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Najafizadeh, M., Alavi, M., Salmasi, F., Azari, S. (2008). Bending Analysis of Rectangular FGM Plates based on the Extended Kantorovich Method. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 1(3), 27-38.
Mohammad Mahdy Najafizadeh; Majid Alavi; Foad Salmasi; Shima Azari. "Bending Analysis of Rectangular FGM Plates based on the Extended Kantorovich Method". Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 1, 3, 2008, 27-38.
Najafizadeh, M., Alavi, M., Salmasi, F., Azari, S. (2008). 'Bending Analysis of Rectangular FGM Plates based on the Extended Kantorovich Method', Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 1(3), pp. 27-38.
Najafizadeh, M., Alavi, M., Salmasi, F., Azari, S. Bending Analysis of Rectangular FGM Plates based on the Extended Kantorovich Method. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 2008; 1(3): 27-38.

Bending Analysis of Rectangular FGM Plates based on the Extended Kantorovich Method

Article 3, Volume 1, Issue 3, Summer 2008, Page 27-38  XML PDF (1292 K)
Document Type: Persian
Authors
Mohammad Mahdy Najafizadeh 1; Majid Alavi2; Foad Salmasi3; Shima Azari4
1Associate Professor, Mechanical Engineering Dept., Islamic Azad University, Arak Branch
2Assistant Professor, Mathematical Dept., Islamic Azad University, Arak Branch
3M.Sc., Mechanical Engineering Dept.,Islamic Azad University, Arak Branch
4M.Sc., Mechanical Engineering Dept., Islamic Azad University, Arak Branch
Abstract
Bending analysis of FGM plates under uniform and sinusoidal loaded result in forth order partial differential equation. In this paper the analytical solution is based on the extended Kantorovich iterative procedure. The differential equations for the iterative procedure is derived using the Galerkin method. The solution was develope based on the classical plate’s theory (CLPT). The reliability of the present analytical method for FGM, under different boundary condition, was verified and approved when comparing Navier solution and finite element results with ANSYS solution. Since the FGM modeling is impossibility at ANSYS, a macro has used for modeling and analysis.The results show a high accuracy and the iterative process converges very rapidly. It was also found that the final form of the generated solutions is independent of the initial trial function.
 
Keywords
Extended Kantorovich method; FGM plate; Galerkin method; Classical plate’s theory
Article Title [Persian]
تحلیل خیز صفحات چهار گوش FGM براساس تئوری کلاسیک صفحات به روش کانتروویچ توسعه یافته
Authors [Persian]
محمد مهدی نجفی زاده, مجید علوی, فؤاد سلماسی, شیما آذری
Abstract [Persian]
تحلیل خیز ورق FGM تحت بارگذاری یکنواخت و سینوسی منجر به حل معادله دیفرانسیل با مشتقات جزئی مرتبه چهار می‌شود که برای حل چنین معادله ای روشهای عددی متفاوتی ارائه شده است. روش تحلیل در این مقاله بر پایه روش تکرار شونده کانتروویچ توسعه یافته است. در روش حل تکرار شونده، معادلات دیفرانسیل به کمک روش گلرکین به‌دست می‌آیند. تحلیل بر مبنای فرضیات تئوری کلاسیک صفحات استوار است. صحت نتایج حاصل  برای ورق FGM، تحت شرایط تکیه گاهی متفاوت، با نتایج حاصل از حل  ANSYS و همچنین حل به روش ناویر مقایسه و تأیید شده است. ازآنجایی که در ANSYSمدلی برای تحلیل ورق FGM وجود ندارد، درمدلسازی و تحلیل از برنامه نویسی ماکرو استفاده شده است.  نتایج نشان می‌دهد روش کانتروویچ، روش دقیقی برای حل معادلات بوده و پاسخ ها به سرعت همگرا می‌شوند. همچنین پاسخ های نهایی مستقل از انتخاب تابع آزمون اولیه برای حل معادله می‌باشد.
Keywords [Persian]
روش کانتروویچ توسعه یافته، ورق FGM، روش گلرکین، تئوری کلاسیک صفحات
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