... stress distributions better than the power law and closer to elastic-plastic solutions for textbook cases such as thick cylinder, beam, etc. This part of the article offers several numerical examples to demonstrate the robustness of the method. Upper and lower bound limit loads are calculated using...

... robustness, more generality, and better stress distributions, consistently leading to lower-bound limit loads that are closer to elastoplastic finite element analysis estimates. It also leads us to question the validity of the prevailing power law-based stationary stress distributions. Part 2 of this paper...