Farklı uç sınır koşullarına sahip kirişin Carrera Birleşik Formulasyon (CUF) çerçevesinde statik analizi

Yıl 2021, , 255 - 265, 15.01.2021

Esra Eylem Karataş

https://doi.org/10.28948/ngumuh.764252

Öz

Bu çalışma kapsamında düzgün yayılı yük etkisinde farklı uç sınır koşullarına sahip dikdörtgen kesitli bir kirişin, birleşik kiriş teorilerinden biri olan Carrera Birleşik Formulasyon (CUF) çerçevesinde lineer statik analizi incelenmiştir. Kesit yer değiştirme alanının birleşik formulasyonu, kesit düzlemi üzerinde tanımlanmış eşdeğer Taylor ve Lagrange tipi açılım fonksiyonları ile ayrı ayrı ifade edilmiştir. Yönetici denklemler ve sonlu elemanlar formulasyonunun elde edilmesinde virtüel iş prensibi kullanılmıştır. İlk olarak, hem Taylor tipi hem de Lagrange tipi açılım fonksiyonlarının ayrı ayrı kullanılması ile farklı uç sınır koşullarına ait dikdörtgen kesitli kiriş için bir yakınsama çalışması ve elde edilen sayısal sonuçların güvenilirliğini test etmek amacı ile literatürden alınan analitik çözümler ile bir karşılaştırma çalışması yapılmıştır. Daha sonra, uygun olan açılım fonksiyonu kullanılarak CUF çerçevesinde, örnek problemlerin lineer statik analizi yapılmış, sayısal sonuçlar tablo ve grafikler ile sunulmuştur. Bu çalışmada kullanılan bilgisayar algoritması MUL2 grubu tarafından geliştirilmiş olup, literatürde mevcut olan pek çok çalışma ile test edilmiştir.

Anahtar Kelimeler

Geliştirilmiş kiriş teorisi,, Carrera Birleşik Formulasyon (CUF),, sonlu elemanlar yöntemi.

Destekleyen Kurum

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Proje Numarası

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Static analysis of a beam with different end boundary conditions via Carrera Unified Formulation (CUF)

Öz

In this study, lineer static analysis of a rectangular beam with compact cross-section for different end boundary conditions subjected to uniformly distributed load is analyzed within the framework of Carrera Unified Formulation (CUF), which is one of the unified beam theory. The unified formulation of cross-section displacement field is expressed by employing both Taylor and Lagrange type expansion functions defined over the cross-section. The Principle of Virtual Displacements (PVD) is used to obtain the governing differential equations and the Finite Element formulation. First, by using separately both Taylor and Lagrange types of expansion functions for a rectangular beam with compact cross-section with different end boundary conditions study of convergence and comparison with results obtained from the analytical solutions in the literature is performed in order to examine the reliability of the results obtained. Then, using the appropriate expansion function, lineer static analysis of sample problems is made within the framework of CUF and numerical results are presented with the help of tables and graphics. The computer algorithm used in the present paper is developed by MUL2 group and tested by many studies, available in the relevant literature.

Anahtar Kelimeler

Refined beam theory, Carrera unified formulation (CUF), Finite element method

Proje Numarası

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Kaynakça

• D. T. Mucichescu, Bounds for stiffness of prismatic beams. Journal of Structural Engineering, 110, 1410-14, 1984.
• E. Carrera, G. Giunta and M. Petrolo, Beam Structures: Classical and Advanced Theories. JohnWiley & Sons, United Kingdom: Chichester, West Sussex, 2011.
• H. T. Thai and T. P. Vo, Bending and Free Vibration of Functionally Graded Beams Using Various Higher-order Shear Deformation Beam Theories. International Journal of Mechanical Sciences, 62(1), 57-66, 2012. https://doi.org/10.1016/j.ijmecsci.2012.05.014.
• K. K. Pradhan and S. Chakraverty, Effects of Different Shear Deformation Theories on Free Vibration of Functionally Graded Beams. International Journal of Mechanical Sciences, 82, 149-60, 2014. https://doi.org/10.1016/j.ijmecsci.2014.03.014.
• M. A. Levinson, An accurate simple theory of statics and Dynamics of elastic plates. Mech. Res. Commun., 7(6), 343-50, 1980.https://doi.org/10.1016/0093-6413(80)90049-X.
• M. A. Levinson, A new rectangular beam theory. Journal of Sound and Vibration, 74(1), 81-7, 1981. https://doi.org/10.1016/0022-460X(81)90493-4.
• M. Z. Wang and W. Wang, A refined theory of beams. J. Eng. Mech., Suppl., 324-327, 2003.
• Y. Gao and M. Wang, A refined theory of rectangular deep beams based on general solutions of elasticity. Sci. China Ser. G, 36(3), 286-97, 2006.
• A. Bekhadda, et al., Static buckling and vibration analysis of continuously graded ceramic-metal beams using a refined higher order shear deformation theory. Multidiscipline Modeling In Materials And Structures, 15(6), 1152-69, 2019.
• J. Cai and C. D. Moen, Elastic buckling analysis of thin-walled structural members with rectangular holes using generalized beam theory. Thin-Walled Structures, 107, 274-86, 2016. https://doi.org/ 10.1016/j.tws.2016.06.014.
• E. Carrera, A. Pagani, M. Petrolo, et al., Recent developments on refined theories for beams with applications. Mechanical Engineering Reviews, 2 (2), 14-00298, 2015.https://doi.org/10.1299/mer.14-00298.
• E. Carrera, A. G. de Miguel, and A. Pagani, Extension of MITC to higher-order beam models and shear locking analysis for compact, thin-walled, and composite structures. International Journal For Numerical Methods In Engineering, 112(13), 1889-908, 2017.https://doi.org/10.1002/nme.5588.
• S. Richard, Generalized Beam Theory-an adequate method for coupled stability problems. Thin-Walled Structures, 19(2-4), 161-80, 1994.
• G. Taig and G. Ranzi, Generalised Beam Theory (GBT) for composite beams with partial shear interaction. Engineering Structures, 99, 582-602, 2015. https://doi.org/10.1016/j.engstruct.2015.05.025.
• S. W. Tsai, Composites Design. Dayton, Think Composites, 1988.
• J. N. Reddy, Mechanics of laminated composite plates and shells. Theory and Analysis. CRC Press, 2004.
• K. Bathe, Finite element procedure. Prentice Hall, Englewood Cliffs, NJ, 1996.
• S. Timoshenko and J. N. Goodier, Theory of Elasticity. McGraw-Hill Book Company, Inc., 1951.
• G. Shi and G. Z. Voyiadjis, A sixth-order theory of shear deformable beams with variational consistent boundary conditions. J. Appl. Mech. 78(2), 021019-1-021019-11, 2011.