Theoretical Research Of Modified Force Analogy Method Using IRS Dynamic Condensation

The increasingly complex building structures come with more cost on the structural analysis. There is a urgent need for us to seek a reliable method which can simplify structural modal and save the cost on the analysis. Force analogy method(FAM) is a typical method for non-linear analysis which could be used in strain-hardening materials、strain-softening materials and elastic-plastic materials. Combined with the state space function, it could be used to solve dynamic problems in structural analysis. And the computing efficiency is significantly improved.Currently, researches and applications about FAM are mostly based on static condensation, ignoring the inertia force on slave coordinates. Then the relation of the displacement between master and slave degrees of freedom is derived from the dynamic equation. A reduced order model is got when the condensation of the system matrix is based on it. However, great calculation errors come up when this method is used to analyze high order models. Improved reduced system (IRS) dynamic condensation method is based on static condensation and takes inertial effects into account which is more accurate for reducing dynamic model with condensation. Considering the error of structural analysis from static condensation, IRS dynamic condensation is used to modify the force analogy method. Theoretical formulas of the modified force analogy method are then derived in this paper. And structural non-linear time history analysis is presented by using the modified method. The basic theory of force analogy method is further improved.Based on the existing theoretical research results, this paper has carried on the revision and improvement, and the main research contents include:(1) The general situation of the basic theory and researches of force analogy method are reviewed in great detail. The present commonly used dynamic condensation theories and researches are summarized and compared, and the formula derivations and their applications are pointed out, in terms of their advantages and disadvantages. The derivation process of IRS dynamic condensation is presented in detail.(2) The idea of using IRS dynamic condensation to modify force analogy method is put forward. The formulas of force analogy method using IRS dynamic condensation are derived, then the energy equations and state space equations are presented. Programs of the modified method are compiled using MATLAB software to realize nonlinear time history analysis of the steel frame structure.(3) A steel structure analysis model is established, and force analogy method based on static condensation is applied to study non-linear time history analysis of the structural seismic response, then the results are compared with that of using force analogy method based on IRS dynamic condensation. The results show that the modified force analogy method for nonlinear analysis is feasible and accurate.