Efficient and Robust Load and Displacement Transfer Scheme Using Weighted Least Squares

Nomenclature Σ diagonal matrix of singular values λ D vector of Lagrange multipliers for displacement transfer residual λ L vector of Lagrange multipliers for load transfer residual D displacement transfer residual H covariance matrix I identity matrix L load transfer residual R rotation U left singular vectors V right singular vectors X matrix of Lagrange multipliers enforcing SVD constraint Y symmetric matrix of Lagrange multipliers enforcing unitary constraint Z matrix of Lagrange multipliers in second-order Lagrangian d vector from weighted centroid of initial structural node locations to initial aerodynamic node location fA force on aerodynamic surface node fS,n force on structural node n *Graduate Research Assistant, School of Aerospace Engineering, and AIAA Student Member †Assistant Professor, School of Aerospace Engineering, and AIAA Senior Member