Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec
each timestep is considered a valid solution. Therefore the structural code can be called from within the flow code repeatedly at given timesteps of the flow solution. See Figure 1 for a flow chart of the process.
Initial Shape
RANSE Solver
No
Convergence achieved?
occurrences considered in dynamic simulations. A
typical application is shown in [1]. 3. DESCRIPTION OF THE CST ELEMENT 3.1
GENERAL Yes Exit Program
Generally the stress – strain relationship is given by: σ H ε
with ε 2xy Flow Forces
New Flying Shape
xx ; yy ;
and σ 2 T
xx ; yy ; xy T .
The factor √2 is included just for mathematical convenience later on.
To discretise the sail, Constant Stress Triangle elements as described in Figure 2 are used.
Structural Solver
Figure 1: Flow Chart of FSI process
The coupling utilises two interfaces provided by CFX: User CEL Routine and Junction Box Routine. The two interfaces differ in their capabilities and the way they are called [13]:
The User CEL Routine provides a direct interface to data used by CFX. It is called from within CFX at a point during the calculation determined by CFX from the data used and allows out- and input of selected data as calling arguments. It is called by each partition individually for the data used by that partition.
The Junction Box Routine is called from CFX at a point determined by the user. It does not provide any calling arguments. What is does provide is full access to the CFX Memory Management System (MMS), the system used to manage all calculation data. While being called individually by each partition as well, it allows totransfer data between
partition using the
Parallel Virtual Machine (PVM) setup used by CFX for its own communication.
A User CEL Routine called from the mesh deformation loop is used to write and read the nodal pressures and locations to and from a user defined section of the local MMS of each partition. A Junction Box Routine is used to transfer all nodal pressure data to the master partition, initiate the FE-run (local) and return the new nodal coordinates to each partition via PVM. Most probably this is not the most elegant way but it is robust.
The coupling method (fully explicit) results in a weak two-way coupling
between
simulation. Therefore the timestep length has to be significantly smaller than any natural periods of dynamic
B-72 flow and structural Figure 2: Description of triangle element Note that edge 3 is parallel to the x-axis.
In FlexSail linear Hookean materials are assumed. The generalised stress-strain relationship, the Hessian matrix H
ˆ , for the linear behaviour of an arbitrary material in
material coordinate system 1-2 (see Figure 3) is the partial derivative of stress by strain and can be written as:
H ˆ
11 11
11 22
11 12
22 11
22 22
22 12
12 11
12 22
12 12
This linear description of element stress-strain relationship only holds true under the assumption of small strains.
The stress strain relations for arbitrary directions, where the material directions have been rotated a positive angle from the x-axis (see Figure 3), can be written as follows:
σ T H T ε 1 ˆ
With T being the transformation matrix from element to material coordinate system:
©2011: The Royal Institution of Naval Architects
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