aero2struct_force_mapping¶

Maps the aerodynamic forces at the lattice to the structural nodes

The aerodynamic forces from the UVLM are always in the inertial G frame of reference and have to be transformed to the body or local B frame of reference in which the structural forces are defined.

Since the structural nodes and aerodynamic panels are coincident in a spanwise direction, the aerodynamic forces that correspond to a structural node are the summation of the M+1 forces defined at the lattice at that spanwise location.

\[\begin{split}\mathbf{f}_{struct}^B &= \sum\limits_{i=0}^{m+1}C^{BG}\mathbf{f}_{i,aero}^G \\ \mathbf{m}_{struct}^B &= \sum\limits_{i=0}^{m+1}C^{BG}(\mathbf{m}_{i,aero}^G + \tilde{\boldsymbol{\zeta}}^G\mathbf{f}_{i, aero}^G)\end{split}\]

where \(\tilde{\boldsymbol{\zeta}}^G\) is the skew-symmetric matrix of the vector between the lattice grid vertex and the structural node.

param aero_forces: Aerodynamic forces from the UVLM in inertial frame of reference
type aero_forces: list
param struct2aero_mapping: Structural to aerodynamic node mapping
type struct2aero_mapping: dict
param zeta: Aerodynamic grid coordinates
type zeta: list
param pos_def: Vector of structural node displacements
type pos_def: np.ndarray
param psi_def: Vector of structural node rotations (CRVs)
type psi_def: np.ndarray
param master: Unused
param conn: Connectivities matrix
type conn: np.ndarray
param cag: Transformation matrix between inertial and body-attached reference A
type cag: np.ndarray
param aero_dict: Dictionary containing the grid’s information.
type aero_dict: dict
returns: structural forces in an n_node x 6 vector
rtype: np.ndarray