مدلسازی تحلیلی و عددی ضریب شدت تنش در تیرهای دارای ترک با مقطع I شکل

نوع مقاله: مقاله مکانیک

نویسندگان

1 دانشکده فنی دانشگاه گیلان

2 هیات علمی دانشگاه آزاد اسلامی واحد بندرانزلی

چکیده

در این مقاله، با استفاده از دو رهیافت تحلیلی و عددی، ضریب شدت تنش برای مود اول (بازشدگی) در تیرهای دارای ترک با مقطع I شکل تحت بار محوری بررسی می‌شود. در مقاطع دارای ترک، به دلیل تغییر مکان مرکز هندسی و یا به‌عبارتی دیگر عدم هم‌راستایی نیروی محوری، یک کوپل خمشی در مقطع ایجاد می‌شود. در رهیافت تحلیلی، یک مدل ریاضی برای ضریب شدت تنش به کمک تئوری نرخ آزادسازی انرژی در ناحیه‌ی ترک پیشنهاد می‌گردد. این مدل با درنظر گرفتن گشتاور خمشی این کوپل حاصل می شود. این مدل در دو وضعیت برحسب مکان ترک شامل قرارگیری ترک در قسمتی از بال و ترک در بال و قسمتی از جان ارائه می‌شود. در رهیافت عددی، مشخصات هندسی و مادی و نوع بارگذاری تیر دارای ترک با مقطع I شکل به کمک نرم افزار آباکوس مدل و سپس مقادیر ضریب شدت تنش در مود اول استخراج می‌گردد. در حل عددی مسئله‌ی حاضر، از دو روش کانتور انتگرال و اجزای محدود توسعه یافته برای مدل‌سازی ترک استفاده می‌شود. با مقایسه‌ی جواب‌های دو رهیافت عددی و تحلیلی تطابقی مناسب بین نتایج مشاهده و صحت معادلات پیشنهادی تایید می‌گردد.

کلیدواژه‌ها


عنوان مقاله [English]

Analytical and Numerical Modeling of Stress Intensity Factor in I-Shaped Cross Sections of Cracked Beams

نویسندگان [English]

  • Javad Razzaghi 1
  • Morteza Khomami Abadi
  • Ali Alijani 2
2 Assistant Professor, Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University
چکیده [English]

In this paper, the stress intensity factor (SIF) in the opening mode I is investigated in cracked beams with the I-shaped cross sections under axial loading. In cracked cross sections, a couple is made due to shifting the two centroids, or in the other word due to a misalignment between the axes of the axial force. The analysis is carried out through two analytical and numerical approaches. In analytical approach, a mathematical model for SIF is proposed via the theory of the energy release rate in the region around the crack. This model is adapted by considering the moment of the couple. It is presented in two situations in terms of the crack location including the crack in a part of the flange, and the crack in the flange and a part of the web. In numerical approach, geometric and material characteristics and type of loading are modeled by using Abaqus software; then SIF values of the I-shaped cracked beam are determined. In the presented numerical solution, two methods of C-integral and X-FEM are employed to model the crack. The validity of proposed equations is confirmed by the comparison between the presented results of numerical and analytical approaches.

کلیدواژه‌ها [English]

  • Stress intensity factor
  • Cracked beam
  • I-shaped section
  • Energy release rate
  • Analytical approach
  • Abaqus software
 

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