ABSTRACT
ABSTRACT: A rational approach is proposed for the time integration of the dynamic equations arising in nonlinear structural problems, which employs a series of innovative concepts, e.g.: independent assumptions for the velocities and momentum type variables, use of different approximations for the test functions and the variables itself, and abandonment of the convention concerning the vanishing of the test functions at the time boundaries. The presented methodology offers a systematic and mathematically consistent procedure for time integration, ensures consistency and stability, and avoids flaws of existing techniques. Conservation properties are examined employing a form of Noether’s Theorem. Furthermore, existing integration schemes may be theoretically justified by the present approach. The methodology is applied to the analysis of systems under moving loads and masses. Since this class of problems contains Dirac’s delta function and its time derivatives, the effective numerical treatment of the governing equations offers a challenging problem.
