Determination of Optimal Flat-End Head Geometries for Pressure Vessels Based on Numerical and Experimental Approaches

The experimental and numerical analyses of the pressure vessels with different flat ends are presented and discussed in the paper. The main aim of the study is to propose the optimal flat head end geometry. The analyses are focused on the comparison of standardized geometries and with the proposed elliptical cut-out. The experimental tests with the application of strain-gauge measurements and numerical modeling of the pressure vessel are conducted. The behavior under low and high pressures and the influence of the residual welding stresses, material properties, and geometrical tolerances on the level of the plastic deformation in the flat end is discussed. It is presented that the rules given in the recent standard are not sufficient for optimal selection of the optimal geometry. It is observed that in certain geometries the deviations of the pipe thickness may lead to a significant increase of the equivalent stresses. The residual welding stresses have a significant influence on the stress and strain level—particularly in the stress relief groove (SRG). The performed study and comparison of the different geometries allow for the proposal of the optimal shape of the flat end. It appeared that the pressure vessels with SRG are the most optimal choice, particularly when elliptic shapes are in use. In some cases (i.e., pipe with wall-thickness equal to 40 mm and the flat end with circular SRG), the optimal configuration is reached for dimensions beyond the admissible by code range.