RİTZ YÖNTEMİ İLE DEĞİŞKEN KESİTLİ KOLONLARIN BURKULMA ANALİZİ

Yıl 2019, Cilt: 7 Sayı: 2, 452 - 458, 26.06.2019

Bekir Akgöz

https://doi.org/10.21923/jesd.539288

Cited By: 4

Öz

Bu çalışmada, eksenel bir basınç yükü etkisi altındaki
değişken kesitli kolonların burkulma analizi gerçekleştirilmiştir. Kesitin
kolon uzunluğu boyunca sürekli değiştiği dikkate alınmıştır. Büyük narinlik
oranına sahip üniform olmayan ince kolonları modellemek için klasik kiriş
teorisi (kayma deformasyonu etkisiz) kullanılmıştır. Çeşitli koniklik oranları
ve sınır koşulları için üniform olmayan kolonların kritik burkulma yüklerini
elde etmek için Ritz yöntemi uygulanmıştır. Değişken kesitli kolonların burkulma
yükleri üzerindeki koniklik oranı ve sınır koşullarının etkilerini incelemek
için detaylı bir parametrik çalışma gerçekleştirilmiştir. Bu analizin
geçerliliğini ve hassasiyetini kanıtlamak üzere literatürdeki mevcut ilgili
sonuçlar ile bazı karşılaştırmalı tablolar sunulmuştur.    

Anahtar Kelimeler

Burkulma, Kolon, Koniklik oranı, Düzensizlik, Sınır koşulları

BUCKLING ANALYSIS OF COLUMNS WITH VARIABLE CROSS-SECTION VIA RITZ METHOD

Öz

In this study, buckling analysis of columns with variable
cross-section is performed under an axial compressive load. It is considered
that the cross-section varies constantly along the length of the column.
Classical beam theory (without effect of shear deformation) is used to model
the non-uniform thin column with a large slenderness ratio. Ritz method is
applied to obtain the critical buckling loads of the non-uniform columns for
various taper ratios and boundary conditions. A detailed parametric study is
performed to investigate the influences of taper ratio and boundary conditions
on the buckling loads of column with variable cross-section. In order to
demonstrate the validity and sensitivity of the present analysis, some
comparative tables with the related results available in the literature are
presented.

Anahtar Kelimeler

Buckling, Column, Taper ratio, Non-uniformity, Boundary conditions

Kaynakça

• Akbaş, Ş.D., 2017. Post-buckling responses of functionally graded beams with porosities. Steel and Composite Structures, 24 (5), 579-589.
• Akgöz, B., Civalek, Ö., 2013a. Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory. Composite Structures, 98, 314-322.
• Akgöz, B., Civalek, Ö., 2013b. Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity. Structural Engineering and Mechanics, 48 (2), 195-205.
• Akgöz, B., Civalek, Ö., 2017. Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams. Composites Part B-Engineering, 129, 77-87.
• Arbabi, F., Li, F., 1991. Buckling of Variable Cross‐Section Columns: Integral‐Equation Approach. Journal of Structural Engineering, 117 (8), 2426-2441.
• Atay, M.T., 2009. Determination of Critical Buckling Loads for Variable Stiffness Euler Columns Using Homotopy Perturbation Method. International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2), 199-206.
• Avcar, M., 2010. Elastik zemin üzerinde bulunan her iki ucu ankastre mesnetli rastgele ve sürekli homojen olmayan kirişin titreşim analizi. Mühendislik Bilimleri ve Tasarım Dergisi, 1 (1), 33-38.
• Avcar, M., 2016. Pasternak Zemine Oturan Eksenel Yüke Maruz Homojen Olmayan Kirişin Serbest Titreşimi. Politeknik Dergisi, 19 (4), 507-512.
• Avcar, M., Mohammed, W.K.M., 2017. Winkler zemin ve fonksiyonel derecelendirilmiş malzeme özelliklerinin kirişin frekans parametrelerine etkilerinin incelenmesi. Mühendislik Bilimleri ve Tasarım Dergisi, 5 (3), 573-580.
• Coşkun, S.B., 2009. Determination of Critical Buckling Loads for Euler Columns of Variable Flexural Stiffness with a Continuous Elastic Restraint Using Homotopy Perturbation Method. International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2), 191-197.
• Coşkun, S.B., Atay, M.T., 2009. Determination of critical buckling load for elastic columns of constant and variable cross-sections using variational iteration method. Computers and Mathematics with Applications, 58 (11-12), 2260-2266.
• Darbandi, S.M., Firouz-Abadi, R.D., Haddadpour, H., 2010. Buckling of variable section columns under axial loading. Journal of Engineering Mechanics, 136 (4), 472-476.
• Eisenberger, M., 1991. Buckling loads for variable cross-section members with variable axial forces. International Journal of Solids and Structures, 27 (2), 135-143.
• Euler, L., 1744. Methodus Inveniendi Lineas Curvas Maximi Minimive Propreietate Gaudentes (Appendix, De Curvis Elasticis). Lausanne and Geneva: Marcum Michaelem Bousquet.
• Huang, Y., Li, X.-F., 2011. Buckling analysis of nonuniform and axially graded columns with varying flexural rigidity. Journal of Engineering Mechanics, 137 (1), 73-81.
• Li, Q.S., 2001. Exact solutions for buckling of non-uniform columns under axial concentrated and distributed loading. European Journal of Mechanics A/Solids, 20 (3), 485-500.
• Li, Q.S., Cao, H., Li, G.Q., 1995. Stability analysis of bars with varying cross-section. International Journal of Solids and Structures, 32 (21), 3217-3228.
• Khaniki, H.B., Hosseini-Hashemi, S., 2017. Buckling analysis of tapered nanobeams using nonlocal strain gradient theory and a generalized differential quadrature method. Materials Research Express, 4 (6), 065003.
• Mirjavadi, S.S., Matin, A., Shafiei, N., Rabby, S., Afshari, B.M., 2017. Thermal buckling behavior of two-dimensional imperfect functionally graded microscale-tapered porous beam. Journal of Thermal Stresses, 40 (10), 1201-1214.
• Mohammadimehr, M., Alimirzaei, S., 2017. Buckling and free vibration analysis of tapered FG-CNTRC micro Reddy beam under longitudinal magnetic field using FEM. Smart Structures and Systems, 19 (3), 309-322.
• Nguyen, T.K., Nguyen, B.D., Vo, T.P., Thai, H.T., 2017. Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams. Composite Structures, 176, 1050-1060.
• Nguyen, T.K., Vo, T.P., Nguyen, B.D., Lee, J., 2016. An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory. Composite Structures, 156, 238-252.
• Paul, A., Das, D., 2017. A study on non-linear post-buckling behavior of tapered Timoshenko beam made of functionally graded material under in-plane thermal loadings. Journal of Strain Analysis for Engineering Design, 52 (1), 45-56.
• Rajasekaran, S., Khaniki, H.B., 2017. Bending, buckling and vibration of small-scale tapered beams. International Journal of Engineering Science, 120, 172-188.
• Rayleigh, L., 1877. The Theory of Sound, vol. 1, The Macmillan Company.
• Rezaiee-Pajand, M., Masoodi, A.R., 2018. Exact natural frequencies and buckling load of functionally graded material tapered beam-columns considering semi-rigid connections. Journal of Vibration and Control, 24 (9), 1787-1808.
• Ritz, W., 1909. Theorie der Transversalschwingungen einer quadratische Platte mit freien Rändern, Annalen der Physik, 28, 737–786.
• She, G.L., Yuan, F.G., Ren, Y.R., 2017. Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory. Applied Mathematical Modelling, 47, 340-357.
• Siginer, A., 1992. Buckling of columns of variable flexural rigidity. Journal of Engineering Mechanics, 118 (3), 640-643.
• Timoshenko, S.P., Gere, J.M., 1961. Theory of Elastic Stability, McGraw-Hill, New York.
• Wang, C.M., Wang, C.Y., Reddy, J.N., 2005. Exact Solutions for Buckling of Structural Members, CRC Press, Florida.
• Yaylı, M.Ö., 2014. Free vibration behavior of a gradient elastic beam with varying cross section. Shock and Vibration, Article ID 801696.
• Yaylı, M.Ö., 2015a. Stability analysis of gradient elastic microbeams with arbitrary boundary conditions. Journal of Mechanical Science and Technology, 29 (8), 3373-3380.
• Yaylı, M.Ö., 2015b. Buckling analysis of a rotationally restrained single walled carbon nanotube. Acta Physica Polonica A, 127(3), 678-683.
• Yaylı, M.Ö., 2016. Buckling analysis of a microbeam embedded in an elastic medium with deformable boundary conditions. Micro & Nano Letters, 11(11), 741-745.
• Yaylı, M.Ö., 2018. Buckling analysis of Euler columns embedded in an elastic medium with general elastic boundary conditions. Mechanics Based Design of Structures and Machines, 46(1), 110-122.