Uncertain Loading and Quantifying Maximum Energy Concentration within Composite Structures

TL;DR

This paper presents a systematic eigenvalue-based method to identify the worst-case boundary load that maximizes energy concentration within a subdomain of composite structures, aiding in structural safety analysis.

Contribution

It introduces a novel eigenvalue approach for quantifying maximum energy concentration under uncertain boundary loads in composite structures.

Findings

Eigenvalue problem effectively identifies worst-case loads.

Method applied to heterogeneous structures with random boundary loads.

Provides bounds on maximum energy transfer within subdomains.

Abstract

We introduce a systematic method for identifying the worst case load among all boundary loads of fixed energy. Here the worst case load is defined to be the one that delivers the largest fraction of input energy to a prescribed subdomain of interest. The worst case load is identified with the first eigenfunction of a suitably defined eigenvalue problem. The first eigenvalue for this problem is the maximum fraction of boundary energy that can be delivered to the subdomain. We compute worst case boundary loads and associated energy contained inside a prescribed subdomain through the numerical solution of the eigenvalue problem. We apply this computational method to bound the worst case load associated with an ensemble of random boundary loads given by a second order random process. Several examples are carried out on heterogeneous structures to illustrate the method.