نویسندگان
دانشکده مهندسی عمران، دانشگاه صنعتی شاهرود، شاهرود
چکیده
در این مقاله، به‌منظور تحلیل اجزای محدود ورق‌های نازک ویسکوالاستیک المان‌های جدیدی با استفاده از توابع شکل مختلط فوریه تحت عنوان المان ورق کیرشهف فوریه (DKFT) پیشنهاد شده است. به‌منظور ساختن المان‌های ورق DKFT میدان توابع چند‌جمله‌ای در یک المان مثلثی مرتبه دوم شش‌گرهی با میدان توابع پایه شعاعی مختلط فوریه غنی‌سازی شده است. برای بررسی صحت و دقت روش پیشنهادی و کارامدی المان‌های پیشنهادی، تحلیل اجزای محدود ورق‌های چهارضلعی و بیضوی نازک ویسکوالاستیک با استفاده از این المان‌ها صورت گرفته است و نتایج آن با حل تحلیلی و نتایج حاصل از المان‌های کیرشهف (DKT) و حل با کمک نرم‌افزار تجاری آباکوس مقایسه شده است. نتایج نشان می‌دهد که المان‌های DKFT در مقایسه با المان‌های کلاسیک ورق و المان‌های DKT بسیار کارامدتر و توانمندتر هستند، چرا که نسبت به آنها از دقت بالایی برخوردارند و هزینه محاسباتی را نیز به‌میزان قابل توجهی کاهش می‌دهند.
کلیدواژه‌ها
عنوان مقاله [English]
New DKFT Elements for the Finite Element Analysis of Thin Viscoelastic Plates
نویسندگان [English]
- S. A. Ghazi Mirsaeed
- V. Kalatjari
چکیده [English]
In this paper, finite element analysis of thin viscoelastic plates is performed by proposing new plate elements using complex Fourier shape functions. New discrete Kirchhoff Fourier Theory (DKFT) plate elements are constructed by the enrichment of quadratic function fields in a six-noded triangular plate element with complex Fourier radial basis functions. In order to illustrate the validity and accuracy of the presented approach and robustness of the proposed elements in viscoelasticity, finite element analysis of square and elliptical viscoelastic thin plates is performed and the results are compared to those of analytical solutions and with those obtained by discrete Kirchhoff Theory (DKT) elements and the commercial software ABAQUS. The results show that FE solutions using DKFT elements have an excellent agreement with the analytical solutions and ABAQUS solutions, even though noticeably fewer elements, in comparison to DKT and classic plate elements, are employed, which means that the computational costs are reduced effectively.
کلیدواژه‌ها [English]
- finite element method
- Bending of thin plates
- viscoelasticity
- DKFT plate element
- Complex Fourier radial basis functions
- Complex Fourier shape functions
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