Dynamic time-history analysis

Dynamic analysis is commonly used to predict the nonlinear inelastic response of a structure subjected to earthquake loading (evidently, linear elastic dynamic response can also be modelled for as long as elastic elements and/or low levels of input excitation are considered). The direct integration of the equations of motion is accomplished using the numerically dissipative -integration algorithm [Hilber et al., 1977] or a special case of the former, the well-known Newmark scheme [Newmark, 1959], with automatic time-step adjustment for optimum accuracy and efficiency (see Automatic adjustment of load increment or time-step).

Modelling of seismic action is achieved by introducing acceleration loading curves (accelerograms) at the supports, noting that different curves can be introduced at each support, thus allowing for representation of asynchronous ground excitation.

In addition, dynamic analysis may also be employed for modelling of pulse loading cases (e.g. blast, impact, etc.), in which case instead of acceleration time-histories at the supports, force pulse functions of any given shape (rectangular, triangular, parabolic, and so on), can be employed to describe the transient loading applied to the appropriate nodes.