Research On Equivalent Linearization Method Applied In Earthquake Engineering

The displacement-based seismic design approach is one of the effective ways to realize the structural performance-based seismic design and one of its main subjects is to determine the structural displacement demand. The equivalent linearization method (ELM) is a common method to calculate the structural nonlinear displacement demand, in which the maximum deformation of a nonlinear structure is estimated by the maximum deformation of an equivalent linear structure with more flexible lateral equivalent stiffness and higher viscous equivalent damping than those of the nonlinear structure. The appropriate values of equivalent system parameters are the key points to insure the validity of ELM in practical application.Previous researches have proved that using the secant stiffness as the equivalent stiffness of ELM will produce a relative large error to estimate the displacement demand. As a result of research progress of ELM, currently the statistical approach becomes the regular method adopted for determining the system parameters of ELM. However, the traditional statistical approach still exist two following deficiencies:â‘ The evaluation criterions based only on the standard deviation or the probability distrubtion of displacement error, which adopted by the traditional statistical approach, will bring errors to the results. And both evalucation criterions can not consider the structural safety in ELM.â‘¡Since it will search the optimal combination of equivalent parameters in their whole possible ranges, the extensive demand of computation is needed and its sloving efficiency is very low.Based on the above consideration, a new evaluation criterion taking account of both the standard deviation and probability distrubtion of the displacement error is proposed to determine the equivalent parameters. The criterion not only fetchs up the deficiency of previous ones but also makes it possible to consider the structural safety in ELM. In order to improve the solving efficiency of the traditional statistical approach, a new statistical approach utilizing the technique of particle swarm optimization (PSO) is developed to determine the parameters of equivalent linearization method. Numerical analyses indicate that the proposed PSO algorithms improve the parameter solving efficiency to a great extent with the similar evaluation precision. Meanwhile, four PSO algorithms are investigated respectively for their solving efficiency and the results indicate that PSO algorithm with the constriction factor is the best one.Numerical analyses are carried out to calculate the equivalent parameters of two SDOF systems using the above research results with the consideration of different struactual safety level. The SDOF systems hold the bilinear hysteretic and stiffness degrading nonlinear properties and the assumption of constant ductility ratio and constant strength reduction ratio are adopted respectively. For the convenience of engineering application, the analytical expressions for both equivalent parameters are deduced and their precisions are checked by the followed error analysis.