Soroushian A.

Time integration is a practically accepted tool for the analysis of nonlinear dynamic structural models. The responses computed by these methods are, however, approximate, and even more, they do not always converge. Since, probable improper convergence is a significant shortcoming, many researches are in the last decades carried out on this subject. Nevertheless, yet, the problem is unresolved. After a comprehensive review on the concept, the author(s) have recently proposed a new methodology to overcome the problem. The efficacy of the new methodology is numerically verified through several papers. Nevertheless, since one of the deficiencies of the previous methodologies was in maintaining convergence in lengthy oscillations, in this paper, the new methodology is applied to nonlinear dynamic models studied in lengthy time intervals. The obtained results, clearly demonstrate the efficacy of the proposed methodology. Some References: 1- Soroushian, A. et al. (2005), “On practical integration of semi-discretized equations of motion Part 1: reasons for probable instability and improper convergence”, Journal of Sound and Vibration, 284(3-5), 705-731. 2- Soroushian, A. etal. (2005), 'Time integration of nonlinear equations of motion - Numerical Instabilty or numerical inconsistency ?', Proceedings of ENOC2005, Eindhoven, August 3- Soroushian, A. and Farjoodi, J. (2003), 'Responses' Convergence in time integration of non-linear semi-discrete equations of motion', Proceedings of RASD2003, Southampton, July. 4- Soroushian, A., et al. (2004), 'Responses' convergence for impact problems analyzed with different integration methods', Proceedings of SEMC2004, Cape Town, July.