RESPONSES OF BLAST LOADING BY COMPLEX TIME STEP METHOD - Fung, T.C.; Chow, S.K. (Journal of sound and vibration, 1999)
Blast loading is often described by means of high order functions, and step-by-step time integration algorithms are commonly used to evaluate the numerical solutions. The time step size for the Newmark method has to be very small in order to integrate the high order loading accurately. Recently, a complex time step formulation has been proposed to construct unconditionally stable higher order accurate time step integration algorithms with controllable numerical dissipation where loading with high order variation can be tackled without difficulties. The responses at the end of a time step are obtained by linearly combining the responses at various complex sub-step locations with different weighting factors. In this paper, the complex time step method is extended to evaluate the responses within a time step. The required weighting factors anywhere within a time step can be worked out systematically. Besides, there are some locations within a time step with one order higher in accuracy. A procedure is also proposed to evaluate the modified excitation at various complex sub-step locations. To verify the complex time step method, a single-degree-of freedom system subject to blast loading described by a fourth order polynomial is considered in detail. A multi-degree-of-freedom system is also analyzed. Excellent performance over the Newmark method is noted. It is possible to evaluate the responses due to blast loading by using just one time step.