Unified Solutions to the Limit Load of Thick-Walled Vessels

Unified solutions to the elastoplastic limit load of thick-walled cylindrical and spherical vessels under internal pressure are obtained in terms of the unified strength theory (UST) and the unified slip-line field theory (USLFT). The UST and the USLFT include or approximate an existing strength criterion or slip-line field theory by adopting a parameter $b$⁠, which varies from 0 to 1. The theories can be used on pressure-sensitive materials, which have the strength difference (SD) effect. The solutions, based on the Tresca criterion, the von Mises criterion, the Mohr–Coulomb criterion, and the twin shear strength criterion, are special cases of the present unified solutions. The results based on the Mohr–Coulomb criterion $(b=0)$ give the lower bound of the plastic limit load, while those according to the twin shear strength criterion $(b=1)$ are the upper bound. The solution of the von Mises criterion is approximated by the linear function of the UST with a specific parameter $(b≈0.5)$⁠. Plastic limit solutions with respect to different yield criteria are illustrated and compared. The influences of the yield criterion as well as the ratio of the tensile strength to the compressive strength on the plastic limit loads are discussed.