r5.06.04 Algorithms for the time integration of the operator DYNA_VIBRA/BASE_CALCUL =” GENE “

Summary

This document describes the temporal integration schemes that are used to solve transient dynamic problems in linear mechanics in mode space, with, for some schemes, the possible consideration of localized nonlinearities such as shocks, friction, effort-displacement relationships and effort-speed relationships, and the possible use of substructuring. The diagrams of NEWMARK (implicit, limited here to the linear), DEVOGELAERE, and four explicit diagrams with adaptive time steps, ADAPT_ORDRE1 and ADAPT_ORDRE2RUNGE_KUTTA_32 and RUNGE_KUTTA_54 are shown.

• 1. Introduction
• 2. Methods for the temporal integration of a dynamic problem
  • 2.1. Introduction
  • 2.2. Implicit integration methods
  • 2.3. Explicit integration methods
• 3. Conclusion
• 4. Bibliography