علوم و فناوری کامپوزیت

ارائه‌ی‌ یک رابطه‌ی صریح جهت تحلیل تنش صفحات دارای گشودگی‌ شبه مربّعی و تحت کشش با استفاده از رگرسیون خطی چندگانه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجو کارشناسی ارشد، مهندسی مکانیک، دانشگاه صنعتی شاهرود، شاهرود، ایران

2 دانشیار، مهندسی مکانیک، دانشگاه صنعتی شاهرود، شاهرود، ایران

3 استادیار، مهندسی مکانیک بیوسیستم، دانشگاه فردوسی مشهد، مشهد ، ایران

10.22068/jstc.2018.81097.1417

چکیده

تمرکز تنش در ناپیوستگی‌های هندسی یکی از عوامل شکست سازه می‌باشد. امروزه با توجه به اینکه صفحات دارای گشودگی جزء جدانشدنی طراحی‌ها و قطعات می‌باشند؛ لذا مطالعه در مورد تمرکز تنش ناشی از این گشودگی‌ها جهت جلوگیری از شکست سازه ضروری است. ازاینرو طراح برای ارائه‌ی یک طرح بایستی از مقدار تمرکز تنش در گشودگی آگاه باشد و با توجه به آن طرح را پایه‌ ریزی کند. در این پژوهش سعی می‌شود به کمک روش رگرسیون، رابطه‌ای صریح جهت تخمین تمرکز تنش در صفحات ارتوتروپیک دارای گشودگی شبه مربّعی، بر حسب خواص مکانیکی مادّه و شعاع انحنای گوشه گشودگی ارائه گردد. این رابطه علاوه بر سهولت در استفاده و کنار گذاشتن فرآیند سخت و پیچیده‌ی حلّ تحلیلی، این امکان را برای طراح فراهم می‌آورد تا با استفاده از روش مدول مؤثر و یا اصل برهمنهی بولتزمن، تنش صفحات ویسکوالاستیک دارای گشودگی را نیز محاسبه کند. در ابتدا به‌ کمک حلّ تحلیلی بر پایه روش لخنیتسکی، مقادیر تنش در بسیاری از صفحات کامپوزیتی دارای گشودگی شبه مربّعی محاسبه می-شود. سپس با استفاده از رگرسیون خطی چندگانه، رابطه‌ای صریح برای ضریب تمرکز تنش برحسب خواص مکانیکی ارائه می‌گردد. نتایج بیان می‌کند که مدل رگرسیونی قادر به پیش بینی تنش محیطی با حداکثر خطای دو درصد می‌باشد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Presenting an explicit relation for analyzing stress of plates with quasi-square holes and under tension by using multiple linear regression

نویسندگان [English]

  • Ali Abbasnia 1
  • Mohhamad Jafari 2
  • Abbas Rohani 3

1 Department of Mechanical Engineering, Shahrood University, Shahrood, Iran

2 Department of Mechanical Engineering, Shahrood University, Shahrood, Iran

3 Department of Bio Mechanical Engineering, Ferdowsi University, Mashhad, Iran

چکیده [English]

Stress concentration on the geometric discontinuities is one of the factors of structure failure. Nowadays, plates with holes are inseparable parts of designs and pieces, therefore studying the stress concentration caused by these holes is necessary to prevent structure failure. So the designer for presenting a design must be aware of the stress concentration in the hole and according to it design the basis. In this research, by using the regression method and on the basis of the mechanical properties of the materials and the radius of curvature in the corner of the hole, we try to present an explicit relation for estimating stress concentration in the orthotropic plates with quasi-square hole. This relation, in addition to easing the use and bypassing the hard and complex process of analytical solution, provides designer with the opportunity to calculate stress of perforated viscoelastic plates by using the effective module method or Boltzmann's superposition principle. At first, with analytical solution based on the Lekhnitskii method the stress values are calculated in many composite plates with quasi-square hole. Then, by using multiple linear regression and on the grounds of mechanical properties, is given an explicit relation for the stress concentration coefficient. The results show that the multiple regression model is able to predict the circumferential stress with a maximum error of 2%.

کلیدواژه‌ها [English]

  • Stress Concentration Factor
  • Quasi-Square Hole
  • Multiple Linear Regression
  • Complex Variable Method
مراجع
 
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علوم و فناوری کامپوزیت
دوره 6، شماره 1
خرداد 1398
صفحه 21-30
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هم رسانی
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