Bending Analysis of Carbon Nanotubes with Small Initial Curvature Embedded on an Elastic Medium Based on Nonlocal Elasticity and Galerkin Method
محورهای موضوعی : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیک
اعظم عارفی
1
(دانشجو، دانشکده مکانیک، دانشگاه صنعتی اصفهان)
محمود سلیمی
2
(استاد، دانشکده مکانیک، دانشگاه صنعتی اصفهان)
کلید واژه: Galerkin Method, Nonlocal elasticity theory, Bending Analysis, Carbon Nanotube with Initial Curvature, Newton Raphson Method,
چکیده مقاله :
Carbon nanotubes have an important role in reinforcing nanocomposits. Many experimental observations have shown that in the most nanostructures such as nanocomposites, carbon nanotubes (CNTs) are often characterized by a certain degree of waviness along their axial direction. In the present paper, the effects of initial curvature, influence of surrounding medium that is modeled as Winkler elastic foundation on behavior of slightly curved carbon nanotubes are investigated. To capture the small size effects, nonlocal elasticity theory is implemented. Bending governing equations are derived using the principle of minimum total potential energy and these nonlinear equations are solved by Newton Raphson method. It is shown that the larger the initial curvature, the higher deflection can occur. Furthermore, neglecting the effect of initial curvature of CNTs can lead to incorrect results.
نانولولههای کربنی در تقویت کامپوزیتها نقش بسزایی ایفا میکنند. بدیهی است که برخی از نانولولهها در هنگام کاربرد، شکل منظم ابتدایی خود را حفظ نمی کنند و دچار اعوجاج میشوند. این اعوجاج میتواند در حین فرآیند ساخت یا بعد از آن درنتیجهی تأثیر ماتریس رخ دهد. بر این اساس، مدلسازی این نوع نانوساختار به صورت پوسته یا تیر بدون انحنا، میتواند خطایی قابل ملاحظه را با نتایج همراه کند. در این مقاله، خمش نانولولههای دارای انحنای اولیه مورد مطالعه قرار میگیرد. معادلات تعادل بر پایه تئوری الاستیسیته غیر محلی به کمک اصل کمینهسازی انرژی پتانسیل کل، استخراج و از روش گالرکین برای حل آنها بهره گرفته میشود. از مدل وینکلر برای مدلسازی بستر الاستیک استفاده میشود. حل خیز حاصل از دستگاه معادلات غیرخطی به کمک روش عددی نیوتن رفسون صورت میگیرد و در نهایت تأثیر مقیاس کوچک، انحنای اولیه و مدول فونداسیون بر روی خیز نانولولهها مورد بررسی قرار خواهد گرفت
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