Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses

Öz

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. 

Anahtar Kelimeler

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

DEĞİŞKEN KALINLIKLI ELİPTİK FGM PLAKLARIN BURKULMA SICAKLIKLARININ BELİRLENMESİ

Öz

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.

Anahtar Kelimeler

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

Kaynakça

1. Bacciocchi, M., Eisenberger, M., Fantuzzi, N., Tornabene, F. and Viola, E. (2016) Vibration analysis of variable thickness plates and shells by the Generalized Differential Quadrature method, Composite Structures, 156, 218-237.
2. Delale, F. and Erdoğan, F. (1983) The crack problem for a non-homogenous plane, ASME Journal of Applied Mechanics, 50, 609-614.
3. Duc, N. D. and Van Tung H. (2011) Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations, Composite Structures, 93, 2874-2881.
4. Ganapathi, M. and Prakash, T. (2006) Thermal buckling of simply supported functionally graded skew plates, Composite Structures, 74, 247-250.
5. Javaheri, R. and Eslami, M. R. (2002) Thermal buckling of functionally graded plates based on higher order theory, Journal of Thermal Stresses, 25, 603-625.
6. Kobayashi, H. and Sonada, K. (1990) Buckling of rectangular plates with tapered thickness, Journal of Structural Engineering, 116, 1278-1289.
7. Lanhe, W. (2004) Thermal buckling of a simply supported moderately thick rectangular FGM plate, Composite Structures, 64, 211-218.
8. Na, K. S. and Kim, J. H. (2004) Three dimensional thermal buckling analysis of functionally graded materials, Composites Part B, 35, 429-437.

9. Na, K. S. and Kim, J. H. (2006) Thermal postbuckling investigations of functionally graded plates using 3-D finite element method, Finite Elements in Analysis and Design, 42, 749-756.
10. Najafizadeh, M. M. and Heydari, H. R. (2004) Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory, European Journal of Mechanics A/Solids, 23, 1085-1100.
11. Najafizadeh, M. M. and Heydari, H. R. (2008) An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression, International Journal of Mechanical Sciences, 50, 603-612.
12. Nerantzaki, M. S. and Katsikadelis, J. T. (1996) Buckling of plates with variable thickness-an analog equation solution. Engineering Analysis with Boundary Elements, 18:149-154.
13. Prakash, T., Singha, M. K. and Ganapathi, M. (2008). Thermal post-buckling analysis of FGM skew plates. Engineering Structures, 30:22-32.
14. Shariat, B. A. S. and Eslami, M. R. (2005). Effect of initial imperfections on thermal buckling of functionally graded plates, Journal of Thermal Stresses, 28, 1183-1198.
15. Shariat, B. A. S. and Eslami, M. R. (2006) Thermal buckling of imperfect functionally graded plates, International Journal of Solids and Structures, 43, 4082-4096.
16. Shariat, B. A. S. and Eslami, M. R. (2007) Buckling of thick functionally graded plates under mechanical and thermal loads, Composite Structures, 78, 433-439.
17. Shen, H. S. (2007) Thermal post-buckling behavior of shear deformable FGM plates with temperature-dependent properties, International Journal of Mechanical Sciences, 49, 466-478.
18. Shen, H. S. and Li, S. R. (2008) Postbuckling of sandwich plates with FGM face sheets and temperature dependent properties, Composites Part B-Engineering, 39, 332-344.
19. Tornabene, F. (2009) Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution, Computer Methods in Applied Mechanics and Engineering, 198, 2911-2935.
20. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2016) The local GDQ method for the natural frequencies of doubly-curved shells with variable thickness: A general formulation, Composites Part B Engineering, 92, 265-289.
21. Van Tung, H. and Duc N. D. (2010) Nonlinear analysis of stability for functionally graded plates under mechanical and thermal loads, Composite Structures, 92, 1184-1191.
22. Wang, C. M., Wang, L. and Liew, K. M. (1994) Vibration and buckling of super elliptical plates, Journal of Sound and Vibration, 171, 301-314.
23. Wang, C. M., Hong, G. M. and Tan, T. J. (1995) Elastic buckling of tapered circular plates, Computers and Structures, 55, 1055-1061.
24. Wu, L. (2004) Thermal buckling of simply supported moderately thick rectangular FGM plate, Composite Structures, 64, 211-218.