Stress Classification Using the $r$-Node Method

The ASME Code Secs. III and VIII (Division 2) provide stress-classification guidelines to interpret the results of a linear elastic finite element analysis. These guidelines enable the splitting of the generated stresses into primary, secondary, and peak. The code gives some examples to explain the suggested procedures. Although these examples may reflect a wide range of applications in the field of pressure vessel and piping, the guidelines are difficult to use with complex geometries. In this paper, the $r$-node method is used to investigate the primary stresses and their locations in both simple and complex geometries. The method is verified using the plane beam and axisymmetric torispherical head. Also, the method is applied to analyze 3D straight and oblique nozzles modeled using both solid and shell elements. The results of the analysis of the oblique nozzle are compared with recently published experimental data.