A New Family of Generalized-a Time Integration Algorithms for Structural Dynamics with Nonlinear Stiffness

摘要

The new numerical algorithm, which is called the new Generalized-α(G-α) method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-αmethod inherit undesired overshoot properties of a class of α- method. The algorithmic overshoot behavior leads often to convergence problems of the employed Newton-Raphson algorithm and overshoot is clearly exhibited by displacement and velocity even in the case of convergent Newton-Raphson iterations. Seven free parameters are introduced into the single-step three-stage algorithm formulations and the nonlinear internal force was approximated by means of the generalized trapezoidal rule. Then an analysis of the stability, accuracy, energy and overshoot properties of the proposed scheme was performed in the nonlinear regime. A value or range of value of the seven free parameters is given sequentially in the analysis process. The displacement, velocity and acceleration evaluated with the new algorithm was fully consistent and of order two. Significantly, new schemes eliminate inherent overshoot behavior of a class of traditional G-α method. The presented algorithms are zero-stable and can guarantees energy conservation or energy decay in the high-frequency range and are stable in an energy sense.