A computational procedure for the implementation of equivalent linearization in finite element analysis. - Emam, H.H (Earthquake engineering & structural dynamics.)
This paper deals with the practical implementation of the statistical equivalent linearization method (EQL) in conjunction with general FE-analysis to evaluate non-linear structural response under random excitation. A computational procedure is presented which requires the non-linear part of the system to be subdivided into suitable sub-domains (elements). Each element is independently linearized using only a minimum number of co-ordinates. A local co-ordinate system is introduced using linear transformations of the global (master) degrees of freedom. Restoring forces and non-linear constitutive laws are defined by the local co-ordinates of each element. The linearization coefficients are further transformed back to establish the global linearized system. The procedure has, on one hand, the ability to use any desired linearization criterion and, on the other hand, it can be combined with highly developed procedures to determine the response of arbitrary large FE-models. To illustrate the applicability of the procedure, two different non-linear systems are analysed under bi-directional earthquake excitation.