Uncertain Loading and Quantifying Maximum Energy Concentration within Composite Structures
For engineers designing composite structures, this provides a systematic way to quantify worst-case energy concentration, but the method is incremental as it extends existing eigenvalue-based approaches to uncertain loading.
This paper introduces a method to identify the worst-case boundary load that maximizes energy concentration in a subdomain of a composite structure, formulated as an eigenvalue problem. The method is applied to bound worst-case loads under random boundary conditions, with numerical examples on heterogeneous structures.
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.