Insight Into Feasibility of Structure-Dependent Methods for Dynamic Analysis

The first family of structure-dependent integration methods have been successfully developed for nonlinear dynamic analysis. Although its numerical properties were evaluated and its performance was numerically corroborated for both linear and nonlinear systems, its feasibility is still under debate due to the lack of a theoretical background. It seems that an eigen-based theory can provide a fundamental basis for the proof of the feasibility of structure-dependent integration methods. This can be manifested from each major stage of the development of structure-dependent integration methods. Therefore, the development of the first family of structure-dependent integration methods will be presented and the correlation between each major stage and an eigen-based theory will be explored and explained. Besides, this developing sequence can lay a typical procedure for developing a general structure-dependent integration method.