Simulation-free hyper-reduction for geometrically nonlinear structural dynamics: A quadratic manifold lifting approach

[+] Author and Article Information
Shobhit Jain

Institute for Mechanical Systems, ETH Zrich, Leonhardstrasse 21, 8092 Zrich, Switzerland

Paolo Tiso

Institute for Mechanical Systems, ETH Zrich, Leonhardstrasse 21, 8092 Zrich, Switzerland

1Corresponding author.

ASME doi:10.1115/1.4040021 History: Received October 19, 2017; Revised April 10, 2018


We present an efficient method to significantly reduce the offline cost associated to the construction of training sets for hyper-reduction of geometrically nonlinear, finite element discretized, structural dynamics problems. The reduced order model is obtained by projecting the governing equation onto a basis formed by vibration modes and corresponding modal derivatives, thus avoiding cumbersome manual selection of high-frequency modes to represent nonlinear coupling effects. Cost-effective hyper-reduction is then achieved by lifting inexpensive linear modal transient analysis to a quadratic manifold constructed with dominant modes and related modal derivatives. The training forces are then computed from the so obtained representative displacement sets. In this manner, the need of full simulations required by traditional, proper orthogonal decomposition based projection and training is completely avoided. In addition to significantly reducing the offline cost, this technique selects a smaller hyper-reduced mesh as compared to proper orthogonal decomposition based training and therefore leads to larger online speedups as well. The proposed method constitutes a solid alternative to direct methods for the construction of the reduced order model, which suffer from either high intrusiveness into the finite element code or expensive offline nonlinear evaluations for the determination of the nonlinear coefficients.

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