Slender Element

Long, slender elements can be used to model jacket legs and bracings or spool pieces. A slender object such as a spool piece will normally have a 3-D geometry consisting of a number of straight elements with different orientation, and can be modeled by a set of slender elements. End connectors can be modeled either by a short element or by a concentrated, fixed element. Small-body theory is used to calculate forces both for the slender element and the concentrated fixed element. Stiff connection implies that all the sub-body (slender element or fixed, concentrated element) forces are calculated and transferred to the main body. Each slender element specified by the user is divided into strips with equal length.

1. Properties

  • Wave Integration Method: Wave force integration method.

    • Actual wave elevation (default): Force integrated to actual wave elevation.

    • Strictly linear wave: Force integrated to z=0 (strictly linear wave theory).

  • Load Type: Controls whether gravity and buoyancy forces are included.

    • Gravity and buoyancy included (default): Gravity and buoyancy force included.

    • Gravity and buoyancy NOT included: Gravity and buoyancy not included.

  • Wave Particle Method: Controls inclusion of wave particle velocity and acceleration.

    • Not included: No wave particle kinematics.

    • Velocity: Velocity only (drag forces).

    • Velocity and acceleration (default): Velocity and acceleration included.

    • Velocity (first and last strip only): Wave kinematics calculated at mid-point of strip 1 and the last strip only. Linear interpolation is used for the other strips.

    • Velocity and acceleration (first and last strip only): As above, but including acceleration.

  • Specific Volume: Cross-section area of element [m2].

  • Distributed Mass: Distributed mass of element [kg/m].

  • Number Of Strips: Number of strips the element is divided into (default: 10).

In a normal analysis of a pipe (or other slender element) in the splash zone, use Actual wave elevation, Gravity and buoyancy included, and Velocity and acceleration.

1.1. Calculated values

The following read-only fields are derived from the element geometry and properties:

  • Calc Mass [kg]: Calculated mass (Distributed Mass x Calc Length).

  • Calc Length [m]: Distance between end point 1 and end point 2.

  • Calc Volume [m3]: Calculated volume (Specific Volume x Calc Length).

  • Calc COG: Calculated centre of gravity (midpoint between end points) in body-fixed coordinates.

2. Coordinates

2.1. End points

The element geometry is defined by two end points in the body-fixed coordinate system.

  • End Point 1: Coordinates (X, Y, Z) of element end 1 [m].

  • End Point 2: Coordinates (X, Y, Z) of element end 2 [m].

2.2. Reference point

  • Reference Point: Coordinates (X, Y, Z) of the reference point [m] in the body-fixed coordinate system.

The reference point is used to define the orientation of the local element coordinate system:

  • The local XS-axis extends along the element from end point 1 to end point 2.

  • The local ZS-axis is perpendicular to the plane defined by the XS-axis and the reference point, computed as the cross product of XS and the vector from end point 1 to the reference point.

  • The local YS-axis completes the right-hand coordinate system. It lies in the plane containing XS and the reference point, with positive direction towards the reference point.

3. Hydrodynamic properties

3.1. Hydrodynamic coefficients

The coefficients are given with dimension in the local element coordinate system, and are valid for a fully submerged strip.

  • C2x: Quadratic longitudinal drag coefficient [N*s2/m3].

  • C2y: Quadratic transverse (Y) drag coefficient [N*s2/m3].

  • C2z: Quadratic transverse (Z) drag coefficient [N*s2/m3].

  • C1x: Linear longitudinal drag coefficient [N*s/m2].

  • C1y: Linear transverse (Y) drag coefficient [N*s/m2].

  • C1z: Linear transverse (Z) drag coefficient [N*s/m2].

  • Amx: Longitudinal added mass coefficient [kg/m].

  • Amy: Transverse (Y) added mass coefficient [kg/m].

  • Amz: Transverse (Z) added mass coefficient [kg/m].

3.2. Diffracted wave application

Diffracted wave points can be specified for each end of the element. The diffracted wave points must contain transfer functions for both wave elevation and velocity in x, y, and z direction.

  • Diffracted Wave End 1: Diffracted wave point associated with element end 1.

  • Diffracted Wave End 2: Diffracted wave point associated with element end 2.

3.3. Depth-dependent hydrodynamic coefficients

As an additional modelling option, depth-dependent scaling of hydrodynamic coefficients can be specified. If the element will be fully submerged and assumed unaffected by surface effects throughout the simulation, this section can be left empty. However, if a slender element with nearly horizontal angle crosses the water surface, the slamming force is calculated only if depth-dependent data are given.

The depth-dependent scaling coefficients are applied to the centre of each strip, and are mainly intended for nearly horizontal slender elements. For tilted elements a scaling factor will be calculated, proportional to the submerged part of each strip.

  • Zcoef: Vertical position used as reference for depth dependency [m].

The input for interpolation in the depth table is:

  • \(Z_{in} = Z - Zcoef - \xi\) when Wave Integration Method is Actual wave elevation

  • \(Z_{in} = Z - Zcoef\) when Wave Integration Method is Strictly linear wave

where Z is the vertical position of the strip centre, and \(\xi\) is the wave elevation.

The depth-dependent coefficients table has the following columns:

  • Zd: Vertical position [m] (default: 1.0). Given for increasing or decreasing vertical position.

  • Rvol: Volume relative to fully submerged volume [-] (default: 1.0).

  • Rc21, Rc22, Rc23: Relative quadratic drag in local element x, y, z direction [-].

  • Rc11, Rc12, Rc13: Relative linear drag in local element x, y, z direction [-].

  • Ramx, Ramy, Ramz: Relative added mass in local element x, y, z direction [-] (default: 1.0).

4. Aerodynamic properties

When Wind Forces is enabled, wind forces are calculated on the slender element using a Morison-like drag formulation in the local element coordinate system.

  • Quadratic Longitudinal Drag: Quadratic longitudinal wind drag coefficient [N*s2/m3].

  • Quadratic Transverse Y: Quadratic transverse (Y) wind drag coefficient [N*s2/m3].

  • Quadratic Transverse Z: Quadratic transverse (Z) wind drag coefficient [N*s2/m3].