The present paper describes the theoretical basis of a new explicit virtual-pulse time integral methodology for nonlinear dynamics problems. Different from the existing numerical methods such as direct time integration or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed virtual-pulse time integral methodology has improved accuracy and stability characteristics, and is thus an excellent alternative for solving general nonlinear dynamic problems.
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The authors are very pleased to acknowledge the support, in part, by NASA-Johnson Space Center/LESC, Houston, TX. Partial support by the US Army High Performance Computing Research Center (AHPCRC) at the University of Minnesota on a contract from the Army Research Office and the Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN, is also gratefully acknowledged.