تحليل خمش غير‌خطي پانل‌هاي استوانه اي كامپوزيتي تقويت شده با نانوتيوب هاي كربني هدفمند

Nonlinear Bending Analysis of Cylindrical Composite Panels Reinforced by Functionaly Graded Carbon Nanotubes

در اين مقاله رفتار غيرخطي خمشي پانل استوانه‌اي تقويت‌شده با نانوتيوب هاي كربني هدفمند تحت بار گسترده و تغيير درجه حرارت بررسي شده‌است. معادلات حاكم با استفاده از روش انرژي ريتز براساس روابط كرنش- تغييرمكان غيرخطي فون كارمن استخراج شده‌است. تاثيرات نحوه توزيع، ميزان درصد حجمي، تغييرات درجه حرارت وهمچنين شرايط مرزي مختلف نانوتيوب‌ها بر پارامترهايي از قبيل تغييرمكان عرضي و منتجه ممان خمشي مركز پانل استوانه‌اي مورد بررسي قرار گرفته‌است. مي‌توان نتيجه گرفت به ازاي يك بارگذاري معين، پانل استوانه‌اي تقويت‌شده با نانوتيوب‌هاي كربني با توزيع FG-X داراي بيشترين و با توزيع FG-Ʌ داراي كمترين منتجه ممان خمشي مي باشد.

In this study, for the first time, the nonlinear bending analysis of a deep cylindrical panel reinforced with gradient carbon nanotubes under uniform load and temperature variation has been investigated. Detailed study have been done on the effect of carbon fiber distribution and the volume fraction of carbon nanotubes in bending behavior of cylindrical panels. The variation of transverse displacement component and bending moment distribution, versus uniform loading under different boundary conditions are investigated. First, the governing equations are extracted using nonlinear equations governing the deep cylindrical panel and energy relations. Regarding the complexity of the equations and the impossibility to solve them analytically, numerical methods are used to solve the equations. The bending analysis will be done using the Ritz method which is known as a semi-analytic and precise method. Based on this method, the distribution of displacement components is assumed as series functions to satisfy the essential boundary conditions. Then, these functions are placed in the Lagrangian energy equation and the governing relations are obtained by minimizing the energy relation. The most important advantage of this method is that, by satisfying the geometric boundary conditions, the natural boundary conditions governing the panel are automatically met. Finally, it is concluded that the maximum moment of bending is obtained by FG-X distribution pattern while the least by FG-Λ distribution pattern of the fibers.