مجله ی مهندسی مکانیک شریف

مجله ی مهندسی مکانیک شریف

تحلیل خمش استاتیکی در نانولوله‌های کربنی تک‌جداره با استفاده از تئوری پوسته‌ها و تئوری الاستیسیته ی غیرموضعی

نوع مقاله : مقاله پژوهشی

نویسندگان
مهدی باباخانی
عیسی احمدی
گروه‌ مهندسی مکانیک، دانشگاه زنجان، زنجان، ایران.
10.24200/j40.2026.68562.1762
چکیده
خمش استاتیکی نانولوله‌های کربنی تک‌جداره با استفاده از تئوری پوسته‌ها و تئوری الاستیسیته‌ی غیرموضعی تحلیل شده است. در نوشتار حاضر، معادله‌های حاکم بر رفتار استاتیکی نانولوله با استفاده از تئوری پوسته‌ی لاو استخراج و شرایط مرزی مناسب در نظر گرفته شده است. حل معادله‌های دیفرانسیل با مشتق‌های جزئی حاصل برای نانولوله، با روش تعمیم‌یافته‌ی مربعات تفاضلی (GDQM) صورت گرفته و تغییرشکل استاتیکی نانولوله استخراج شده است. در قسمت نتایج عددی، تأثیر پارامترهای مختلف، نظیر: پارامتر غیرموضعی، شرایط مرزی و ابعاد هندسی، و نوع بار وارده در پاسخ خمش نانولوله بررسی شده است. نتایج عددی با نتایج مدل‌سازی نانولوله با تئوری تیر‌ها و اختلاف نتایج دو تئوری در پیش‌بینی خمش به‌وجودآمده در نانولوله مقایسه و مشاهده شده‌اند که درنظرگرفتن آثار غیرموضعی منجر به افزایش خیز پیش‌بینی‌شده برای نانولوله‌ها می‌شود. نتایج عددی نشان داده‌اند که با درنظرگرفتن تئوری غیرموضعی، اختلاف پیش‌بینی تئوری پوسته‌ها با تئوری تیر‌ها حتی برای نانولوله‌های بلند افزایش یافته و اهمیت مدل‌سازی نانولوله‌ها با تئوری پوسته‌ها مشهود شده است.
کلیدواژه‌ها
خمش استاتیکی نانولوله‌ها
نانولوله‌های تک‌جداره
تئوری پوسته‌ها
تئوری الاستیسیته‌ی غیرموضعی
روش تعمیم‌یافته‌ی مربعات تفاضلی (GDQM).
موضوعات

عنوان مقاله English

Static bending analysis of single walled carbon nanotubes using shell theory and nonlocal elasticity

نویسندگان English

Mahdi Babakhani
Isa Ahmadi
Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran.
چکیده English

This study investigates the static bending behavior of single-walled carbon nanotubes (SWCNTs) using Love’s shell theory combined with Eringen’s nonlocal elasticity to properly account for size-dependent effects. The nonlocal model incorporates the influence of neighboring strains on stress, improving the representation of nanoscale behavior. The governing equations are formulated based on Love’s shell theory and are solved using the generalized differential quadrature method (GDQM), which Achieves high accuracy using few grid points .The influence of key parameters—including the nonlocal length scale, geometric dimensions, boundary conditions, and loading type—on the bending response is examined. Numerical results are compared with those predicted by classical beam theory. The comparison shows that while both models agree reasonably well for large length-to-radius ratios in the absence of size effects, significant discrepancies arise once nonlocal behavior is considered. The results demonstrate that nonlocal effects reduce the bending stiffness and increase deflection, indicating that beam theory cannot reliably capture the actual bending behavior of CNTs at the nanoscale.

کلیدواژه‌ها English

Bending of nanotubes
shell theory
nonlocal elasticity theory
generalized differential quadrature method (GDQM)
nanoscale analysis
 
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