Static condensation optimal port/interface reduction and error estimation for structural health monitoring

TL;DR

This paper introduces optimal reduced port spaces for static condensation in structural health monitoring, enabling accurate and efficient analysis of structures with changing geometries and defect detection.

Contribution

It generalizes existing port spaces to accommodate geometry changes and demonstrates their optimality and reusability in structural health monitoring applications.

Findings

Exponential convergence of reduced port spaces for geometry changes

Reusability of port spaces across different geometries

Numerical evidence of minimized approximation error

Abstract

Having the application in structural health monitoring in mind, we propose reduced port spaces that exhibit an exponential convergence for static condensation procedures on structures with changing geometries for instance induced by newly detected defects. Those reduced port spaces generalize the port spaces introduced in [K. Smetana and A.T. Patera, SIAM J. Sci. Comput., 2016] to geometry changes and are optimal in the sense that they minimize the approximation error among all port spaces of the same dimension. Moreover, we show numerically that we can reuse port spaces that are constructed on a certain geometry also for the static condensation approximation on a significantly different geometry, making the optimal port spaces well suited for use in structural health monitoring.