Final report for WP4.3: Enhancement of design methods ... - Upwind

• Time domain simulation in ADCoS-Offshore.
As an example, the central joint of a tripod [16] is modelled with shell elements in ANSYS as shown in
Figure 4.1. The figure shows the tripod as a whole as well (small figure on the left). The model consists of
the shell structure (blue), the master nodes which are connecting points to the rest of the tripod structure
(black dots) and the stiff connections which are implemented between the masters and the detailed joint
(pink lines between master nodes and shell structure). The real deformation of a loaded joint includes an
ovalization of the tubular members near the connection. This must be taken into account when deciding
on the position of the master nodes, which means that the distance between master node and the welding
should not be too short.
Figure 4.1: Super-element approach in ADCoS-Offshore. The central joint of a tripod is condensed and the superelement
is included in the overall turbine model for time domain simulation.
In the next step, a Guyan reduction procedure is used and the model is reduced to the number of DOF of
the five master nodes. Six DOFs at each of the five master nodes lead to a super-element with 30 DOFs.
The super-element, in detail a linear stiffness matrix, a mass matrix and a load vector for the master DOF,
is included in ADCoS-Offshore in the next step. As already mentioned, the stiffness matrix has 30 DOF. In
the reduction procedure, the transformation of the stiffness matrix is not an approximation: the stiffness
representation is exact and therefore the stiffness properties between the master nodes in the superelement
model are defined with the same accuracy as in the detailed shell model.
The mass matrix has the same number of DOF as the stiffness matrix and contains the mass of the joint
that is distributed to the master's DOF. Those mass properties are included in the overall system later on
to describe the dynamic behavior of the system forming the inertia term of the equation of motion. Obviously,
the reduction of the mass matrix is an approximation, as it is not possible to reduce the number of
DOF of a dynamic system and to conserve the level of accuracy at the same time. But this is not considered
to be of vital importance for time domain simulation of OWT with branched support structures as the
internal mass distribution in the super-element (here the tripod central joint) has no significant influence on
the overall dynamic behavior of the OWT. It is expected that in the described case even a lumped mass
for the whole joint would not lead to significant errors. The accuracy of the described mass representation
is comparable to the mass representation of the basic beam model that has been used before the implementation
of the super-element feature.
The static load vector, that is part of the super-element, comprises the forces and moments on the master
nodes resulting from dead weight of the joint. The super-element load vector is added to the system load
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