The Application of Finite Element Based Limit Load Analysis

Pressure vessel design methods advanced in the 1960s due to the early demands of the emerging Nuclear industry. Codes and Standards such asASME Section III [1] were being developed to address the relevant failure criteria. Most notable at that time was the introduction of fatigue analysis methods for vessel design.However, it is often overlooked that these were the days before computing methods were readily available, never mind the Finite Element (FE) analysis method we now take for granted that spawned the origins of NAFEMS and the Benchmark magazine you are now reading. Shell discontinuity or shell interaction theory was the ‘stateof-art’ technique that enabled membrane and bending stresses to be determined directly from interaction forces and moments from simple axisymmetric models. Hence the acceptance criteria used in the ASME Code were based upon limits of membrane stress or membrane plus bending stress. Stresses had to be categorised as being either primary or secondary (load or displacement controlled respectively) and the additional peak stress for fatigue was obtained from a fatigue strength reduction factor from test data, if you were lucky, but more often from conservatively applying a theoretical elastic stress concentration factor.