الگوريتم شبيه ‌سازي تصادفي براي تعيين توزيع احتمالاتي و بيشينه‌ي پاسخ لرزه‌ يي سيستم‌هاي ديناميكي

A Stochastic Simulation Algorithm for Determination of Probability Distribution and Extreme Value of Seismic Response of Dynamic Systems

با توجه به رفتار غيرخطي سيستم‌هاي سازه‌يي و تصادفي‌بودن تحريك ورودي، يكي از راه‌حل‌هاي منطقي براي تعيين پاسخ احتمالاتي سازه‌ها تحليل تاريخچه‌ي زماني تحت مجموعه‌يي از ركوردهاست. اما اين موضوع مستلزم انجام تعداد زيادي تحليل‌هاي ديناميكي است، كه مي‌تواند با هزينه‌ي محاسباتي زيادي همراه باشد. اين در حالي است كه نياز به روشي ساده و نسبتاً دقيق جهت تعيين خصوصيات پاسخ سيستم است. بنابراين، توسعه‌ي يك روش محاسباتي كه جايگزين روش‌هاي دقيق ديناميكي غيرخطي قرار گيرد، هدف اين پژوهش است. در اين پژوهش يك روش جامع و بسته‌ي مبتني بر يك الگوريتم محاسباتي ساده براي تعيين توزيع احتمالاتي و بيشينه‌ي پاسخ سيستم‌هاي ديناميكي يك و چند درجه‌ي آزاد تحت تحريك‌هاي گوسي مانا و غيرمانا ارايه شده است. دقت روش مذكور در مقايسه با روش دقيق، از طريق تعداد زيادي تحليل ديناميكي غيرخطي ارزيابي شده است.

A comprehensive closed-form approach is presented to approximately evaluate the probability distribution of displacement of SDOF and MDOF systems subjected to stationary and non-stationary Gaussian excitations. The probability distribution of displacement of a SDOF system is investigated on the basis of statistical relations, and a closed-form method is presented to approximately detect the structural response without any need to perform exact dynamic analysis. Buildings with BW hysteretic behavior can easily be modeled with the aid of the proposed approach. The approximate procedure can significantly facilitate the utilization of non-stationary models in engineering practice, because it avoids computational difficulties. The method is based on the approximation of a non?stationary process by an equivalent stationary process. In this study, six systems with initial periods of 0.4, 0.6, 0.8, 1, 1.2 and 1.4 sec. are considered for the validation of the presented relations. With the aid of the determined linearization coefficients of the system, the target displacement and IDA curves are also determined. The previous investigations into development and evaluation of the coe?cient method to compute the target displacement used computer models of the buildings; an exhaustive list of references is available in the FEMA-440 report. The “exact” value of the target roof displacement was taken as the peak roof displacement computed by nonlinear response history analysis of the computer model subjected to selected earthquake motion at its base. But, generally, determining the probability distribution of structural demands and the response of structural systems at different confidence levels, based on nonlinear dynamic analysis, can be very time consuming. With regard to this need, developing a simple computational approach that replaces exact methods and the time consuming dynamic analysis of structures is the aim of this research. The computed target displacements for six systems are compared with the target displacement under 300 non-stationary records and from nonlinear static procedure in FEMA-440. In comparison to the exact dynamic analysis procedure, the proposed approach provides an acceptable probabilistic result with less computational time and cost.