Hinges and flex joints are considered as separate entities in Flexcom. A hinge in an articulation with typically a zero or low rotational stiffness value, while a flex joint has a finite linear or nonlinear stiffness. A hinge has zero length and acts at a single point in the model, whereas a flex joint has a short but non-zero length. A hinge constrains the displacements of its two end nodes to be exactly the same, while a flex joint includes a physical separation between its ends nodes. If a hinge is assigned a rotational stiffness, it must be a linear value. Flex joints accommodate a linear stiffness value or a non-linear moment-angle relationship. Hinges are massless (although you could include a point mass in conjunction with a hinge) while flex joints may have associated weights in air and in water.
The following table summarises the differences between hinges and flex joints.
Feature |
Hinge |
Flex Joint |
Length |
Zero |
Short |
Stiffness |
Zero or low |
Linear or non-linear |
Mass/buoyancy |
Zero |
Wet and dry weights |
Finite element modelling |
Single point |
Short beam element |
All hinge elements should have zero length in your Flexcom model (the program will issue an appropriate warning message if any hinge element has a non-zero length). This ensures that the displacements of its two end nodes are exactly the same. Rotational stiffness, if specified, acts at a single point in the model, ensuring a pure hinge is modelled. The rotational stiffness acts equally in all directions.
Flex joints are modelled in Flexcom using (typically short) beam elements. Using a combination of the user-specified rotational stiffness and the length of joint, the software automatically computes an appropriate bending stiffness for a beam element used to represent the flex joint. The bending moment across the flex joint must be replicated by the moment across the equivalent beam element, therefore:
(1)
where is the applied moment,
is the rotational stiffness of the flex joint,
is the rotation (in degrees) across the joint,
is the bending stiffness of the equivalent beam element, and
is the curvature of the element.
Considering a segment of a circle, the radian measure of an angle is defined as:
(2)
where is the angle (in radians),
is the arc length subtended by the angle, and
is the radius of the circle. Assuming
is the length of a curved beam element, relating bend radius to curvature, converting radians to degrees, and substituting for
in the first Equation above gives:
(3)
The torsional stiffness of the beam element used to represent the flex joint is assigned the same value as the bending stiffness. The axial stiffness is set equal to the larger axial stiffness of the beam elements connected by the flex joint.
•*HINGE is used to specify hinge elements.
•*FLEX JOINT is used to define flex joint elements.
If you would like to see an example of how these keywords are used in practice, refer to A01 - Deepwater Drilling Riser.