تحلیل کمانش جانبی تیر جدار نازک با مقطع متغیر از جنس مواد مدرج تابعی تحت شرایط مرزی مختلف

نوع مقاله : علمی - پژوهشی

نویسندگان

1 استادیار، دانشکده مهندسی، دانشگاه کاشان، کاشان، ایران

2 دانشجوی کارشناسی ارشد، دانشکده مهندسی، دانشگاه کاشان، ایران

3 دانشیار، دانشکده مهندسی مکانیک، دانشگاه کاشان، کاشان، ایران

چکیده

در این پژوهش پایداری جانبی-پیچشی تیر غیرمنشوری با مقطع جدار نازک متقارن ساخته شده از مواد مدرج تابعی تحت بارگذاری عرضی مورد مطالعه قرار گرفته‌است. خواص مکانیکی ماده مدرج براساس تابع توزیع توانی در راستای طول عضو به‌طور پیوسته تغییر می‌کند. نسبت پواسون بعلت تغییرات اندک در مواد مهندسی ثابت فرض شده است. معادلات دیفرانسیل حاکم بر پایداری تیر جدار نازک ناهمگن براساس فرضیات حاکم بر تئوری کلاسیک ولاسو و صرف‌نظر نمودن از تغییر شکل‌های برشی به کمک روش انرژی استخراج شده ‌است. سپس، با استفاده از روش عددی مربعات دیفرانسیل و فرضیات حاکم بر این روش، دستگاه معادلات پایداری حل می‌گردد. در ادامه، با توجه به شرایط مرزی حاکم بر اعضای جدار نازک با مقطع متقارن و با استفاده از روش حل مقادیر ویژه، مقدار بار کمانش بحرانی محاسبه می‌شود. پس از صحت سنجی نتایج و اثبات دقت و کارآمدی روش مذکور در خصوص تیر همگن با مقطع متغیر، تاثیر پارامترهای مختلف همچون شرایط مرزی گوناگون، محل اعمال بار عرضی، توان ماده مدرج تابعی و تغییر ابعاد بال و جان نیم‌رخ I-شکل بر روی بار کمانش جانبی بدون بعد مورد ارزیابی قرار گرفته است. نتایج حاصل از این تحقیق نشان می‌دهد که تغییر ابعاد مقطع و شاخص کسر حجمی تاثیر بسیاری بر پایداری جانبی-پچشی تیر ماهیچه‌ای دارد. همچنین در تمامی شرایط، بیشترین ظرفیت کمانشی مربوط به حالتی است که بار عرضی به بال پایین نیم‌رخ اعمال می‌گردد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Lateral buckling analysis of axially functionally graded thin-walled beam with varying cross-section under different boundary conditions

نویسندگان [English]

  • Masoumeh Soltani 1
  • Fahimeh Sajjadi-nejad 2
  • Ahmad Reza Ghasemi 3
1 Department of Civil Engineering, Faculty of Engineering, University of Kashan, Kashan, Iran
2 Department of Civil Engineering, Faculty of Engineering, University of Kashan, Kashan, Iran
3 Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
چکیده [English]

In this article, lateral-torsional stability of axially functionally graded (AFG) non-prismatic beam with doubly symmetric thin-walled cross-section under transverse loading is investigated. Material properties of FG beam with variable cross-section are supposed to vary through longitudinal direction of the constituents according to simple power-law distribution (P-FGM). Based on Vlasov’s model and using small displacements theory, the governing equilibrium equations are derived through the energy principle for AFG web and/or flanges tapered I-beams. The differential quadrature method is then selected to numerically solve the resulting system of governing fourth-order differential equations with variable coefficients. In this approach, a non-uniform mesh point distribution (Chebyshev-Gauss-Lobatto) is used for provide accuracy of solutions and convergence rate. Finally, the lateral-torsional buckling loads are calculated by solving an eigenvalue problem of the obtained algebraic system. In the case of homogenous members with variable cross-section, the outcomes of this work are compared with the available benchmarks and there is an excellent agreement. Finally, the impacts of involved parameters such as boundary conditions, load height parameter, power law index and web and flanges tapering ratios on the non-dimensional lateral buckling load are discussed. The results of this research reveal that the impacts of non-uniformity in the cross-section and gradient index play significant roles on lateral-torsional stability behavior of tapered I-beams. Furthermore, the highest buckling capacity is acquired when the transverse load is applied to the bottom flange.

کلیدواژه‌ها [English]

  • Functionally Graded Material
  • Thin-walled beam
  • Lateral-torsional stability
  • Tapered Beam
  • Differential Quadrature Method
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