حل صفحات میندلین به روش رهایی پویا

نوع مقاله : مقاله علمی

نویسندگان
حسین استیری 1
مهدی آدینه 2
1 استادیار، گروه مهندسی عمران، دانشکده فنی و مهندسی، مجتمع آموزش عالی گناباد، گناباد، ایران
2 استادیار، گروه مهندسی مکانیک، دانشکده فنی و مهندسی، مجتمع آموزش عالی گناباد، گناباد، ایران
10.22034/stme.2025.531701.1137
چکیده
نظریه صفحه‌ی میندلین، که شامل اثرات تغییر شکل برشی است، برای اطمینان از مدل‌سازی دقیق صفحات نسبتاً ضخیم به کار می‌رود. این مقاله به بررسی کارایی روش‌های مختلف رهایی پویا برای تحلیل الاستیک صفحات میندلین می‌پردازد. هدف اصلی، ارزیابی مزایای دوازده شیوه‌ی رهایی است. تفاوت این راه‌کارها در چگونگی تعیین پارامترهای ساختگی مانند میرایی و جرم می‌باشد که برای همگرایی رهایی پویا لازم هستند. این مطالعه بر ارزیابی این روش‌ها بر اساس پایداری عددی، سرعت همگرایی و کارایی محاسباتی تمرکز دارد. چندین نمونه از صفحات میندلین با هندسه‌ها و شرایط مرزی متنوع برای مقایسه‌ی عملکرد راه‌کارهای گوناگون رهایی پویا حل می‌شوند. با توجه به تنوع نمونه‌های حل‌شده، می‌توان از نتایج آن به ‌عنوان مسائل بنچمارک در حل صفحه‌های میندلینی بهره جست. معیارهای کلیدی، از جمله تعداد تکرارهای مورد نیاز برای همگرایی و کل زمان محاسباتی، برای هر روش ثبت شده‌اند. نتایج، تغییرات قابل توجهی در کارایی بین دوازده الگوریتم را نشان می‌دهد. به طوری که برخی دارای همگرایی سریعی هستند؛ در حالی که برخی دیگر به تکرارهای قابل توجهی بیشتری نیاز دارند. یک رتبه‌بندی جامع بر اساس این معیارهای محاسباتی ایجاد شده است که کارآمدترین و قوی‌ترین تکنیک‌ها را برای کاربردهای عملی شناسایی می‌کند. همچنین، این مطالعه حساسیت همگرایی رهایی پویا به انتخاب پارامترهای ساختگی را نشان می‌دهد. نتایج عددی، نمایانگر کارایی مناسب روش آندوود در زمان تحلیل و شیوه‌ی کمینه انرژی پسماند در شمار تکرارها برای تحلیل صفحات میندلینی است.
کلیدواژه‌ها
رهایی پویا
صفحه‌ی میندلین
جرم
میرایی
گام زمانی
موضوعات

عنوان مقاله English

Analysis of Mindlin Plates by Dynamic Relaxation Method

نویسندگان English

Hossein Estiri 1
Mahdi Adineh 2
1 Assistant Professor, Department of Civil Engineering, University of Gonabad, Gonabad, Iran
2 Assistant Professor, Department of Mechanical Engineering, University of Gonabad, Gonabad, Iran
چکیده English

The Mindlin plate theory, which accounts for shear deformation effects, is employed to ensure accurate modeling of moderately thick plates. This paper investigates the efficiency of various dynamic relaxation methods for the elastic analysis of Mindlin plates. The main objective is to evaluate the advantages of twelve different relaxation schemes. The distinctions among these approaches lie in the determination of artificial parameters such as damping and mass, which are essential for the convergence of dynamic relaxation. The study focuses on assessing these methods based on numerical stability, convergence rate, and computational efficiency. Several Mindlin plate examples with diverse geometries and boundary conditions are solved to compare the performance of different dynamic relaxation techniques. Given the variety of the analyzed cases, the obtained results can serve as benchmark problems for Mindlin plate analysis. Key criteria, including the number of iterations required for convergence and the total computational time, are recorded for each method. The results reveal significant variations in efficiency among the twelve algorithms, with some exhibiting rapid convergence while others require considerably more iterations. A comprehensive ranking based on these computational metrics is established to identify the most efficient and robust techniques for practical applications. Furthermore, the study demonstrates the sensitivity of dynamic relaxation convergence to the selection of artificial parameters. Numerical results indicate that the Underwood method is efficient in terms of analysis time, while the minimum residual energy scheme achieves the fewest iterations for Mindlin plate analysis.



Several benchmark cases of Mindlin plates with diverse geometries and boundary conditions are solved to compare the performance of the proposed DR schemes. Given the variety of solved examples, the results can serve as benchmark problems for Mindlin plate analyses. Key metrics, including the number of iterations required for convergence and total computational time, are recorded for each method. The results reveal significant variations in efficiency among the twelve algorithms: some exhibit rapid convergence, while others demand substantially more iterations. A comprehensive ranking system is established based on these computational criteria, identifying the most efficient and robust techniques for practical applications.



Furthermore, this study highlights the sensitivity of dynamic relaxation convergence to the selection of fictitious parameters. Numerical results demonstrate the effectiveness of the Underwood method in computational time and the minimum residual energy technique in iteration count for analyzing Mindlin plates.

کلیدواژه‌ها English

dynamic relaxation
Mindlin plate
mass
damping
time step

اصل مقاله

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  • تاریخ دریافت 08 تیر 1404
  • تاریخ بازنگری 22 شهریور 1404
  • تاریخ پذیرش 29 مهر 1404
  • تاریخ اولین انتشار 29 مهر 1404
  • تاریخ انتشار 01 بهمن 1404