Buckling performance of elliptical and tori-spherical heads with multi-mode geometric imperfections and variable wall thickness

This study delves into the buckling performance of elliptical and tori-spherical heads under internal pressure, focusing on the effects of multi-mode geometric imperfections and variable wall thickness. The research highlights the significant influence of geometric imperfections, such as eigenmode-affine imperfections, localized dimples, and circular cutouts, on the buckling behavior of these structures. It also explores how variations in wall thickness can enhance structural stability, particularly in critical regions like the apex. The study employs advanced numerical simulations using finite element modeling in Abaqus, providing a robust framework for capturing complex post-buckling paths and imperfection sensitivity interactions. The findings reveal that combined eigenmode imperfections produce intermediate buckling pressures, with localized effects dominating in flatter geometries. Hemispherical heads show reduced sensitivity, while torispherical heads are identified as the most vulnerable due to geometric discontinuities. The presence of local dimples further decreases buckling resistance, especially when interacting with the destabilizing second eigenmode. The analyses confirm that imperfection location is critical, with flaws near the apex causing the most severe reductions in buckling capacity. Variable wall thickness offers a practical countermeasure, significantly improving resistance, particularly against mode-2 deformation patterns. Overall, the study provides valuable insights into the design and optimization of pressure vessel heads, emphasizing the importance of accounting for compound imperfections, spatial sensitivity, and non-uniform wall thickness.