Automatic time stepping algorithms for implicit numerical simulations of non-linear dynamics

When an implicit integration scheme is used, variable step strategies are especially well suited to deal with problems characterized by high non-linearities. Constant step size strategies generally lead to divergence or extremely costly computations. An automatic time stepping algorithm is proposed that is based on estimators of the integration error of the differential dynamic balance equations. Additionally, the proposed algorithm automatically takes decisions regarding the necessity of updating the tangent matrix or stopping the iterations, further reducing the computational cost. As an illustration of the capabilities of this algorithm, several numerical simulations of both academic and industrial problems are presented.

[1]  T. Belytschko,et al.  Computational Methods for Transient Analysis , 1985 .

[2]  Anjan Dutta,et al.  Accurate computation of design sensitivities for structures under transient dynamic loads using time marching scheme , 1998 .

[3]  Jean-Philippe Ponthot.  Traitement unifié de la Mécanique des Milieux Continus Solides en Grandes Transformations par la Méthode des Eléments Finis , 1995 .

[4]  Michel Hogge,et al.  Efficient Implicit Schemes for Transient Problems in Metal Forming Simulation , 1996 .

[5]  Gregory M. Hulbert,et al.  Automatic time step control algorithm for structural dynamics , 1995 .

[6]  Dan Givoli,et al.  A simple time‐step control scheme , 1993 .

[7]  M. Géradin,et al.  Flexible Multibody Dynamics: A Finite Element Approach , 2001 .

[8]  J. Z. Zhu,et al.  The finite element method , 1977 .

[9]  Laurent Stainier,et al.  Augmented Lagrangian procedure for implicit computation of contact-impact between deformable bodies. , 2001 .

[10]  Jean-Philippe Ponthot,et al.  On relative merits of Implicit/Explicit Algorithms for Transient Problems in Metal Forming Simulation , 1994 .

[11]  Tod A. Laursen,et al.  Formulation and treatment of frictional contact problems using finite elements , 1992 .

[12]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[13]  Jean-Philippe Ponthot,et al.  Efficient implicit schemes for the treatment of the contact between deformable bodies: Application to shock-absorber devices. , 1999 .

[14]  Alberto Cardona,et al.  A Comparison Between Three Variable-Step Algorithms for the Integration of the Equations of Motion in Structural Dynamics , 1991 .