Seismic response analysis of nonlinear structures

Abstract

A solution method for the response of a class of nonlinear viscoelastic shear building structures subjected to stochastic excitation has been developed by means of a stochastic equivalent linearlization technique. The nonlinear viscoelastic properties of the structures are modelled in terms of an equation of motion which linearly involves the auxiliary variables as part of the restoring force and in terms of the auxiliary equation which describes a nonlinear relationship among the story displacements and auxiliary variables and their time derivatives. This auxiliary equation is linearized using a stochastic linearization technique. The integration of the equation of motion together with the linearized auxiliary equation is carried out numerically using the state-vector formulation. In doing so, an iterative upgrading of the values of the linearization coefficients is performed simultaneously for all the stories in the first time interval until a convergence criterion is satisfied. The iterative process is then repeated in the time intervals that follow, until the entire time interval for which the dynamic analysis is performed is covered. The analysis is based on the modal method which, however, requires the use of complex eigenvalues and eigenvectors. The proposed analysis produces covariance functions of the story displacements and velocities among other response quantities. These covariance functions play an important role in estimating structural reliability. The covariance function thus developed agrees very well with that obtained by the Monte Carlo technique. © 1986.