The post yield behavior of rigid-perfectly plastic solids at the collapse load is studied based on the finite deformation theory. By using the general duality theory developed by Gao-Strang (1989), a global stability criteria is proposed and a pair of dual extremum principles, expressed in terms of displacements, displacement rates and the Kirchhoff stresses are established for plastic collapse analysis. It is proved that under large deformations, the existence of the plastic limit state at the collapse load depends on the directional derivative of a so-called complementary gap function. The application to the nonlinear plastic collapse theory yields a pair of dual bounding theorems for limit loading factor associated with any transient displacement of the deformed body when the global extremum criteria are satisfied.
Gao Y. Extended bounding theorems for nonlinear limit analysis.Int J Solids Structures, 1991, 27 (5): 523–531MATHCrossRefGoogle Scholar
Bielski WR and Telega JJ. A contribution to contact problems for a class of solid and structures.Arch Mech, 37: 303–320Google Scholar
Galka A and Telega JJ. The complementary energy principle for a model of shells with an independent rotation vector.Z ang Math Mech, 1990, 70: T253–256MATHMathSciNetGoogle Scholar
Galka A and Telega JJ. The complementary energy principle as a dual problem for a specific model of geometrically nonlinear elastic shells with an independent rotation vector: general results.Eur J Mech, A/Solids, 1992, 11(2): 245–270MATHMathSciNetGoogle Scholar