Constrained Optimal Layouts through Prager‐Shield Criteria

Abstract

The Prager-Shield condition is used for determining optimal layouts with an upper limit on the member sizes. The above extended theory is then applied to grillages and it is shown that both the primal problem (stress-field) and the dual problem (strain-field) furnish the same minimum cost. It is also concluded that an upper constraint on the generalized stresses often results in impulse-like concentrations in the optimal strain-field. The above results complement recent work by Strang and Kohn.