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We introduce a systematic method for identifying the worst case load amongall boundary loads of fixed energy. Here the worst case load is defined to bethe one that delivers the largest fraction of input energy to a prescribedsubdomain of interest. The worst case load is identified with the firsteigenfunction of a suitably defined eigenvalue problem. The first eigenvaluefor this problem is the maximum fraction of boundary energy that can bedelivered to the subdomain. We compute worst case boundary loads and associatedenergy contained inside a prescribed subdomain through the numerical solutionof the eigenvalue problem. We apply this computational method to bound theworst case load associated with an ensemble of random boundary loads given by asecond order random process. Several examples are carried out on heterogeneousstructures to illustrate the method.

Uncertain Loading and Quantifying Maximum Energy Concentration within Composite Structures