Eksenel yönde tabakalı fonksiyonel derecelendirilmiş kirişlerin mekanik burkulma davranışı üzerinde tabaka pozisyonlarının etkilerinin incelenmesi

Yıl 2019, Cilt: 25 Sayı: 1, 20 - 26, 26.02.2019

Savaş Evran

Öz

Bu araştırmanın amacı eksenel yönde çoklu
tabakalı fonksiyonel derecelendirilmiş kirişlerin mekanik burkulma
davranışlarını incelemektir. Sayısal burkulma analizleri ANSYS olarak bilinen
sonlu elemanlar yazılımı kullanılarak gerçekleştirilmiştir. Her kiriş
konfigürasyonu Zirkonyum (ZrO₂)
ve Alüminyum (Al)
malzemelerinin değişik yüzde hacim fraksiyonları kullanılarak hazırlanmış üç
tabaka olarak önerilmiştir. Tabaka seviyeleri ve kirişlerin tabaka pozisyonları
Taguchi L₉ (3³) ortogonal
dizi tekniğine göre incelenmiştir. Tabakalar kontrol faktörleri olarak
değerlendirildi ve böylece dokuz sayısal analiz tutulu-tutulu sınır şartları
altında gerçekleştirildi. Görsel olarak en çok etkilenen tabakaları tespit
etmek için eksenel yönde tabakalı olarak fonksiyonel derecelendirilirmiş
kirişlerin birinci mod şekilleri gösterildi. Tabakaların optimum seviyelerini
elde edebilmek için sinyal-gürültü oran analizi kullanıldı. Sayısal sonuçlar
üzerinde önemli etkilere sahip tabakalar ve onların yüzde katkı oranlarını
çözmek için Varyans Analizi (ANOVA) uygulandı. En yüksek burkulma yükü Taguchi
metodolojisine bağlı elde edilen optimum seviyeli tabakaların değişik
pozisyonları kullanılarak karar verildi.

Anahtar Kelimeler

Fonksiyonel derecelendirilmiş malzemeler, Kiriş, Burkulma, Sonlu elemanlar metodu

Investigation of effects of layer positions on mechanical buckling behavior of axially layered functionally graded beams

Öz

The
aim of this research is to examine the mechanical buckling behavior of
multi-layered functionally graded beams in the axial direction. Numerical
buckling analyses were performed using finite element software called ANSYS.
Each beam configuration is suggested to be three layers prepared using various
percent volume fractions of Zirconia (ZrO₂) and Aluminum (Al)
materials. The levels of layers and layer positions of the beams were evaluated
according to Taguchi’s L₉ (3³) orthogonal array
technique. Layers were determined as control factor and so nine numerical
analyses were performed under clamped-clamped boundary conditions. The first
mode shapes of the axially layered functionally graded beams were demonstrated
in order to detect the most affected layers as visually. Analysis of
signal-to-noise ratio was applied to obtain the optimum levels of layers.
Analysis of Variance (ANOVA) was employed to solve the layers with significant
impacts and their percent contributions on numerical results. The maximum
buckling load was determined using various positions of layers with the optimum
levels obtained based on Taguchi methodology.

Anahtar Kelimeler

Functionally graded materials, Beam, Buckling, Finite element method

Kaynakça

• Li X, Li L, Hu Y, Ding Z, Deng W. "Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory". Composite Structures, 165, 250-265, 2017.
• Kahya V, Turan M. "Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory". Composites Part B: Engineering, 109, 108-115, 2017.
• Trinh LC, Vo TP, Thai H-T, Nguyen TK. "An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads". Composites Part B: Engineering, 100, 152-163, 2016.
• Vo TP, Thai HT, Nguyen T-K, Maheri A, Lee J. "Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory". Engineering Structures, 64, 12-22, 2014.
• Şimşek M. "Buckling of timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions". Composite Structures, 149, 304-314, 2016.
• Huang Y, Zhang M, Rong H. "Buckling analysis of axially functionally graded and non-uniform beams based on timoshenko theory". Acta Mechanica Solida Sinica, 29(2), 200-207, 2016.
• Yilmaz Y, Girgin Z, Evran S. "Buckling analyses of axially functionally graded nonuniform columns with elastic restraint using a localized differential quadrature method". Mathematical Problems in Engineering, 2013, 1-12, 2013.
• Aydogdu M. "Semi-Inverse method for vibration and buckling of axially functionally graded beams". Journal of Reinforced Plastics and Composites, 27(7), 683-691, 2008.
• Totry EM, Altus E, Proskura A. "Buckling of non-uniform beams by a direct functional perturbation method". Probabilistic Engineering Mechanics, 22(1), 88-99, 2007.
• Coşkun SB, Atay MT. "Determination of critical buckling load for elastic columns of constant and variable cross-sections using variational iteration method". Computers & Mathematics with Applications, 58(11-12), 2260-2266, 2009.
• Coşkun S. "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), 191-198, 2009.
• Arbabi F, Li F. "Buckling of variable cross-section columns: integral-equation approach". Journal of Structural Engineering, 117(8), 2426-2441, 1991.
• Yuan S, Ye K, Xiao C, Williams FW, Kennedy D. "Exact dynamic stiffness method for non-uniform Timoshenko beam vibrations and bernoulli-euler column buckling". Journal of Sound and Vibration, 303(3-5), 526-537, 2007.
• Bahar U, Metin A. "Three-dimensional vibration analyses of functionally graded plates under various boundary conditions". Journal of Reinforced Plastics and Composites, 26(18), 1847-1863, 2007.
• Shen HS. Functionally Graded Materials: Nonlinear Analysis of Plates and Shells. Boca Raton, New York, London, CRC Press, 2009.
• Ross PJ. Taguchi Techniques for Quality Engineering. 2nd ed. New York, USA, McGraw-Hill International Editions 1996.
• ANSYS Help, Version 13.