The M-Beta Multiplier Method for Limit Load Determination of Components With Local Plastic Collapse

The mβ-multiplier method based on Mura’s extended variational principles in plasticity relies on a reference stress that is obtained from an entire stress distribution in a structure. The method is relatively insensitive to components that undergo localized plastic action and generates limit load bounds that are better than the classical and mα-multiplier methods. The multiplier mβ is determined by evaluating a reference parameter βR, which may be difficult to determine if the stress distribution obtained using elastic modulus adjustment procedures does not converge to a limit type of distribution. In this paper, physical insights relating to the reference parameter βR are provided by linking the concept of reference volume to the local collapse of the structure. As well, a systematic procedure to identify the converged limit state is presented. The mβ-multiplier method, developed in conjunction with the reference volume concept, is applied to a number of cracked component configurations. The results are compared with the corresponding inelastic finite element analysis.