کاربرد روش انرژی اصلاح‌شده در تحلیل رفتار غیرخطی چرخه‌ای سازه‌ها

نوع مقاله : علمی - پژوهشی

نویسندگان

1 گروه عمران، دانشگاه تربیت دبیر شهید رجایی

2 دانشیار، دانشکده مهندسی عمران، دانشگاه تربیت دبیر شهید رجایی، تهران، ایران

3 گروه ریاضی، دانشگاه تربیت دبیر شهید رجائی

چکیده

المان‌های سازه در برابر بارهای لرزه‌ای رفتار چرخه‌ای یا هیسترزیس از خود نشان می‌دهند، به همین دلیل تحلیل این نوع رفتار سازه‌ای از اهمیت بالایی در مهندسی زلزله برخوردار است. از طرفی، با توجه به پیچیدگی این نوع از رفتار غیرخطی و عدم وجود یک تابع صریح برای بیان نیروی مقاوم برحسب تغییر شکل در این حالت، مدل‌سازی و تحلیل پدیده هیسترزیس یکی از پیچیده‌ترین مسائل در دینامیک غیرخطی سازه‌ها است. در این تحقیق، روش انرژی اصلاح‌شده، به‌عنوان یک روش عددی برای تحلیل این نوع سیستم‌ها به کار گرفته می‌شود. به منظور نیل به اهداف این تحقیق، در ابتدا مرور کوتاهی بر روی مدل‌های هیسترزیس الاستوپلاستیک می‌گردد. در ادامه با فرمول‌بندی معادلات تعادل انرژی سیستم برای سازه‌های تک درجه آزادی با رفتار غیرخطی مادی چرخه‌ای، الگوریتم اجرای کامپیوتری این روش به‌صورت گام‌به‌گام ارائه می‌شود. یک مثال تک درجه آزادی ساده با سختی دوخطی- الاستیک تحت ارتعاش آزاد با استفاده از روش پیشنهادی به‌صورت جزئی برای آشنایی هر چه بیشتر خواننده با مفهوم روش پیشنهادی ارائه می‌گردد. سپس، سازه‌های تک درجه و چند درجه آزادی با رفتار الاستوپلاستیک با استفاده از روش پیشنهادی تحلیل شده و نتایج با روش‌های عددی رایج دیگر صحت سنجی می‌گردند. به‌طورکلی، نتایج این تحقیق نشان داده است که این روش در مقایسه با سایر روش‌های موجود در تحلیل رفتار چرخه‌ای سازه‌ها از دقت مناسبی برخوردار بوده و با کاهش مرتبه در معادله حاکم بر مساله، عدم نیاز به تعریف پارامترهای تنظیم‌کننده اضافی در حل عددی و سادگی در اجرای کامپیوتری، به‌خوبی می‌تواند با ایجاد حس فیزیکی در تحلیلگر در بررسی پاسخ سیستم‌های هیسترزیس در برابر بارهای لرزه‌ای به کار گرفته شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Application of modified energy method in the nonlinear cyclic behavior of structures

نویسندگان [English]

  • mohammad Jalili Sadr Abad 1
  • Mussa Mahmoudi 2
  • reza Mollapour Asl 3
1 Department of Civil Engineering. Shahid Rajaee Teacher Training University
2 Associate professor, Department of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
3 Department of mathematics. Shahid Rajaee Teacher Training University
چکیده [English]

Structural elements exhibit cyclic behavior or hysteresis under seismic loads; therefore, the analysis of this type of response is of great importance in Earthquake Engineering. On the other hand, due to the complexity of this nonlinear behavior and the absence of an explicit function to express the restoring-force regarding deformation, the modeling and analyzing of the phenomenon of hysteresis is one of the most complex problems in nonlinear dynamics of structures. In this research, the modified energy method is used as a numerical method to analyze this type of systems. To achieve the objectives of this research, a brief review on elastoplastic hysteresis models is initially considered. Then, by formulating the energy equilibrium equations for single-degree freedom structures with nonlinear material-cyclic behavior, the computer-implemented algorithm of this method is presented in a step-by-step manner. A simple single-degree-of-freedom example with bilinear-elastic stiffness under free vibration using the proposed method is provided for the reader's familiarity with the concept of the proposed method. Subsequently, a one-story structure and a multiple-degrees-of-freedom system with elastoplastic behavior are analyzed using the given method, and conventional numerical methods are utilized to verify the results. In general, the results of this study showed that this method has a good accuracy compared to other techniques in the analysis of hysteresis behavior of structures. In addition, this approach decreases the order in the governing equation of the problem; and, there is no need to define the additional adjustable parameters in numerical solution. On the whole, the presented technique with simplicity in computer execution can be used by creating a physical sense in the analyst to calculate the response of hysteresis structural systems.

کلیدواژه‌ها [English]

  • Cyclic behavior
  • modified energy method
  • elasto plastic behavior
  • seismic analysis
  • time history analysis
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