A quadratic manifold for model order reduction of nonlinear structural dynamics. (August 2017)

• Record Type: Journal Article
• Authors: Jain, Shobhit; Tiso, Paolo; Rutzmoser, Johannes B.; Rixen, Daniel J.
• Is Part Of: Computers & structures. Volume 188(2017)
• Page Start: 80
• Page End: 94
• Publication Date: 2017-08
• Subjects: Reduced-order modeling -- Nonlinear manifold -- Geometric nonlinearities -- Structural dynamics; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2017.04.005
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: We propose model reduction for nonlinear structural dynamics via quadratic manifold. The manifold is formed by a third order tensor comprising modal derivatives. The modal unknowns are minimized by enslaving modal derivatives on the manifold. The method is applied to the geometrically nonlinear transient analysis of a wing. Abstract: 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.