Responses of blast loading by complex time step method

Blast loading is often described by means of high order functions, and step -by-step time integration algorithms are commonly used to evaluate the nume rical solutions. The time step size for the Newmark method has to be very s mall in order to integrate the high order loading accurately. Recently, a c omplex time step formulation has been proposed to construct unconditionally stable higher order accurate time step integration algorithms with control lable numerical dissipation where loading with high order variation can be tackled without difficulties. The responses at the end of a time step are o btained by linearly combining the responses at various complex sub-step loc ations with different weighting factors. In this paper, the complex time st ep method is extended to evaluate the responses within a time step. The req uired weighting factors anywhere within a time step can be worked out syste matically. Besides, there are some locations within a time step with one or der higher in accuracy. A procedure is also proposed to evaluate the modifi ed excitation at various complex sub-step locations. To verify the complex time step method, a single-degree-of freedom system subject to blast loadin g described by a fourth order polynomial is considered in detail. A multi-d egree-of-freedom system is also analyzed. Excellent performance over the Ne wmark method is noted. It is possible to evaluate the responses due to blas t loading by using just one time step. (C) 1999 Academic Press.