Extrapolation Effects on Coupled Computational Fluid Dynamics/Computational Structural Dynamics Simulations

between them, passing loads from the e ow code to the structural code,and displacements back theother way. Forunsteady problems the sequencing is done within the pseudotime loop used for the e ow solver and removes sequencing errors. The mesh movement for the aerodynamic solver is done using transe nite interpolation of displacements. 7 We restrict ourselves in this Note to the case of a wing modeled structurally by a plate. This case is interesting as a building block to more complex structural descriptions. Transformation of data between the two grids is broken into two components in and out of the plane of the structural model. The outplane treatment follows the considerations of Ref. 5. The in-plane treatment turns out to have a much stronger ine uence on the test case considered next. The two approaches used are the ine nite plate spline (IPS) 8 and linear interpolation. For IPS a solution of the thin-plate equation is forced to pass through the known structural points and is then evaluated at the projected aerodynamic points for the required displacements. For linear interpolation each projected e uid point is associated with a triangle on the structural mesh, and the deformation is calculated using a linear approximation within the triangle. In both cases the relationship between displacements on the e uid and structural grids is linear, and the principle of virtual work is then applied for transferring forces. III. Test Cases