مدل‌سازي رفتار چرخه‌‌يي سازه‌ها با درنظرگرفتن اثرات باريك شدگي، كاهش سختي، كاهش مقاومت، و لغزش

Modeling of Cyclic Performance of Structures Considering Pinching, Stiffness Degradation, Strength Deterioration, and Sliding Phenomena

شناخت و بررسي دقيق عملكرد چرخه‌يي سازه‌ها و توسعه‌ي مدل‌هاي تحليلي پارامتري آن مي‌تواند در پيش‌بيني و تخمين عملكرد و طراحي سازه‌ها كاربرد زيادي داشته باشد. در اين نوشتار به معرفي و توسعه‌ي يك مدل رياضي چرخه‌يي بر مبناي معادلات ديفرانسيل با مشتقات جزيي شامل تمامي اثرات كاهندگي از قبيل باريك‌شدگي، كاهش سختي، كاهش مقاومت، و لغزش پرداخته شده است. مدل ارايه‌شده براساس مدل توسعه داده‌شده‌ي دكتر مستقل است؛ كه براي انواع سيستم‌هاي چند درجه‌ي آزادي- چند خطي و با درنظرگرفتن هر يك از اثرات كاهندگي مذكور تحت تحريك‌هاي ديناميكي بررسي و توسعه داده شده است. در مدل ذكرشده، مشخصات اصلي سيكل‌هاي چرخه‌يي با استفاده از پارامترهاي قابل اندازه‌گيري سيستم سازه‌يي از طريق آزمايش قابل محاسبه است. به منظور نشان‌دادن توصيف واقعي عملكرد سيستم‌هاي چند درجه‌ي آزادي از طريق مدل پيشنهادي، مثال‌هايي تحت اثر بارهاي هارمونيكي بيان شده است.

Nonlinear hysteresis behavior is an important inherited property of any structural system. The shape of structural hysteretic behavior is a result of either changing material properties beyond the elastic range or changes in structural geometry (e.g. buckling, cracks) due to the subjected loads. The hysteretic response of a structure depends not only on the immediate deformation of elements, but also on the past history of the deformations, as it represents the energy dissipated by the structure. While, in some cases, such as well-designed hot-rolled structures, the hysteretic loops are quite smooth and stable, in some other cases, like cold-formed steel structures, they exhibit pinching, stiffness degradation, load deterioration, and sliding. Increasing the displacement under strong dynamic forces such as earthquakes, the hysteresis cycles enter from the elastic phase into the plastic phase. Hence, ignoring non-linearity in hysteresis behavior and neglecting degradation effects lead to ignoring much energy loss by dissipated energy mechanisms. Consequently, the designs would be uneconomical. In contrast, improper inclusion of the nonlinear hysteretic performance, such as neglecting sliding and strength deterioration, causes non-conservative structural design. Thus, considering real plastic deformation and proper non-linear behavior are essential and important in the assessment of structural stability. In this paper, an analytical model is introduced to show the hysteresis behavior of the structures, considering degradation phenomena, including pinching, stiffness degradation, strength deterioration and sliding effects. This model is based on a modified Mostaghel model, which is developed considering a single degree of freedom (SDOF) mechanical system; and is characterized using a system of partial differential equations and some specific functions which are mainly derived from the Signum function. The proposed model is developed to a multi-degree of freedom (MDOF) multi-liner model and would be able to capture the key features of the hysteretic cycles of any structure using some measurable system parameters through tests. In order to demonstrate the degrading phenomena of the hysteresis behavior of the structures, several examples are presented to show that the proposed analytical model is capable of providing realistic description of the structural hysteretic performance.