TABAKALI KOMPOZİT KİRİŞLERİN EĞİLME ANALİZİ

Year 2020, Issue: 001, 19 - 33, 30.06.2020

Mustafa Haluk Saraçoğlu Mustafa Emin Gürlek

Abstract

Bu çalışmada; tabakalı kompozit kirişlerin gerilme ve şekil değiştirme analizleri sonlu farklar yöntemi kullanılarak yapılmıştır. Analizlerde farklı mesnet koşulları ve farklı yüklemeler etkisi altındaki kirişler, Euler-Bernoulli ve Timoshenko kiriş teorilerine göre incelenmiştir. İncelenen bu kirişler farklı tabaka sayıları ve farklı oryantasyon açılarına sahiptirler. Tabakalı kompozit kirişler, düzlem gerilme problemi olarak ele alınmıştır. Gerilme ve şekil değiştirme analizleri yapılırken ilgili bünye bağıntıları ve denge denklemleri için bazı kabuller yapılmıştır. Üç boyutlu doğrusal olmayan şekil değiştirme ifadeleri, iki boyutlu ve doğrusal şekil değiştirme ifadelerine indirgenmiştir. Bu diferansiyel denklemlerin çözümü için merkezi sonlu fark ifadeleri kullanılmıştır. Her sonlu fark düğüm noktası için merkezi sonlu fark ifadesi yazılmıştır. Daha sonra bu ifadeler sınır şartlarına göre tekrar düzenlenmiştir. Elde edilen bünye bağıntıları ve denge denklemlerinin çözümü için açık kaynak kodlu olan DEV-C++ V 5.8.3 editörü kullanılarak bir bilgisayar programı geliştirilmiştir. Geliştirilen bu program kullanılarak sayısal uygulamalar yapılmıştır. Literatürde bulunan örnek problemler çözülerek geliştirilen bilgisayar programının doğruluğu test edilmiştir.Sonuç olarak tabaka dizilişleri ve sınır şartları farklı tabakalı kompozit kirişlerin yük altındaki gerilme ve şekil değiştirme davranışları ortaya konulmuştur. Elde edilen sonuçlar tablo ve grafiklerle sunulmuştur.

Keywords

Gerilme, Oryantasyon Açısı, Sonlu Farklar Metodu, Şekil Değiştirme, Tabakalı Kompozit Kiriş

BENDING ANALYSIS OF LAMINATED COMPOSITE BEAMS

Abstract

In this study; stress and displacement analysis of laminated composite beams were performed using finite difference method. In the analyses, different support conditions and beams under different loading conditions were investigated according to Euler-Bernoulli and Timoshenko beam theories. These examined beams have different lamination scheme and different orientation angles. Laminated composite beams are considered as plane stress problem. When stress and strain analyses were carried out, some assumptions were made for related constitutive links and equilibrium equations. The three-dimensional non-linear deforming expressions were reduced to two-dimensional and linear strain expressions. The central finite difference relations were used to solve these differential equations. For each finite difference node a central finite difference statement was written. These expressions were then rearranged according to the boundary conditions. A software has been developed using the open- source DEV-C++ V 5.8.3 editor for solving the obtained constitutive and equilibrium equations. Numerical applications were performed using this developed program. The sample problems in the literature have been solved and the accuracy of the developed software has been tested. As a result, stress and displacement behaviour of laminated composite beams under loads which has different boundary conditions, lamination scheme and orientation angle were presented. The results were presented in tables and graphs.

Keywords

Stress, Orientation Angle, Finite Difference Method, Strain, Laminated composite beam

References

• [1] Gürlek, M.E., (2018), Tabakalı Kompozit Kirişlerin Sonlu Farklar Metodu İle Analizi, Yüksek Lisans Tezi, Dumlupınar Üniversitesi Fen Bilimleri Enstitüsü, Kütahya, 92s.
• [2] Karama, M., Afaq, K.S., Mistou, S., (2003), Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity. International Journal of Solids and Structures, 40(6), 1525-1546.
• [3] Reddy, J. N., (2004), Mechanics of laminated composite plates and shells: theory and analysis. (2nd ed.). Boca Raton: CRC Press, 81-244.
• [4] Carrera, E., Giunta, G., Petrolo, M., (2011), Beam structures : classical and advanced theories. (1st ed.). New Delhi, India: John Wiley & Sons, Ltd, 9-42.
• [5] Dökmeci, M, C., (1973), Stress and strain analysis in elastic laminated composite beams. Journal of Elasticity, 3 (1), 27-43.
• [6] Khedir, A.A., Reddy, J.N., (1997), An exact solution for the bending of thin and thick cross-ply laminated beams. Composite Structures, 37, 195-203.
• [7] Tahani, M., (2007), Analysis of laminated composite beams using layerwise displacement theories. Composite Structures, 79, 535-547.
• [8] Catapano, A., Giunta, G., Belouettar, S., and Carrera, E., (2011), Static analysis of laminated beams via a unified formulation. Composite Structures, 94, 75-83.
• [9] Chen, W., Li, L., and Xu, M., (2011), A modified couple stress model for bending analysis of composite laminated beams with first order shear deformation. Composite Structures, 93, 2723-2732.
• [10] Aguiar, R. M., Moleiro, F., and Mota Soares, C. M., (2012), Assessment of mixed and displacement-based models for static analysis of composite beams of different cross-sections. Composite Structures, 94, 601-616.
• [11] Vo, T. P., Thai, H., (2012), Static behavior of composite beams using various refined shear deformation theories. Composite Structures, 94, 2513-2522.
• [12] Afshin, M., Taheri-Behrooz, F., (2015), Interlaminar stresses of laminated composite beams resting on elastic foundation subjected to transverse loading. Computational Materials Science,96, 439-447.
• [13] Özütok, A., Madenci E., (2017), Static analysis of laminated composite beams based on higher- order shear deformation theory by using mixed-type finite element method, International Journal of Mechanical Sciences, 130, 234-243.
• [14] Boay, C. G., Wee, Y. C., (2008), Coupling effects in bending, buckling and free vibration of generally laminated composite beams. Composites Science and Technology, 68, 1664-1670.
• [15] Abadi, M. M., Daneshmehr, A. R., (2014), An investigation of modified couple stress theory in buckling analysis of micro composite laminated Euler–Bernoulli and Timoshenko beams. International Journal of Engineering Science, 75, 40-43.
• [16] Nguyen, T-K., Nguyen, N-D., Vo, T. P, and Thai, H-T., (2017), Trigonometric-series solution for analysis of laminated composite beams. Composite Structures, 160, 142-151.
• [17] Sayyad, A. S., Ghugal, Y. M., (2017), Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature. Composite Structures, 171, 486-504.
• [18] Loja, M. A. R., Barbosa, J. I., Soares, C. M. M., (2001), Static and dynamic behaviour of laminated composite beams. International Journal of Structural Stability and Dynamics, 1 (4), 545-560.
• [19] Aydoğdu, M., (2005), Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method. International Journal of Mechanical Sciences, 47, 1740-1755.
• [20] Jun, L., Hongxing, H., and Rongying, S., (2008), Dynamic finite element method for generally laminated composite beams. International Journal of Mechanical Sciences, 50, 466-480.
• [21] Manoach, E., Warminski, J., Mitura, A., and Samborski, S., (2013), Dynamics of a laminated composite beam with delamination and inclusions. European Physical Journal Special Topics,222 (7), 1649-1664.
• [22] Staab, G. H., (2015), Laminar Composites (2nd ed.). USA: Elsevier Inc., 294-295.