Analysis of Static Bending of Plates FGM Using Refined High Order Shear Deformation Theory

S Merdaci, S Boutaleb, H Hellal, S Benyoucef


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Abstract


This work deals with the analysis of the mechanical bending behavior of a rectangular plate simply supported on four sides (FGM), subjected to transverse static loading. The high order theory is used in this work, The developed models are variably consistent, have a strong similarity with the classical plate theory in many aspects, do not require correction to the shear factor, and give rise to variations transverse shear stresses such as transverse shear parabolically varies across the shear thickness and satisfies surface conditions without stresses. Equilibrium equations are obtained by applying the principle of virtual works. The mathematical expressions of the arrow, the stresses are obtained using Navies approach to solve the system of equilibrium equations. The influence of mechanical loading and the change of the parameter of the material on mechanical behavior of the plate P-FGM are represented by a numerical example.

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Koizumi, M. (1992). Recent progress of functionally gradient materials in Japan. In 16th annual conference on composites and advanced ceramic materials (Vol. 13, p. 333).

Lü, C. F., Lim, C. W., & Chen, W. Q. (2009). Exact solutions for free vibrations of functionally graded thick plates on elastic foundations. Mechanics of Advanced Materials and Structures, 16(8), 576-584.

Merdaci, S. (2017). Study and Comparison of Different Plate Theory. International Journal of Engineering Research and Advanced Technology 3(8), 48-59.

Merdaci, S., Belghoul, H., Benyoucef, S., Tounsi, A., Adda Bedia, E.A. (2016). Étude à la Flexion Statique des Plaques Symétriques en FGM Functionally Graded Materials. 9ème édition des Journées d'Etudes Techniques JET'2016, Hammamet, Tunisie.

Merdaci, S., Benyoucef, S., Tounsi, A., Adda Bedia, E.A. (2015). Analyse Statique des Plaques Homogènes en Matériaux à Gradient Variable (FGM) , 2nd International Conference on Aeronautical Sciences I.C.A.S’02 , Oran, Algeria .

Merdaci, S., Tounsi, A., Houari, M. S. A., Mechab, I., Hebali, H., & Benyoucef, S. (2011). Two new refined shear displacement models for functionally graded sandwich plates. Archive of Applied Mechanics, 81(11), 1507-1522.

Mostefa, A. H., Merdaci, S., & Mahmoudi, N. (2018). An Overview of Functionally Graded Materials «FGM». In International Symposium on Materials and Sustainable Development (pp. 267-278). Springer.

Nguyen, T. K., Sab, K., & Bonnet, G. (2008). First-order shear deformation plate models for functionally graded materials. Composite Structures, 83(1), 25-36.

Praveen, G. N., & Reddy, J. N. (1998). Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. International Journal of Solids and Structures, 35(33), 4457-4476.

Reddy, J. N. (1984). A refined nonlinear theory of plates with transverse shear deformation. International Journal of solids and structures, 20(9-10), 881-896.

Reddy, J. N. (1984). A simple higher-order theory for laminated composite plates. Journal of applied mechanics, 51(4), 745-752.

Shi, G. (2007). A new simple third-order shear deformation theory of plates. International Journal of Solids and Structures, 44(13), 4399-4417.

Shimpi, R. P., & Patel, H. G. (2006). A two variable refined plate theory for orthotropic plate analysis. International Journal of Solids and Structures, 43(22-23), 6783-6799.

Şimşek, M. (2010). Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nuclear Engineering and Design, 240(4), 697-705.

Timoshenko, S. P., & Gere, J. M. (1972). Mechanics of Materials. van Nordstrand Reinhold Company. New York.

Woo, J., & Meguid, S. A. (2001). Nonlinear analysis of functionally graded plates and shallow shells. International Journal of Solids and structures, 38(42-43), 7409-7421.

Wu, C. P., & Li, H. Y. (2010). An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates. Composite Structures, 92(10), 2591-2605.

Ying, J., Lü, C. F., & Lim, C. W. (2009). 3D thermoelasticity solutions for functionally graded thick plates. Journal of Zhejiang University-SCIENCE A, 10(3), 327-336.

Zenkour, A. M. (2004). Thermal effects on the bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory. Acta Mechanica, 171(3-4), 171-187.

Zhong, Z., & Yu, T. (2007). Analytical solution of a cantilever functionally graded beam. Composites Science and Technology, 67(3-4), 481-488.


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Civil Engineering and Architecture Faculty- University Amar Telidji of Laghouat JBMS@2019.