The Earthquake Engineering Online Archive

Discrete Relative Equilibria of Time-Stepping Algorithms for a Model Problem of Nonlinear Dynamics

Romero, Ignacio; Armero, Francisco

UCB/SEMM-1999/03, Dept. of Civil and Environmental Engineering, University of California, Berkeley, 1999-02, 23 pages (500/C23/1999/03)

A simple analysis is presented that highlights the behavior of commonly used time-integration schemes when applied to mechanical systems that possess relative equilibria. Using a spring/mass nonlinear system, the authors study discrete solutions to relative equilibrium conditions of the trapezoidal rule, a one-parameter family of dissipative Newmark methods, the midpoint rule, the energy-momentum and a new method developed by the authors, the energy-dissipating momentum-conserving (EDMC) scheme. The simplicity of the mechanical model allows to be found explicit conditions for the discrete dynamics generated by each of the schemes that either prohibit or assure the existence of discrete motions which accurately approximate relative equilibria.

Available online: http://nisee.berkeley.edu/documents/SEMM/SEMM-99-03.pdf (1 MB)