تحلیل تقریبی پیچش مقاطع ذوزنقه‌ای دلخواه با استفاده از روش کانتوروویچ

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه اراک، اراک، ایران

2 گروه مهندسی عمران، دانشکده مهندسی، دانشگاه اراک، اراک، ایران

چکیده

بسیاری از اعضای موجود در سازه‌ها تحت اثر لنگر پیچشی قرار دارند، بنابراین شناخت رفتار پیچشی این اعضا از اهمیت بسیاری برخوردار است. بررسی رفتار پیچشی مقاطع جدار نازک و مقاطعی با شکل هندسی ساده با استفاده از روش‌های تحلیلی و رایج امکان‌پذیر است. در صنعت‌های خاص ممکن است در تحلیل و طراحی سازه‌ها مقاطعی نیاز باشند که هندسه‌ی آنها خارج از چارچوب مقاطع مرسوم طبقه‌بندی شود و از آنجایی که محاسبه پاسخ این مقاطع با روش‌های رایج امکان‌ناپذیر یا دشوار است، بنابراین توسعه روش‌های جدیدتر بسیار ضروری به نظر می‌رسد. از جمله این مقاطع می‌توان به مقطع ذوزنقه‌ای اشاره نمود. به علت دشواری تحلیل دقیق مسائل با دامنه‌های نامتقارن، روش‌های نیمه‌تحلیلی و عددی بهترین جایگزین برای حل این دسته از مسائل است. یکی از روش‌های مناسب برای حل مسائل مقدار مرزی، روش حساب تغییرات است که از میان این روش‌ها روش نیمه‌تحلیلی کانتوروویچ که تعمیم‌یافته روش رایلی-ریتز است به دلیل عدم محدودیت انتخاب تابع اولیه جهت برآورد شرایط مرزی یک روش قدرتمند جهت حل مسائل است. هدف از پژوهش حاضر توسعه روش کانتوروویچ برای حل معادله حاکم بر مسئله پیچش، محاسبه اعوجاج و میدان تنش مقطع دلخواه ذوزنقه به صورت مستقیم است. به منظور ارزیابی دقت روش کانتوروویچ، حل حاصل از این روش با سایر روش‌های موجود مقایسه شده است. نتایج حاکی از دقت بالا و همگرایی سریع روش مذکور است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Approximate Torsional Analysis of Arbitrary Trapezoidal Bars by Kantorovich Method

نویسندگان [English]

  • Ali Mahdavi 1
  • Mahdi Yazdani 2
  • Zahra Khosravi Enjedani 1
1 Arak University, Arak, Iran
2 Department of Civil Engineering, Faculty of Engineering, Arak University, Arak, Iran
چکیده [English]

A variety of structural members are expected to safely tolerate torsional moments. These include irregularly-shaped cross-sections (e.g., trapezoidal or triangular sections) in some industries which deserve special considerations for the analysis and design under torsional loading. Therefore, the development of novel methods as alternative approaches seems very necessary, partially because of the deficiency of analytical solutions in treating asymmetric solution domains. Semi-analytical and numerical methods appear as desirable alternatives in most cases. One of the proper tools for dealing with the boundary value problems encountered in the torsional analysis is the vibrational method. The Kantorovich semi-analytical method, known as an extension of the Rayleigh-Ritz method, has been proven advantageous among the others, mainly because of relaxing the conventional limitations in selecting the primary function for satisfying the boundary conditions. Therefore, the purpose of the present study is to extend the applicability of the Kantorovich method to estimate the warping and stress field of arbitrary trapezoidal sections directly. Finally, the efficiency and accuracy of the present solution is verified against a number of existing analytical and numerical methods. The results indicate high precision and rapid convergence of this semi-analytical method.

کلیدواژه‌ها [English]

  • Torsion problem
  • Kantorovich method
  • Trapezoidal sections
  • Warping function
  • Prandtl’s stress distribution
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