Efficient prediction of static and dynamical responses of functional graded beams using sparse multiscale patches

TL;DR

This paper introduces a multiscale patch scheme for efficiently predicting the static and dynamic responses of heterogeneous functional graded beams, significantly reducing computational costs while maintaining accuracy.

Contribution

The authors develop a novel multiscale patch algorithm that computes microscale dynamics in small patches and accurately predicts macroscale behavior for graded beams.

Findings

The method accurately predicts deflections and frequencies matching experimental data.

Computational time reduces by up to 17 times with minimal accuracy loss.

The scheme is stable, robust, and improves efficiency by focusing on small beam patches.

Abstract

We develop a multiscale patch scheme for studying the system level characteristics of heterogeneous functional graded beams. The algorithm computes the detailed beam dynamics on the microscale, but only in small patches of the beam domain, and then applies symmetry-preserving interpolation to these patches to accurately predict the macroscale behaviour. To validate the algorithm, two examples of functionally graded beams are investigated, namely cross-sectionally graded and axially graded. Gradient patterns are defined via volume fractions of aluminium and silicon carbine either over the beam's cross section or along its axial direction. In these examples the multiscale patch scheme only computes over a fraction of the beam's full-domain. Beam deflection and natural frequencies from the patch computations agree very well with existing experimental data and the full-domain computations. The algorithm is stable and robust, with errors consistently small and reliably reducible by increasing the number of patches. The reduction in the spatial domain of computation substantially improves the computational efficiency, with the computational time reducing by a factor of up to 17 when the patches cover 27% of the beam.