Improved Time‐History Analysis for Structural Dynamics. I: Treatment of Rapid Variation of Excitation and Material Nonlinearity

Methods are studied that permit larger time intervals to be used in structural dynamics calculations than are possible by the usual techniques. The size of time interval is often restricted by the rapidity of variation in excitation or by yielding and unloading in the structural members. In earthquake engineering, the input is proportional to ground acceleration, a rapidly varying function of time. In many structural dynamics problems when nonlinearity is present, rapid or even sudden changes of stiffness occur. Either the times of such rapid stiffness changes must be determined or else very small time intervals must be used nearby. Any factor that limits the size of time interval can result in a large volume of computation. A set of methods is developed to handle these limitations, finally permitting the use of fairly large time intervals while preserving high accuracy. Integrated displacements are used as the new variables in integrated equations of motion; a more accurate numerical integration method is employed; and an interpolation procedure eliminates the difficulties at yield and unloading.