Condensation methods for the dynamic analysis of large models

Calculations concerning the dynamic behaviour of a superstructure including soil-structure interaction require the modelling of the superstructure and of the soil. Discrete modelling of both mechanical systems, for example by finite elements, leads to a very large number n of degrees-of-freedom (dof; - problems which arise when only a finite section is taken instead of the halfspace are not repeated here). Because the calculation expenditure of the corresponding system of equations is proportional to n3, one is mainly interested in the dof of the superstructure including the interface dof with regard to the soil, economic dynamic investigations should be carried out with the number of dof as small as possible and with results as accurate as necessary. However, if one wants to model the subsystem soil (if necessary 3 dimensionally) by finite elements taking into account the wave length needed, the resulting number of dof easily exceeds an acceptible magnitude. In consequence, the number of dof of the submodel of the soil should be reduced with known inaccuracy. Model reduction methods are presented in (Meirovitch 1980, Craig 1981, Natke 1983), an overview is given in (Craig 1985) and a review given in (Greif 1986). In the following, some interesting methods are discussed briefly from the point of view of application; one of the methods is new, and it avoids the eigenfrequency-dependent inversion of a matrix due to condensation by modal decomposition and error modelling (static correction) (Natke 1986). The principle of this approach was introduced by McNeal (1971) (residual flexibility), and in the meantime has also been used in Bucher (1985) for undamped systems. (orig.)