Lower bound limit loads using variational concepts: the mα-method

Abstract In limit analysis, statically admissible stress fields cannot lie outside the hypersurface of the yield criterion, and the stress fields calculated by kinematically admissible velocity fields should be on the hypersurface. On the basis of a variational formulation, Mura and his coworkers have replaced such a requirement by introducing the concept of ‘integral mean of yield’. The method in its present form, however, leads to lower bound limit loads that are no better than the classical method. In the mα-method of lower bound limit load determination presented here, a statically admissible multiplier, mα, is determined on the basis of two linear elastic finite element analyses. The concept of reference volume which is introduced in conjunction with the theorem of nesting surfaces, enables the determination of good lower and upper bounds on limit loads. The method is applied to a number of practical pressure component configurations, such as cylinder, nozzle-sphere intersection, torispherical heads and non-symmetric plates and the results are compared with those obtained by inelastic finite element analyses.