Third M.I.T. Conference on Computational Fluid and Solid MechanicsJune 14–17, 2005

On direct time integration in large deformation dynamic analysis

Mirza Muhammad Irfan Baig, Klaus-Jürgen Bathe*

Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

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Direct time integration is used widely for the solution of large deformation problems in solid and structural mechanics. Direct integration schemes that are unconditionally stable for linear dynamic problems are also used for nonlinear problems. However, unconditional stability may be lost in the nonlinear regime. The Newmark method (trapezoidal rule) is used widely but may become unstable when large deformations and long time durations are considered. A composite scheme is proposed for such analysis cases, and the results obtained using the trapezoidal rule and the composite formula in a test problem are given. These results indicate the value of the composite scheme.

Keywords:  Direct time integration; Nonlinear dynamic analysis; Stability; Large displacements

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