SEISMIC RESPONSE ANALYSIS OF NONLINEAR STRUCTURES USING THE STOCHASTIC EQUIVALENT LINEARIZATION TECHNIQUE

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 linearization technique. The nonlinear viscoelastic properties of the structures are modeled in terms of an equation of motion which linearly involves the auxiliary variables as part of the restoring force and of the auxiliary equation which described a nonlinear relationship among the story displacements and auxiliary variables and their time derivatives. This auxiliary equation is linearized with the aid of a stochastic linearization technique which minimizes the expected value of the square of the difference between the nonlinear and linearized auxiliary equations. The linearized problem then involves a set of two linearization coefficients which are functions of time.; 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 two 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. In each time interval and at each literature cycle, the linearization coefficients are assumed to be time-invariant in each story. The dynamic analysis is based on the modal method which, however, requires the use of complex eigenvalues and eigenvectors. This is due to the fact that one of the matrices involved in the eigenvalue problem is non-symmetric.; The proposed analysis produces covariance functions and hence variance functions of the story displacements and velocities among other response quantities. These covariance and variance functions play an important role in estimating structural safety and reliability.; The variance function developed on the basis of the present analysis and those constructed by means of the Monte Carlo technique show a reasonable agreement.