ADAPTIVE .TIME STEPPING ANALYSIS FOR SOME DYNAMIC PROBLEMS

Abstract

In dynamic analysis, direct time -integration schemes are often used. Once a direct integration scheme is chosen, the accuracy of integration-depends significantly on the-time-step size. As the step size decreases the -accuracy of integration ° as well as computational-cost increases. The adaptive time stepping procedures are aimed at seeking the largest possible , step size to reduce the computational cost while maintaining a prescribed accuracy. For most direct integration schemes, a fixed time step size is usually used and is based frequently on intuition and experience. In practice, the dynamic process for a given problem can be, in some stages, very rapid and, in other stages, quite slow. It is therefore, unrealistic and unpractical to use a fixed step size in the whole process. To control the time discretization error, methods of estimating the error and then adjusting the time step accordingly for single. step algorithm is introduced. To study the efficacy of the adaptive algorithm, the problems of two categories have been tested. One is with analytically defined forcing functions and second is for earthquake excitation (with acceleration time-history as input). Direct integration- of equations -of motion may require -a -time .step_ which is much smaller than the sampling interval- at_ which the accelerogram has b'een--provided-. -This necessitates the need for interpolating the- digital :accelerogram, which is conventionally done by linear interpolation between samples. However, as the original digital accelerogram is essentially a band limited signal, linear interpolation modifies the frequency content of the data and inserts spurious high frequency components at the cost of reducing power in the low frequency range. High 'frequency insertion in input acceleration history, excites high frequency modes of the structure, thereby yielding a jittery response. So -band limited interpolation is employed in this study in conjunction with. adaptive time stepping schemes.