Response analysis of hysteretic multi-storey frames under earthquake excitation

Local incremental stiffness relations are formulated for a class of elasto-plastic beam elements. The earthquake acceleration is modelled as a filtered white noise process. The Itǒ differential equations of the integrated system made up of the structural system and the excitation process are then formulated. Instead of the original system an equivalent nonlinear system is considered, in which the drift vector is given by a series expansion of order n ≧ 1, where n = 1 represents the well-known case of equivalent linearization. Only components of the drift vector representing the non-analytieal constitutive equations are replaced by a polynomial expansion. The coefficients of this expansion are determined from a least mean square criterion, and are sequentially updated. Especially an equivalent system with a cubic expansion to the drift vector is investigated. The hierarchy of statistical moment equations is closed by a cumulant neglect closure scheme. The method has been applied to a two-storey frame. The results are compared to those of numerical simulation, and provide substantial improvements compared to equivalent linearization.