شبيه سازي حلقه هاي پسماند نيرو- تغييرمكان جانبي در جداسازهاي اليافي با درنظرگرفتن اثر مولينز

The Simulation of Mullins’ Effect in Load-Displacement Hysteresis Loops of Fiber-Reinforced Elastomeric lsolators

در اين مقاله جداسازهاي لرزه‌اي الاستومري مسلح به الياف (يا به اختصار جداسازهاي اليافي) معرفي شده‌اند. با توجه به شرايط مرزي در سطوح تماس، جداسازهاي اليافي در دو كاربري متصل (سطوح تماس داراي اتصال مكانيكي با تكيه گاه هاي جداساز) و غير متصل (سطوح تماس بدون اتصال مكانيكي با تكيه گاه هاي جداساز) قابل استفاده است. هدف اصلي اين مقاله شبيه سازي حلقه هاي پسماند نيرو- جابه‌جايي جانبي جداسازهاي اليافي غير متصل است. شاخصه اصلي در رفتار جانبي جداسازهاي ياد شده وجود سخت‌شدگي ثانويه پس از نرم‌شدگي تدريجي اوليه جداساز است. با توجه به اثر مولينز، مشخصات مكانيكي جداساز در سيكل هاي اول جابه‌جايي هاي هم دامنه متفاوت از ساير سيكل هاي جابه‌جايي است. از اين رو نسخه اصلاح شده اي از مدل بوك- ون براي شبيه سازي رفتار جانبي جداسازهاي مورد نظر با توجه به ويژگي رفتاري خاص آنها ارايه شده است. مقايسه حلقه‌هاي پسماند آزمايشگاهي و حلقه‌هاي شبيه سازي شده نشانگر دقت مناسب نسخه ارايه ‌شده مدل بوك- ون در شبيه‌ سازي رفتار تاريخچه زماني نيرو- تغيير مكان جانبي جداسازهاي لرزه اي مورد نظر است.

This paper briefly reviews Fiber Reinforced Elastomeric Isolators (FREIs) as a relatively new type of elastomeric bearings. In comparison with conventional Steel Reinforced Elastomeric Isolators (SREIs) that are reinforced with steel plates, FREIs utilize fiber fabric layers as the reinforcement material. The fiber reinforcement is employed to prevent the lateral bulging of elastomer layers when the bearing is subjected to vertical compression. Fiber reinforced isolators are categorized in two groups depending on the boundary conditions at top and bottom surfaces of the bearing. These are “bonded-“ and “unbonded-“ FREIs. The main objective of this paper is to simulate the lateral load-displacement hysteresis loops of unbonded-FREIs. In an unbonded-FREI, no bonding is provided between the bearing and its top and bottom contact supports. As such, shear forces are transferred via friction at the contact surfaces. When an unbonded-FREI is deformed laterally, portions of its contact surfaces roll off the contact supports, and the bearing exhibits a specific deformation called “rollover deformation”. As a result of rollover deformation, the effective lateral stiffness of the bearing is decreased significantly. This in turn improves the seismic isolation efficiency due to the increased base isolated period of bearing. The ultimate lateral displacement in an unbonded-FREI may achieve when the originally vertical faces of the bearing contact top and bottom supports. Lateral load- displacement response in an unbonded-FREI is characterized with a gradual softening (due to rollover deformation) that is followed by a stiffening behavior at the ultimate stage of lateral bearing displacement. Under a cyclic excitation, the response characteristics of bearing during the first load-cycle are different than the subsequent cycles of the same load amplitude. This phenomenon that is specific to elastomeric materials is known as Mullins’ effect. In this paper an extended Bouc-Wen model is developed to simulate the lateral load-displacement hysteresis loops of unbonded-FREIs. The model captures the gradual softening and ultimate stiffening behavior in the load-displacement curve of the bearing, and addresses the Mullins’ effect in the simulation of hysteresis loops. The proposed model comprises two simultaneous coupled equations which employ six constant coefficients altogether. To determine these coefficients, the model is fitted to experimentally-evaluated load-displacement hysteresis loops of prototype bearings. The experimental loops are obtained from cyclic shear tests that are carried out on the bearing while it is subjected to a constant vertical compression. In order to account for Mullins’ effect, an individual set of coefficients corresponding to unscragged loops (the first cycle of each displacement amplitude) are evaluated. The second set of coefficients is attributed to scragged response (subsequent cycles of each displacement amplitude) of the bearing. To simulate the load-displacement hysteresis loops, the proposed model switches between the first and the second set of coefficients depending on the unscragged or scragged state of the elastomer, respectively. A constraint is imposed on the model to assure its continuity when the model coefficients are alternated. Comparison between analytical and experimental results (shake-table test data) indicates that the proposed model is accurate in dynamic response simulation of the unbonded-FREIs studied in this paper.