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Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses

Year 2019, Volume 24, Issue 1, 75 - 88, 30.04.2019
https://doi.org/10.17482/uumfd.480661

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. 

References

  • 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.
  • Delale, F. and Erdoğan, F. (1983) The crack problem for a non-homogenous plane, ASME Journal of Applied Mechanics, 50, 609-614.
  • 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.
  • Ganapathi, M. and Prakash, T. (2006) Thermal buckling of simply supported functionally graded skew plates, Composite Structures, 74, 247-250.
  • 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.
  • Kobayashi, H. and Sonada, K. (1990) Buckling of rectangular plates with tapered thickness, Journal of Structural Engineering, 116, 1278-1289.
  • Lanhe, W. (2004) Thermal buckling of a simply supported moderately thick rectangular FGM plate, Composite Structures, 64, 211-218.
  • Na, K. S. and Kim, J. H. (2004) Three dimensional thermal buckling analysis of functionally graded materials, Composites Part B, 35, 429-437.
  • 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.
  • 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.
  • 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.
  • 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.
  • Prakash, T., Singha, M. K. and Ganapathi, M. (2008). Thermal post-buckling analysis of FGM skew plates. Engineering Structures, 30:22-32.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Wang, C. M., Hong, G. M. and Tan, T. J. (1995) Elastic buckling of tapered circular plates, Computers and Structures, 55, 1055-1061.
  • Wu, L. (2004) Thermal buckling of simply supported moderately thick rectangular FGM plate, Composite Structures, 64, 211-218.

DEĞİŞKEN KALINLIKLI ELİPTİK FGM PLAKLARIN BURKULMA SICAKLIKLARININ BELİRLENMESİ

Year 2019, Volume 24, Issue 1, 75 - 88, 30.04.2019
https://doi.org/10.17482/uumfd.480661

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.

References

  • 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.
  • Delale, F. and Erdoğan, F. (1983) The crack problem for a non-homogenous plane, ASME Journal of Applied Mechanics, 50, 609-614.
  • 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.
  • Ganapathi, M. and Prakash, T. (2006) Thermal buckling of simply supported functionally graded skew plates, Composite Structures, 74, 247-250.
  • 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.
  • Kobayashi, H. and Sonada, K. (1990) Buckling of rectangular plates with tapered thickness, Journal of Structural Engineering, 116, 1278-1289.
  • Lanhe, W. (2004) Thermal buckling of a simply supported moderately thick rectangular FGM plate, Composite Structures, 64, 211-218.
  • Na, K. S. and Kim, J. H. (2004) Three dimensional thermal buckling analysis of functionally graded materials, Composites Part B, 35, 429-437.
  • 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.
  • 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.
  • 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.
  • 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.
  • Prakash, T., Singha, M. K. and Ganapathi, M. (2008). Thermal post-buckling analysis of FGM skew plates. Engineering Structures, 30:22-32.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Wang, C. M., Hong, G. M. and Tan, T. J. (1995) Elastic buckling of tapered circular plates, Computers and Structures, 55, 1055-1061.
  • Wu, L. (2004) Thermal buckling of simply supported moderately thick rectangular FGM plate, Composite Structures, 64, 211-218.

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

İşıl SANRI KARAPINAR (Primary Author)
MALTEPE ÜNİVERSİTESİ, MÜHENDİSLİK VE DOĞA BİLİMLERİ FAKÜLTESİ
Türkiye

Publication Date April 30, 2019
Application Date November 8, 2018
Acceptance Date February 7, 2019
Published in Issue Year 2019, Volume 24, Issue 1

Cite

Bibtex @research article { uumfd480661, journal = {Uludağ University Journal of The Faculty of Engineering}, issn = {2148-4147}, eissn = {2148-4155}, address = {}, publisher = {Bursa Uludağ University}, year = {2019}, volume = {24}, pages = {75 - 88}, doi = {10.17482/uumfd.480661}, title = {Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses}, key = {cite}, author = {Sanrı Karapınar, İşıl} }
APA Sanrı Karapınar, İ. (2019). Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses . Uludağ University Journal of The Faculty of Engineering , 24 (1) , 75-88 . DOI: 10.17482/uumfd.480661
MLA Sanrı Karapınar, İ. "Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses" . Uludağ University Journal of The Faculty of Engineering 24 (2019 ): 75-88 <https://dergipark.org.tr/en/pub/uumfd/issue/43494/480661>
Chicago Sanrı Karapınar, İ. "Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses". Uludağ University Journal of The Faculty of Engineering 24 (2019 ): 75-88
RIS TY - JOUR T1 - Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses AU - İşıl Sanrı Karapınar Y1 - 2019 PY - 2019 N1 - doi: 10.17482/uumfd.480661 DO - 10.17482/uumfd.480661 T2 - Uludağ University Journal of The Faculty of Engineering JF - Journal JO - JOR SP - 75 EP - 88 VL - 24 IS - 1 SN - 2148-4147-2148-4155 M3 - doi: 10.17482/uumfd.480661 UR - https://doi.org/10.17482/uumfd.480661 Y2 - 2019 ER -
EndNote %0 Uludağ University Journal of The Faculty of Engineering Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses %A İşıl Sanrı Karapınar %T Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses %D 2019 %J Uludağ University Journal of The Faculty of Engineering %P 2148-4147-2148-4155 %V 24 %N 1 %R doi: 10.17482/uumfd.480661 %U 10.17482/uumfd.480661
ISNAD Sanrı Karapınar, İşıl . "Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses". Uludağ University Journal of The Faculty of Engineering 24 / 1 (April 2019): 75-88 . https://doi.org/10.17482/uumfd.480661
AMA Sanrı Karapınar İ. Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses. UUJFE. 2019; 24(1): 75-88.
Vancouver Sanrı Karapınar İ. Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses. Uludağ University Journal of The Faculty of Engineering. 2019; 24(1): 75-88.
IEEE İ. Sanrı Karapınar , "Determination of Buckling Temperatures for Elliptical FGM Plates with Variable Thicknesses", Uludağ University Journal of The Faculty of Engineering, vol. 24, no. 1, pp. 75-88, Apr. 2019, doi:10.17482/uumfd.480661

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