A Quadratic Manifold for Model Order Reduction of Nonlinear Structural   Dynamics
  This paper describes the use of a quadratic manifold for the model order reduction of structural dynamics problems featuring geometric nonlinearities. The manifold is tangent to a subspace spanned by the most relevant vibration modes, and its curvature is provided by modal derivatives obtained by sensitivity analysis of the eigenvalue problem, or its static approximation, along the vibration modes. The construction of the quadratic manifold requires minimal computational effort once the vibration modes are known. The reduced order model is then obtained by Galerkin projection, where the configuration-dependent tangent space of the manifold is used to project the discretized equations of motion. 
Shobhit Jain, Paolo Tiso, Daniel J. Rixen, Johannes B. Rutzmoser
cs.CE