Nonlinear Finite Element Analysis of Class 1 Pressure Vessels

The rules of design by analysis have been widely accepted for the Class 1 Nuclear Pressure Vessel, and two methods, stress classification method (based on the linear analysis) and the direct route (nonlinear analysis by Finite Element (FE) method), have been developed. In the stress classification method, the stress is classified in primary, secondary and peak stresses, and there are many shortcomings in this method. The stress classification is only easy in simple cases, like cylindrical shell under axisymmetric loads. In some cases the elastic analysis result can be non-conservative in particular when a part of primary stresses is considered secondary, like thermal expansion in some piping systems. When the geometry or the loads are more complex (such as, nozzles of reactor pressure vessels (RPV)), it will be an extremely conservative approach if a large part of stresses is considered as primary. Consequently, the direct route based on FE method is an efficient alternative to the linear analyses, and one of the major advantages is to suppress the discussion on the “stress classification in primary versus secondary” associated with the elastic analysis. This work reviews the existing linear design rules in the different codes, such as ASME Code NB 3200 and RCC-M Code B 3200, firstly. Then a typical case study of a large class 1 vessel nozzle, a RPV nozzle, under pressure and piping loads based on linear (stress classification method) and nonlinear rules (direct route) is presented. The case will consider 2D geometries under axisymetrical loads, and the failure models of plastic collapse, plastic instability and local failure are studied. Lastly, a set of proposals to improve the design rules are given.