Remarks on some properties of conic yield restrictions in limit analysis

Description/Abstract

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