Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses

Abstract

In this paper, the thermal buckling loads of elliptical thin plates made of functionally graded material (FGM) with thicknesses that vary parabolically are examined. The aim is to study the effect of parabolic thickness variations in the directions of both axes on the thermal buckling of FGM plates. In the analyses, the boundaries are assumed to be simply supported and clamped. Rayleigh-Ritz method is applied to solve the partial differential equations. The Poisson’s ratios of the plates are kept constant, but their moduli of elasticity and thermal expansion coefficients are assumed to vary functionally in the thickness direction due to the material characteristics of FGMs. The study is carried out for several plate aspect ratios. Thermal buckling results of elliptical FGM plates with parabolically varying thicknesses are determined and the critical temperatures of those plates are obtained. 

Keywords

• Elliptical plate,Thermal buckling,Variable thickness,Temperature,FGM,Rayleigh-Ritz method

DEĞİŞKEN KALINLIKLI ELİPTİK FGM PLAKLARIN BURKULMA SICAKLIKLARININ BELİRLENMESİ

Abstract

Bu çalışmada, bir fonksiyona bağlı olarak değişen malzemeden (FGM) yapılmış, kalınlıkları parabolik olarak değişen, eliptik ince plakların termal burkulma yükleri incelenmiştir. Amaç, her iki eksendeki parabolik kalınlık değişimlerinin FGM plakların termal burkulması üzerindeki etkisini incelemektir. Analizlerde, sınır koşulları basit mesnetli ve ankastre olarak varsayılmaktadır. Kısmi diferansiyel denklemleri çözmek için Rayleigh-Ritz yöntemi kullanılmıştır. Plakların Poisson oranlarının sabit olduğu, ancak elastisite modülü ve ısı genleşme katsayılarının, FGM'lerin malzeme özellikleri nedeniyle kalınlık yönünde fonksiyonel olarak değiştiği varsayılır. Çalışma çeşitli plak en/boy oranları için gerçekleştirilmiştir. Parabolik olarak değişen kalınlıklara sahip eliptik FGM plaklarının termal burkulma sonuçları belirlenip, bu plakların kritik sıcaklıkları elde edilmiştir.

Keywords

• Eliptik plak,Termal burkulma,Değişken kalınlık,Sıcaklık,FGM,Rayleigh-Ritz yöntemi.

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