Two-Level Consistent Secant Operators for Cyclic Loading of Structures

Abstract

Two-level consistent secant operators are proposed for the nonlinear simulation of structures especially under cyclic loading. At the structural level, the quasi-Newton (Q-N) update of stiffness matrix is used to search the equilibrium of the overall system. At the material level, the general formulas of secant operators are proposed for the nonlinear material model. The consistency between the Q-N stiffness matrix at the structural level and the secant operator at the material level is proposed and considered as a good trade-off between efficiency and robustness. Applications are made to numerical examples that include strain-softening and cyclic loading. Significant improvements are demonstrated in relation to the full Newton methods and the inconsistent secant methods.