Lower Bound Limit Load Determination: The $mβ$-Multiplier Method

The existing lower bound limit load determination methods, that are based on linear elastic analysis such as the classical and $mα$-multiplier methods, have a dependence on the maximum equivalent stress. These methods are therefore sensitive to localized plastic action, which occurs in components with thin or slender construction, or those containing notches and cracks. Sensitivity manifests itself as relatively poor lower bounds during the initial elastic iterations of the elastic modulus adjustment procedures, or oscillatory behavior of the multiplier during successive elastic iterations leading to limited accuracy. The $mβ$-multiplier method proposed in this paper starts out with Mura’s inequality that relates the upper bound to the exact multiplier by making use of the “integral mean of yield.” The formulation relies on a “reference parameter” that is obtained from considering a distribution of stress rather than a single maximum equivalent stress. As a result, good limit load estimates have been obtained for several pressure component configurations.