure. Specifically, the net linear hydrostatic forces F(s), acting at the center of gravity of a structure, when the structure is at an arbitrary position X, is given by:
F(s) = K ( X(e) - X ) + B(e)
where
K = stiffness matrix
X(e) = equilibrium position
B(e) = buoyancy force at equilibrium
If the ASTF data record is used, the program will use X(e) and B(e) as calculated by the program. However, it should be checked that the above expression, which is used to calculate the LINEAR hy- drostatic forces throughout the Aqwa suite, produces the forces on the structure intended by the user.
• Effect of the ASTF data record when running Aqwa-Line
Additional hydrostatic stiffness is stored in the database and used in the calculation of the RAOs. However, it is not used in the calculation of the 2nd order drift forces.
• Effect of the ASTF data record when running Aqwa-Librium/Fer/Drift/Naut
Note that in the equation above the term X(e) is the Aqwa-Line equilibrium position. If the initial position in a subsequent Librium/Fer/Drift/Naut analysis is not as defined in the Line run then there will be restoring forces which will try to return the structure to the Aqwa-Line equilibrium position.
• Effect of multiple ASTF data records
If additional stiffness is required and stage 2 is run it is always necessary to use the ASTF data record.
11.3.3. The BFEQ Data Record - Buoyancy Force at Equilibrium
This data record is used to specify the vertical buoyancy force when the structure is at its free-floating equilibrium position (i.e. with no articulations and no mooring lines attached), which is used in the calculation of the linear hydrostatic forces.
Wave Frequency Dependent Parameters and Stiffness Matrix - WFS* (Data Category 7)
If a BFEQ data record is used, there must also be a LSTF data record (The LSTF Data Record - Linear Hydrostatic Stiffness Matrix (p. 82)).
2 5 7 11 21
- --- -- ---- --- --- |X| | |BFEQ|XXXXXXXXX| | - --- -- ---- --- --- | | | |
| | | |_(2)Vertical Buoyancy Force at Equilibrium(F10.0) | | |
| | |
| | |_Compulsory Data Record Keyword(A4) | |
| |_Optional User Identifier(A2) |
|_Compulsory END on Last data record in data category(A3)
11.3.4. The GMXX/GMYY Data Record - User-Specified Metacentric Height
The hydrostatic stiffness in the hydrodynamic database can be modified to a user specified value creating additional stiffness automatically. This is achieved by specifying the required GMX and GMY (about the global X/Y axis) in Data Category 7 as follows:2 5 7 11 16 21 31 41 51 - --- -- ---- --- --- --- --- --- |X| | |GMXX| | | | | | - --- -- ---- --- --- --- --- --- |X| | |GMYY| | | | | | - --- -- ---- --- --- --- --- --- | | | | | | | |_ (1) Required Value | | |
| | |_ Data Record Name(A4) | |
| |_Optional User Identifier (A2) |
|_Compulsory END on last data record in Data Category (A3)
(1) Aqwa firstly calculates the hydrostatic stiffness matrix based only on the cut water plane and displaced volume properties. It then adjusts the second moments of area IXX, IYY and recalculates its associated properties, PHI (principal axis), GMX/GMY, BMX/BMY etc. to give the required GM values. The associated additional hydrostatic stiffness is calculated automatically and stored in the hydrodynamic database.
Note that if the GM value input is less than that based on the geometry alone, the resulting additional stiffness will be negative. This would be the case if ballast tanks were being modeled, making the structure less stable, statically.