PSI - Issue 8

N. Di Domenico et al. / Procedia Structural Integrity 8 (2018) 422–432 N. Di Domenico et al. / Structural Integrity Procedia 00 (2017) 000–000

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P is the constraint matrix containing the coordinates of source points in the space:

P =    

   

1 x k 1 y k 1 z k 1 1 x k 2 y k 2 z k 2 .. . .. . .. . 1 x k N y k N z k N

(13)

Once the weights and and coe ffi cients of the system have been obtained, displacement values for the three directions can be obtained for a given X point as:   S x ( x ) = N i = 1 γ x i φ ( x − x k i ) + β x 1 + β x 2 x 1 + β x 3 x 2 + β x 4 x n S y ( x ) = N i = 1 γ y i φ ( x − x k i ) + β y 1 + β y 2 x 1 + β y 3 x 2 + β y 4 x n S z ( x ) = N i = 1 γ z i φ ( x − x k i ) + β z 1 + β z 2 x 1 + β z 3 x 2 + β z 4 x n (14) 3. Modal FSI workflow Proposed workflow is shown in Figure 1. The undeformed configuration is first studied using a structural solver (dotted red square in the workflow) in order to extract the chosen number of modes with an eigenvalue analysis. Modal shapes are at this point extracted from the FEM solver and employed by the RBF morpher to properly generate an RBF solution for each shape, constraining far field conditions and rigid surfaces and mapping FEA fields on deformable surfaces.

structural mode analysis

RBF solution database (one per mode)

undeformed geometry

CFD time-step iterations

modal coordinates calculation

mesh update

update model

yes

no

simulation ended?

stop

Fig. 1: Transient modal superposition FSI workflow

Taking advantage of RBF’s meshless nature, the shape variations calculated using FEM displacements can be directly used to deform the CFD numerical grid, avoiding complex mappings between FEM and CFD displacements. At this point RBF shapes are imported directly inside the CFD solver, ANSYS Fluent, ready to be used to move the mesh and making the grid deformable. Deformations associated with each modal shape are stored in memory in order to speed up the mesh update process, being structural response, and then the variation of nodal positions, a matter of a multiplication. It is indeed: