Inf–sup conditions on convex cones and applications to limit load analysis

Abstract

The paper is devoted to a family of specific inf–sup conditions generated by tensor-valued functions on convex cones. First, we discuss the validity of such conditions and estimate the value of the respective constant. Then, the results are used to derive estimates of the distance to dual cones, which are required in the analysis of limit loads of perfectly plastic structures. The equivalence between the static and kinematic approaches to limit analysis is proven and computable majorants of the limit load are derived. Particular interest is paid to the Drucker–Prager yield criterion. The last section exposes a collection of numerical examples including basic geotechnical stability problems. The majorants of the limit load are computed and expected failure mechanisms of structures are visualized using local mesh adaptivity.