Çatlaklı Kompozit Plakaların Dinamik Kararlılığı

Yıl 2022, Cilt: 9 Sayı: 1, 208 - 224, 30.06.2022

Özgür Sayer , Hasan Öztürk , Emine Çınar Yeni , Aysun Baltacı , Rafet Can Ümütlü

https://doi.org/10.35193/bseufbd.1003607

Öz

Bu çalışmada, sonlu elemanlar yöntemi kullanılarak periyodik eksenel yüklemeye maruz kalan çatlaklı kompozit plakaların dinamik kararsızlık bölgesi sayısal olarak incelenmiştir. Klasik laminasyon teorisine dayanan kompozit plaka, sonlu elemanlar yöntemi kullanılarak modellenmiştir. Kompozit plakanın sınır şartlarının bir taraftan sabitlendiği, diğer tarafların serbest olduğu varsayılmaktadır. Kompozit plaka, her biri dört düğüme sahip kare plaka elemanlarına bölünmüştür. Her düğümün bir vektörel ve iki dönme serbestlik derecesine sahiptir, bu yüzden bu kare plaka elemanlar on iki serbestlik derecesine sahiptir. Plakanın dinamik kararsızlık bölgesi hesaplamak için kullanılan Mathieu-Hill tipi hareket denklemi, Lagrange denkleminden elde edilen enerji ifadeleri kullanılarak oluşturulmuştur. Geliştirilen MATLAB sonlu elemanlar kodu kullanılarak çatlağın kompozit plakalar için dinamik kararsızlık bölgesi üzerindeki etkisi incelenmiştir. 

Anahtar Kelimeler

Dinamik Kararsızlık Bölgesi, Çatlaklı Kompozit Plakalar, Sonlu Elemanlar Metodu

Dynamic Stability of Cracked Composite Plates

Öz

In this study, the dynamic instability region of cracked composite plates subjected to periodic axial loading has been investigated numerically by using the finite element method. A composite plate based on classical lamination theory is modeled by using the finite element method. It is assumed that the boundary condition of the composite plate is fixed on one side and the other sides are free. The composite plate is divided into square plate elements, each having four nodes. Each node has one translational and two rotational degrees of freedom, therefore, the square plates have twelve degrees of freedom. Mathieu-Hill type motion equation, which is used to calculate the dynamic instability region of the plate is created by using energy expressions obtained from the Lagrange equation. The developed MATLAB finite element code is used to examine the effect of crack on dynamic instability region for composite plates. 

Anahtar Kelimeler

Dynamic Instability Region, Cracked Composite Plates, Finite Element Method

Kaynakça

• Chen, L. W., & Yang, J. Y. (1990). Dynamic stability of laminated composite plates by the finite element method. Computers & Structures, 36 (5), 845-851.
• Reddy, J. N. (2003). Mechanics of laminated composite plates theory and analysis 2nd ed. CRC Press, New York, 858.
• Voyiadjis, G. Z., & Kattan, P. I. (2005). Mechanics of composite materials with MATLAB. Springer, Berlin, 337.
• Daniel, I. M., & Ishai, O. (2006). Engineering mechanics of composite materials 2nd ed. Oxford University Press, New York, 463.
• Aggarwal, V. D. (2013). Optimization of variable stiffness composite plate structures. M.Sc. Thesis, San Diego State University, San Diego.
• Krawczuk, M., & Ostachowicz, W. M. (1994). A finite plate element for dynamic analysis of a cracked plate. Computer methods in applied mechanics and engineering, 115 (1-2), 67-78.
• Avadutala, V. S. (2005). Dynamic analysis of cracks in composite materials. M.Sc. Thesis, Blekinge Institute of Technology, Karlskrona.
• Khoei, A. R. (2015). Extended finite element method: theory and applications. John Wiley & Sons, West Sussex, 584.
• Timoshenko, S. P., & Gere, J. M. (1961). Theory of elastic stability 2nd ed. McGraw- Hill Book Company, New York, 541.
• Bolotin, V. V. (1964). The dynamic stability of elastic systems. Holden-Day Inc., San Francisco, 455.
• Dey, P., & Singha, M. K. (2006). Dynamic stability analysis of composite skew plates subjected to periodic in-plane load. Thin-Walled Structures, 44 (9), 937-942.
• Ozturk, H., & Sabuncu, M. (2005). Stability analysis of a cantilever composite beam on elastic supports. Composites Science and Technology, 65, 1982–1995.
• Goren Kiral, B., Kiral, Z., & Ozturk, H. (2015). Stability analysis of delaminated composite beams. Composites Part B: Engineering, 79, 406-418.
• Singha, M. K., & Daripa, R. (2009). Nonlinear vibration and dynamic stability analysis of composite plates. Journal of Sound and Vibration, 328 (4), 541-554.
• Hutt, J. M. (1968). Dynamic stability of plates by finite elements. Ph.D. Thesis, Oklahoma State University, Oklahoma.
• Srivastava, A. K. L., Datta, P. K., & Sheikh, A. H. (2003). Dynamic instability of stiffened plates subjected to non-uniform harmonic in-plane edge loading. Journal of Sound and Vibration, 262 (5), 1171-1189.
• Sahoo, R., & Singh, B. H. (2018). Assessment of dynamic instability of laminated composite-sandwich plates. Aerospace Science and Technology, 81, 41-52.
• Radu, A. G., & Chattopadhyay, A. (2002). Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach. International Journal of Solids and Structures, 39 (7), 1949-1965.
• Abramovich, H. (2017). Stability and vibrations of thin-walled composite structures. Woodhead, Cambridge, 772.
• Gu, X. J., Hao, Y. X., Zhang, W., & Chen, Jie. (2019). Dynamic stability of rotating cantilever composite thin walled twisted plate with initial geometric imperfection under in-plane load. Thin-Walled Structures, 144 (1).
• Sayer, O. (2020). Dynamic stability of cracked composite plates, M.Sc. Thesis, Dokuz Eylul University, Izmir.