شبیه‌سازی میرایی تشعشعی با استفاده از لایه کاملاً تطبیق یافته در مدل‌سازی عددی به روش اجزای محدود

نوع مقاله : Articles

نویسندگان

پژوهشکده مهندسی ژئوتکنیک، پژوهشگاه بین المللی زلزله شناسی و مهندسی زلزله، تهران، ایران

چکیده

در مسائل الاستودینامیک که پدیده انتشار امواج بخش عمده­ای از آن را تشکیل می­دهد، مدل‌سازی و محاسبات مربوط به محیط نامحدود، مستلزم استفاده از مرز مصنوعی برای لحاظ نمودن میرایی تشعشعی است. در پژوهش حاضر، برای تحلیل پاسخ دینامیکی یا لرزه­ای ساختگاه با استفاده از روش اجزای محدود در حوزه زمان، برنامه­ای به کمک نرم‌افزار MATLAB تهیه شد. در مدل‌سازی پدیده انتشار موج، لایه کاملاً تطبیق یافته1 (PML) که توانایی جذب و میرا نمودن امواج تحت هر زاویه برخورد و فرکانس را به لحاظ تئوریک دارد در روش اجزای محدود پیاده­سازی و برای در نظر گرفتن میرایی تشعشعی استفاده شده است. آنچه در مقاله حاضر ارائه می­شود، اعتبارسنجی و بررسی عملکرد لایه تطبیق یافته می­باشد که این امر از طریق حل سه مسئله مورد ارزیابی قرار گرفته است. در مسئله اول، ارتعاش شالوده صلب بدون جرم واقع بر سه حالت نیم­فضای بینهایت، لایه بر روی بستر صلب و لایه بر روی نیم­فضای بینهایت با استفاده از PML تحلیل و نتایج با مدل گسترده2 مقایسه شده است. در مسئله دوم، کارایی PML در مدل‌سازی انتشار امواج سطحی مورد ارزیابی قرار گرفته است. در مسئله سوم نیز، به بررسی بزرگنمایی امواج در دره نیم‌دایره­ای به کمک PML پرداخته شده است. نتایج حاصل، نشان­دهنده‌ی قابلیت مناسب PML در شبیه­سازی میرایی تشعشعی برای محیط نامحدود می­باشد که در واقع بیان­کننده‌ی جذب امواج برگشتی غیرواقعی و سازگار بودن PML با محیط اصلی است.

کلیدواژه‌ها


عنوان مقاله [English]

Radiation Damping Simulation in Finite Eelements Method Analysis Using Perfectly Matched Layer (PML)

نویسندگان [English]

  • Mohammad Davoodi
  • Abbas Pourdeilami
  • Mohammad Kazem Jafari
Geotechnical Engineering Department, International Institute of Earthquake Engineering and Seismology
چکیده [English]

In this research, perfectly matched layer has been implemented in the finite element method to simulate the radiation damping for soil-structure interaction analysis application. The perfectly matched layer (PML) has the ability to absorb and attenuate scattered waves under any angle of incidence and frequency, such that with the minimum dimensions of the modeling and the minimum amount of calculations, high-precision responses can be achieved. In order to time domain dynamic analysis by finite element method, a program is written utilizing MATLAB mathematical language, which is capable of analysis of different geometries, layering and dynamic/seismic loading in models with linear elastic behavior. The present program uses four-noded quadrilateral elements and uses the implicit Newmark method to solve the dynamic equation. The feature of theprogram is the implementation of PML, which can address the simulation of radiation damping in the finite element method correctly. This is done by rewriting the PML formulation, implementation in the finite element method, and step-by-step verifying the analysis of dynamic problems. First of all, to verify the dynamic analysis performance of the program, three simple examples have been solved, and the results show that theyare consistent with existing theories and the literature. Next, using PML, the problem of a rigid massless foundation vibration has been studied. Computing the impedance/compliance functions and comparing them with analytical or semi-analytical approaches existing in the technical texts, the efficiency and the precision of PML for surface loading conditions has been evaluated. In the frequency domain, the results are in good agreement with the previous studies. Besides, comparing the response from the reduced model (using PML) with the expected response from the extended mesh indicates that there is a complete match in the time domain. It is worth noting that this match is achieved while the model dimensions and the volume of data storage have been drastically reduced, but the accuracy of the answers has not varied. This reduction of dimension is such that if PML is located at a distance of up to a quarter of the foundation width, similar responses to larger models can be achieved.

کلیدواژه‌ها [English]

  • Perfectly Matched Layer
  • Radiation Damping
  • wave propagation
  • Finite elements method
  • Soil-Structure Interaction
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