I worked on a 2007 ASME B&PV Code, Section VIII, Div 2 analysis of what was essentially an elbow casting with some additional detail. The more traditional approach would be to use stress linearization on an elastic analysis for stress categorization. However, since the elbow was thick-walled relative to the radius, stress linearization can be non-conservative because the stress distribution is non-linear. Think about the difference between a thick walled cylinder and. thin walled cylinder.
I used the limit load analysis method instead. The limit load analysis has established itself as the preferred method, subject to its limitations, to assess primary sizing (Protection Against Plastic Collapse). The limit load analysis eliminates the need for stress categorization because it is a pass-fail criterion. The material definition is elastic-perfectly plastic. So, the limit load analysis is trying to predict when a plastic hinge forms in a plate an uncontrolled deformation with result with any additional applied load.
The basis for the limit load is straightforward. A value of 1.5 is applied to the desired load (i.e. design pressure+static head+dead weight). Recall that a plastic hinge is formed in a rectangular cross-section beam with an elastic-perfectly plastic material when the moment is 1.5 X the moment required for initial yield. You can find this discussion in a Continuum Mechanics textbook in a section on Beams. I have the book by Shames and Cozzarelli, "Elastic and Inelastic Stress Analysis," which has a pretty good description of this derivation with lots of pictures. So, if you enter 1.5*S (in some cases 1.5S is equal to yield strength at temperature) as your FEA yield strength, and the model converges, you will not develop a plastic hinge in the component you are analyzing. There will likely be plastic strain, especially at structural discontinuities.
Did the analysis model converge at the desired load (i.e.1.5*Design Pressure)? If yes, Section 5.2, Protection Against Plastic Collapse is satisfied. If not, Section 5.2, Protection Against Plastic Collapse is NOT satisfied.
Advances in the capabilities of computers have enabled the method, since the limit load analysis will take longer to run than an elastic stress analysis. However, post-processing effort is reduced to near zero. Also, there is no question about whether or not the stress categorization line (stress cutline) is in the limiting location.