Remarks on some properties of conic yield restrictions in limit analysis

Abstract

A major difficulty when applying the kinematic theorem in limit analysis is the derivation of expressions ofthe dissipation functions and the set of plastically admissible strains. At present, no standard methodologyexists. Here, it is shown that they can be readily obtained, provided that the yield restriction can berewritten as an intersection of cones, and that the expression defining the dual cones is available. This isalways possible for the case of self-dual cones and some other classes, and covers many of the well-knowncriteria. Therefore, a difficult obstacle with respect to the use of the kinematic theorem in conjunctionwith any numerical method can be overcome. The methodology is illustrated by giving the expressions ofthe dissipation functions for various conic yield restrictions. A special emphasis is given on upper boundfinite element limit analysis. Taking advantage of duality in conic programming, we can obtain the dualproblem, where knowledge of the dual cone is not necessary. Therefore, this formulation is feasible forany cone. Finally, it is interesting that the form of the dual problem, for varying yield strength within thefinite element, differs from that presented in other papers