Application of an Innovative Precise Integration Method in Solving Structural Dynamics, Phase(I): Linear Systems

Application of an Innovative Precise Integration Method in Solving Structural Dynamics, Phase(I): Linear Systems

A very popular approach to conduct structural dynamic response analysis is to first formulate its dynamic equilibrium equations of motion, and then employ a step-by-step time integration scheme to solve the equations such that dynamic equilibrium is satisfied at discretized time instants. The selection of time step size depends on the features of the time integration approach, and should consider its numerical stability, desired accuracy, predominant frequencies of the analyzed structure as well as the major characteristics of the external loadings. In case of high dominant structural frequencies or large loading variation, a sufficiently small time step is usually favored in order to achieve satisfactory numerical accuracy. The authors conduct two major case studies of employing both force and momentum equations of motion together with a so-called “Precise Integration Method(PIM)” to solve for dynamic structural response. The proposed method is insensitive to the selection of time step size in case of large loading variation and is able to keep superior numerical stability and accuracy characteristics of the original PIM.