Abstract




 
   

Volume 25 - 1 - Transactions A: Basics, January 2012, pp. 89-106    Article in Press

Link: http://www.ije.ir/Vol25/No1/A/9.pdf
 
  BUCKLING ANALYSIS OF FUNCTIONALLY GRADED MINDLIN PLATES SUBJECTED TO LINEARLY VARYING IN-PLANE LOADING USING POWER SERIES METHOD OF FROBENIUS
 

Mahdi Bodaghi
Mechanical Engineering Department, Shahid Bahonar University of Kerman
Jomhouri Blvd. Kerman, Iran
mahdibodaghi@gmail.com

Ali Saidi
Mechainical Engineering, Shahid Bahounar university of Kerman
Jomhouri Blvd. Kerman.
saidi@mail.uk.ac.ir
 
( Received: August 02, 2011 – Accepted: November 17, 2011 )
 
 

Abstract    In this paper, buckling behavior of moderately thick functionally graded rectangular plates resting on elastic foundation subjected to linearly varying in-plane loading is investigated. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. Based on the first-order shear deformation plate theory and the neutral surface concept, the equilibrium and stability equations are derived. An analytical approach is employed to decouple the stability equations, as these equations are converted into two decoupled equations. Employing Levy-type solution, the buckling equation is reduced to an ordinary differential equation with variable coefficients and solved exactly using power series method of Frobenius. To examine accuracy of the present formulation and procedure, several convergence and comparison studies are investigated. Furthermore, the effects of different parameters of plate and elastic foundation on the critical buckling load of functionally graded rectangular plate are discussed.

 

Keywords    Buckling analysis, Functionally graded material, Power series solution, Linear in-plane loading, Elastic foundation, Mindlin plate

 

چکیده    در اين مقاله رفتار کمانشي ورق هاي مستطيلي ساخته شده از مواد هدفمند بر روي بستر الاستيک و تحت بارگذاري درون صفحه­اي که به طور خطي تغيير مي­کند مورد بررسي قرار گرفته است. موقعيت رويه خنثي براي ورق هدفمند که خواص آن در جهت ضخامتش تغيير مي­کند تعيين شده است. براساس تئوري تغيير شکل برشي مرتبه اول ورق و مفهوم رويه خنثي فيزيکي، معادلات تعادل و پايداري به دست آمده است. به منظور جداسازي معادلات پايداري، يک روش تحليلي به کار گرفته شده است به گونه­اي که اين معادلات به دو معادله مستقل تبديل شده­اند. با استفاده از روش حل لوي، معادله کمانش به يک معادله ديفرانسيل معمولي با ضرايب متغير تبديل گشته و سپس به صورت دقيق با استفاده از روش سري تواني فروبنيوس حل شده است. به منظور بررسي دقت حل حاضر چند مطالعه مقايسه­اي و همگرايي انجام شده است. همچنين تاثير پارامترهاي مختلف ورق و بستر الاستيک روي بار بحراني کمانش ورق مستطيلي ساخته شده از مواد هدفمند مورد بررسي قرار گرفته است.

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