Applying Differential Transform Method on the Effect of the Elastic Foundation on the out - Plane Displacement of the Functionally Graded Circular Plates
محورهای موضوعی : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیکسمیه عباسی 1 , فاطمه فرهت نیا 2 , سعید رسولی جزی 3
1 - کارشناس ارشد، دانشکده مکانیک، دانشگاه آزاد اسلامی واحد خمینی شهر
2 - استادیار، دانشکده مکانیک، دانشگاه آزاد اسلامی واحد خمینی شهر
3 - استادیار، دانشکده مکانیک، دانشگاه آزاد اسلامی واحد خمینی شهر
کلید واژه: Circular plates, Differential transform method (DTM), Winkler elastic foundation, Functionally graded materials (FGM), Out of plane displacement,
چکیده مقاله :
In this paper, the effect of elastic foundation on the out of plane displacement of functionally graded circular plates using differential transform method is presented. Differential transform method is a semi-analytical-numerical solution technique that is capable to solve various types of differential equations. Using this method, governing differential equations are transformed into recursive relations and boundary conditions are changed into algebraic equations. Since the problem of plates on elastic foundation have a great practical importance in modern engineering structures and Winkler foundation model is widely used, plate is assumed on Winkler elastic foundation. In this article functionally graded plate is considered in which material properties vary through the thickness direction by power-law distribution. Analysis results of out of plane displacement of plate on elastic foundation under uniform transverse loads are obtained in different terms of foundation stiffness, material properties and boundary conditions. In order to validate the solution technique, results obtained are compared with the results of the finite element method (FEM).
روش تبدیل دیفرانسیلی یک تکنیک حل نیمه تحلیلی- عددی است که با استفاده از آن، معادلات دیفرانسیل حاکم بر ورق به روابط بازگشتی تبدیل شده و شرایط مرزی به معادلات جبری تبدیل میشوند. در این مطالعه ورق بر روی بستر ارتجاعی از نوع وینکلر قرار گرفته است. ورق از جنس مواد تابعی است؛ به طوری که خواص آن در راستای ضخامت بر اساس مدل توانی تغییر میکند. نتایج تحلیل جابهجایی خارج از صفحه ورق تابعی بر روی بستر ارتجاعی تحت بارگذاری گسترده یکنواخت، به ازای مقادیر مختلفی از سفتی بستر ارتجاعی، توان ماده تابعی و شرایط مرزی به دست آمده است. به منظور نشان دادن دقت روش تبدیل دیفرانسیلی و تأیید نتایج حاصل از آن، پاسخ ها با نتایج روش اجزا محدود مقایسه شده که تطابق خوبی مشاهده شده است.
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