1. FLEX - Description of flex-joint connectors

This component can be used to model ball joints, hinges and universal joints with specified rotational stiffness. It will introduce one extra element with zero length at the segment end to which it is attached, and add 6 degrees of freedom to the system model. The translation dofs of freedom are suppressed by use of linear constraint equations. Note that this component can not be used in branch lines in standard systems, or in combination with bar elements. It should also be used with care at supernodes with user defined boundary conditions for rotations in AR system to avoid singularities in the FEM solution procedure.

In present version, flex-joint connectors may only be used for nonlinear static and dynamic analysis.

1.1. Data group identifier

NEW COMPonent FLEX

1.2. Component type identifier

CMPTYP-ID

  • CMPTYP-ID: character(8): Component type identifier

1.3. Mass and volume

AM AE RGX RGY RGZ CRX CRY CRZ

  • AM: real, default: 0: Mass \(\mathrm {[M]}\)

  • AE: real, default: 0: Displacement volume \(\mathrm {[L^3]}\)

  • RGX: real, default: 0: Radius of gyration around local x-axis \(\mathrm {[L]}\)

  • RGY: real, default: 0: Radius of gyration around local y-axis \(\mathrm {[L]}\)

  • RGZ: real, default: 0: Radius of gyration around local z-axis \(\mathrm {[L]}\)

  • CRX: real, default: 0: Damping coeff. Rotational velocity around local x-axis \(\mathrm {[FLT/deg]}\)

  • CRY: real, default: 0: Damping coeff. Rotational velocity around local y-axis \(\mathrm {[FLT/deg]}\)

  • CRZ: real, default: 0: Damping coeff. Rotational velocity around local z-axis \(\mathrm {[FLT/deg]}\)

1.4. Hydrodynamic coefficients

CDX CDY CDZ AMX AMY AMZ AMXROT AMYROT AMZROT

  • CDX: real, default: 0: Drag coeff. in local x-direction \(\mathrm {[F/(L/T)^2)]}\)

  • CDY: real, default: 0: Drag coeff. in local y-direction \(\mathrm {[F/(L/T)^2)]}\)

  • CDZ: real, default: 0: Drag coeff. in local z-direction \(\mathrm {[F/(L/T)^2)]}\)

  • AMX: real, default: 0: Added mass in local x-direction \(\mathrm {[M]}\)

  • AMY: real, default: 0: Added mass in local y-direction \(\mathrm {[M]}\)

  • AMZ: real, default: 0: Added mass in local z-direction \(\mathrm {[M]}\)

  • AMXROT: real, default: 0: Added mass rotation around local x-direction \(\mathrm {[FL\times T^2]}\)

  • AMYROT: real, default: 0: Added mass rotation around local y-direction \(\mathrm {[FL\times T^2]}\)

  • AMZROT: real, default: 0: Added mass rotation around local z-direction \(\mathrm {[FL\times T^2]}\)

The tangential drag force, the force acting in local x-axis, is computed by:

\(\mathrm {FX=CDX\times VRELX\times |VRELX|}\)

The drag force acting normal to the local x-direction, is assumed to act in the same direction as the relative velocity transverse component and are computed according to:

  • \(\mathrm {FY=CDY\times \sqrt{VRELY^2+VRELZ^2}\times VRELY}\)

  • \(\mathrm {FZ=CDY\times \sqrt{VRELY^2+VRELZ^2}\times VRELZ}\)

1.5. Stiffness properties classification

IDOF IBOUND RAYDMP

  • IDOF: character(4): Degree of freedom

    • IDOF = IRX: Rotation around local x-axis

    • IDOF = IRY: Rotation around local y-axis

    • IDOF = IRZ: Rotation around local z-axis

    • IDOF = IRYZ: Rotation around bending axis

  • IBOUND: integer: Constraint

    • IBOUND = -1: Fixed. Not available for IDOF = IRX

    • IBOUND = 0: Free. Not available for IDOF = IRYZ

    • IBOUND = 1: Constant stiffness

    • IBOUND > 1: Table with IBOUND pairs of moment - rotational angle to be specified

  • RAYDMP: real: Stiffness proportional damping coefficient

3 or 2 input lines to be specified: IRX, IRY, IRZ or IRX, IRYZ

Table 1. Allowed combinations of degrees of freedom and stffness specifications.
Degree of freedom IRX IRY IRZ

Possible combinations

FREE

FREE

FREE

FREE

FIXED

FIXED

FREE

FREE

LIN/NONLINEAR stiffness

FREE

LIN/NONLINEAR stiffness

FREE

LIN/NONLINEAR stiffness

LIN/NONLINEAR stiffness

LIN/NONLINEAR stiffness
Table 2. Allowed combinations of degrees of freedom and stiffness specifications, IRYZ stiffness symmetry.
Degree of freedom IRX IRYZ

Possible combinations

FREE

LIN/NONLINEAR stiffness

LIN/NONLINEAR stiffness

FREE

x, y and z-axes refer to the local coordinate system of the element to which the flex joint is attached. This is similar to the ball joint connector as illustrated in the figure Rotation freedom for a ball joint component.

1.6. Stiffness data

Stiffness data are to be given in the sequence IRX, IRY and IRZ or IRX and IRYZ. Stiffness data are to be omitted for IBOUND <= 0

Linear stiffness

IBOUND = 1, One input line

 STIFF

  • STIFF: real: stiffness with respect to rotation \(\mathrm {[FL/deg]}\)

Nonlinear stiffness; IBOUND > 1

IBOUND > 1, IBOUND input lines

MOMENT ANGLE

  • MOMENT: real: Moment corresponding to rotational angle \(\mathrm {[FL]}\)

  • ANGLE: real: Rotational angle \(\mathrm {[deg]}\)

MOMENT and ANGLE must be given in increasing order. Linear extrapolation will be used outside the specified range of values.

For dofs IRX, IRY and IRZ, both negative and positive values should be given.

For dof IRYZ, MOMENT and ANGLE have to be greater or equal to zero. To avoid convergence problems, the first pair should be 0.0, 0.0.