Prager‐Shield Optimality Criteria with Bounded Spatial Gradients

Abstract

The importance of constraining the rate of spatial change of cross-sections in optimal design has been presented in previous studies. In the context of plastically designed beams, a theory is proposed for optimizing structures with bounded spatial gradients. The procedure is based on an extended version of the Prager-Shield condition which replaces the cost extremum statement with an optimal strain-stress relationship and thus converts the considered optimization problem into that of structural analysis. The associated strain field, as in most constrained problems, usually contains strain impulses (concentrated rotations). The procedure is illustrated with three examples of beam design and the results are verified by independent methods.