Analysis of elasto-plastic thin-shell structures via modified stress resultant approach and absolute nodal coordinate formulation

A new elasto-plastic thin shell finite element of the absolute nodal coordinate formulation is proposed to improve the computation efficiency for the shell structure undergoing both large deformations and finite rotations based on the Kirchhoff–Love theory and stress resultant method. The Ilyushin–Shapiro plastic model with linear isotropic hardening is adopted to develop the plastic formulation of a shell element. The model is formulated directly in terms of stress resultants, and thus the through-thickness integration associated with the classical method is entirely removed. In particular, a modified approach is proposed to solve the problem associated with inaccurate hardening modulus. The corresponding return-mapping algorithm is shown to update the values of stress, and a strategy is introduced to choose the active yielding surfaces in the algorithm. Furthermore, the Jacobian of internal forces is deduced via deriving the consistent elasto-plastic tangent moduli. The arc-length method is used to accurately track the load–displacement equilibrium path in the buckling analysis of an elasto-plastic thin shell. The dynamics of the thin shell is also studied by using the generalized-alpha algorithm. Several numerical examples are presented to verify the accuracy and efficiency of the proposed formulation.