An innovative H∞–norm based worst case scenario approach for dynamic compliance optimization with applications to viscoelastic beams

A novel frequency–based definition of dynamic compliance is introduced within the framework of H∞–norm based structural dynamics in the presence of load uncertainties. The system itself is supposed to depend on a vector of design parameters with respect to which an optimal design is pursued. A three-step worst-case-scenario is then developed that finds the minimum-compliance structure capable of accounting for the entire norm–bounded load sets. Once the problem is initialized, the current worst load is found that is used as input to the minimization of the structural compliance and the procedure is repeated until convergence. Numerical examples are eventually proposed that deal with viscoelastic beams discretized via a truly–mixed finite–element scheme.