# 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