Grassmann interpolation of proper orthogonal modes for robust linear and nonlinear dynamic analysis against parameter variation in structures

The slightest parametric modification could strongly affect the dynamic behavior of mechanical structures. The challenge is to develop numerical models that could be adaptable to the occurrence of modifications without neither significant loss of accuracy, nor significant computational time consuming, compared to high-fidelity models. The present paper proposes a model order reduction procedure which consists of two phases. In an offline phase, a set of reduced bases are built using the snapshot-based Proper Orthogonal Decomposition (POD) for given sets of sample parameters. In an online phase, a Grassmann-manifold-based Interpolation (GI) of the subspaces generated by the POD provides a new reduced basis for a non-sampled set of parameters. Sample points in the parameter space are chosen in a regular or random way without necessarily being in the small neighborhood of a reference point. Time-domain analyses of the linear and nonlinear dynamics of a multilayered composite plate are investigated in presence of variation in orientations or thicknesses of the plies. Investigations are carried out in terms of correlation of the reduced bases, accuracy of the time-domain solutions and reduction of computational cost. Results highlight the efficiency of the POD-GI model to accurately approximate the linear and nonlinear structural behavior of the multilayered composite plate with an interesting reduction of computing time compared to the high-fidelity model considered as reference.

Automated summary

This paper proposes a model order reduction procedure that uses Proper Orthogonal Decomposition (POD) and Grassmann manifold-based Interpolation (GI) to accurately approximate the dynamic behavior of mechanical structures with reduced computational cost. The approach involves building reduced bases using POD in an offline phase and using GI to interpolate subspaces in an online phase. The results demonstrate the efficiency of this approach in terms of accuracy and computing time reduction.