مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

فرمول‌بندی اجزا محدود تیر پلیمری حافظه‌دار با در نظر گرفتن آثار غیرخطی هندسی

نویسندگان
1 پردیس دانشکده‌های فنی، دانشگاه تهران، تهران
2 دانشگاه تهران
چکیده
در این مقاله با استفاده از یک مدل ساختاری ترمومکانیکی برای پلیمرهای حافظه‌دار، یک تحلیل اجزا محدود برای تیر از جنس پلیمر حافظه‌دار با فرضیات هندسی تئوری فون-کارمن ارائه شده است. اهمیت ارائه تئوری فون-کارمن برای پلیمرهای حافظه‌دار از این جهت است که تیر می‌تواند چرخش‌های نسبتا بالا را در حین بارگذاری تجربه کند. همچنین با توجه به این که در فرایند‌های بهینه‌سازی و طراحی نیازمند تعداد دفعات حل متعدد هستیم استفاده از مدل سه‌بعدی با توجه به زمان بالای حل آن‌ها، گزینه مناسبی نمی‌باشد. برای اعتبار‌سنجی روابط ارائه شده، نتایج گزارش شده با حل سه‌بعدی اجزا محدود که پیشتر توسط همین نویسندگان گزارش شده است، مقایسه گردیده است. بر این اساس، اثر کسر حجمی بخش سخت بر روی پاسخ یک تیر نازک مورد بررسی قرار گرفته است و همچنین نتایج تیر اولر-برنولی گزارش شده و با حل سه‌بعدی و فون-کارمن مقایسه شده است. به عنوان نمونه حدود خطای پاسخ تیر در یکی از مثال‌های حل شده، برای تیر اولر-برنولی 27% و برای تیر فون-کارمن 1% نسبت به حل سه‌بعدی می‌باشد. به طور کلی هر چه ضخامت تیر کمتر و یا تیر بلند‌تر باشد، خطای تیر اولر-برنولی بیشتر خواهد بود. مدل اجزا محدود ارائه شده می‌تواند جایگزین مطمئنی برای مدل‌سازی‌های سه‌بعدی که نیازمند زمان پردازش نسبتا زیادی هستند، باشد و همچنین برای تحلیل پارامتری مادی و هندسی این مدل، قابل استفاده است.
کلیدواژه‌ها

موضوعات


عنوان مقاله English

A finite element analysis for shape memory polymer beams considering geometric non-linearity

نویسندگان English

Pouya Fahimi 1
Mostafa Baghani 2
Ghader Faraji 2
1 School of mechanical engineering, College of engineering, University of Tehran, Tehran, Iran
2 School of mechanical engineering, University of Tehran
چکیده English

In this research, using a thermomechanical constitutive model for shape memory polymers and employing the von Kármán theory, a finite element analysis of a shape memory polymer beam is presented. The importance of introducing the von Kármán theory for shape memory polymers is that the beam can have relatively high slopes during loading. Also, for optimization and designing processes we need to solve multiple problems and due to the high processing time the use of 3D model is not suitable. To validate the presented formulations, the reported results are compared with the 3D solution which was previously reported by the same authors. Accordingly, the effect of the hard segment volume on response of a thin beam has been investigated, and the results of the von Kármán beam have been reported and compared with the 3D and Euler-Bernoulli solutions. As an example, the error of the beam response in one of the solved examples is 27% for Euler-Bernoulli beam and 1% for the von Kármán solution compared to the three-dimensional solution. In general, the lower the beam thickness or the beam is longer, the Euler-Bernoulli beam error will be higher. The proposed finite element model can provide a reliable alternative response comparing to 3D modeling that requires a lot of processing time, and can be used for geometry and material parametric study.

کلیدواژه‌ها English

Shape memory polymer
von Kármán theory
Nonlinear finite element method
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