Document Type : Research Paper
Authors
1 Oil and Natural Gas Directorate, Ministry of Energy and Mineral Resources, Amman, Jordan. Department of Mechanical Engineering, Faculty of Engineering, University of Jordan, Amman, Jordan.
2 Department of Mechanical Engineering, University of Jordan, Amman-11942, Jordan.
Abstract
In this paper, layerwise finite element analysis for the bending behavior of two-dimensional functionally graded layered plates with different boundary conditions is presented. The plates consist of three layers; a functionally graded layer embedded between ceramic and metal isotropic layers. The layerwise approach is based on the third-order shear deformation theory for the middle layer, while the first-order shear deformation theory is used for both the upper and lower isotropic layers. A quadrilateral 8-noded element with 13-degrees of freedom per node is used for this purpose. The present results show very good agreements with the published results for similar problems in literature solved by other methods of plates consist of either single or layered functionally graded plates.
Keywords
Main Subjects
- Koizumi, M. F. G. M. (1997). FGM activities in Japan. Composites part b: engineering, 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9
- Mostefa, A. H., Merdaci, S., & Mahmoudi, N. (2017, November). An overview of functionally graded materials «FGM». International symposium on materials and sustainable development(pp. 267-278). Cham: Springer. https://doi.org/10.1007/978-3-319-89707-3_30
- Irfan, S., & Siddiqui, F. (2019). A review of recent advancements in finite element formulation for sandwich plates. Chinese journal of aeronautics, 32(4), 785-798. https://doi.org/10.1016/j.cja.2018.11.011
- Khorramabadi, M. K., Najafizadeh, M. M., Shahraki, J. A., & Khazaeinejad, P. (2008). Effect of shear theories on free vibration of functionally graded plates. World academy of science, engineering and technology, 48(2), 216-221.
- Singha, M. K., Prakash, T., & Ganapathi, M. (2011). Finite element analysis of functionally graded plates under transverse load. Finite elements in analysis and design, 47(4), 453-460. https://doi.org/10.1016/j.finel.2010.12.001
- Moita, J. S., Correia, V. F., Soares, C. M. M., & Herskovits, J. (2019). Higher-order finite element models for the static linear and nonlinear behaviour of functionally graded material plate-shell structures. Composite structures,212, 465-475. https://doi.org/10.1016/j.compstruct.2019.01.046
- Čukanović, D., Radaković, A., Bogdanović, G., Milanović, M., Redžović, H., & Dragović, D. (2018). New shape function for the bending analysis of functionally graded plate. Materials, 11(12), 2381. https://doi.org/10.3390/ma11122381
- Efraim, E. (2011). Accurate formula for determination of natural frequencies of FGM plates basing on frequencies of isotropic plates. Procedia engineering, 10, 242-247. https://doi.org/10.1016/j.proeng.2011.04.043
- Thang, P. T., Nguyen, T. T., & Lee, J. (2016). Nonlinear static analysis of thin curved panels with FG coatings under combined axial compression and external pressure. Thin-walled structures, 107, 405-414. https://doi.org/10.1016/j.tws.2016.06.007
- Nguyen, T. T., Nguyen, N. L., Lee, J., & Nguyen, Q. H. (2021). Analysis of non-uniform polygonal cross-sections for thin-walled functionally graded straight and curved beams. Engineering structures, 226, 111366. https://doi.org/10.1016/j.engstruct.2020.111366
- Lezgy-Nazargah, M., Vidal, P., & Polit, O. (2013). An efficient finite element model for static and dynamic analyses of functionally graded piezoelectric beams. Composite structures, 104, 71-84. https://doi.org/10.1016/j.compstruct.2013.04.010
- Yas, M. H., Shakeri, M., Heshmati, M., & Mohammadi, S. (2011). Layer-wise finite element analysis of functionally graded cylindrical shell under dynamic load. Journal of mechanical science and technology, 25(3), 597-604. https://doi.org/10.1007/s12206-011-0116-6
- Pandey, S., & Pradyumna, S. (2015). A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells. Composite structures, 133, 438-450. https://doi.org/10.1016/j.compstruct.2015.07.087
- Nikbakht, S. J. S. M. S., Salami, S. J., & Shakeri, M. (2017). Three-dimensional analysis of functionally graded plates up to yielding, using full layer-wise finite element method. Composite structures, 182, 99-115. https://doi.org/10.1016/j.compstruct.2017.09.022
- Kurtaran, H. (2014). Shape effect on free vibration of functionally graded plates. International journal of engineering and applied sciences, 6(4), 52-67. https://doi.org/10.24107/ijeas.251237
- Martínez-Pañeda, E. (2019). On the finite element implementation of functionally graded materials. Materials, 12(2), 287. https://doi.org/10.3390/ma12020287
- Al-Hawamdeh, O., Abu-Alshaikh, I., & Al-Huniti, N. (2017). Finite element coding of functionally graded beams under various boundary and loading conditions. Journal of applied research on industrial engineering, 4(4), 279-290.
- Hedia, H. S. (2005). Comparison of one‐dimensional and two‐dimensional functionally graded materials for the backing shell of the cemented acetabular cup. Journal of biomedical materials research part b: applied biomaterials: an official journal of the society for biomaterials, the japanese society for biomaterials, and the australian society for biomaterials and the korean society for biomaterials, 74(2), 732-739. https://doi.org/10.1002/jbm.b.30258
- Nemat-Alla, M. (2003). Reduction of thermal stresses by developing two-dimensional functionally graded materials. International journal of solids and structures, 40(26), 7339-7356. https://doi.org/10.1016/j.ijsolstr.2003.08.017
- Joshi, K., & Kar, V. (2020). Bending analysis of bi-dimensional functionally graded plate using FEA. Materials today: proceedings, 26(2), 1766-1770. https://doi.org/10.1016/j.matpr.2020.02.371
- Asemi, K., Salehi, M., & Akhlaghi, M. (2013). Three dimensional static analysis of two dimensional functionally graded plates. International journal of recent advances in mechanical engineering (IJMECH), 2(2), 21-32.
- Nguyen, T. T., & Lee, J. (2018). Flexural-torsional vibration and buckling of thin-walled bi-directional functionally graded beams. Composites part b: engineering, 154, 351-362. https://doi.org/10.1016/j.compositesb.2018.08.069
- Nguyen, T. T., & Lee, J. (2018). Interactive geometric interpretation and static analysis of thin-walled bi-directional functionally graded beams. Composite structures, 191, 1-11. https://doi.org/10.1016/j.compstruct.2018.01.064
- Lezgy-Nazargah, M. (2015). Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach. Aerospace science and technology, 45, 154-164. https://doi.org/10.1016/j.ast.2015.05.006
- Lezgy-Nazargah, M., & Meshkani, Z. (2018). An efficient partial mixed finite element model for static and free vibration analyses of FGM plates rested on two-parameter elastic foundations. Structural engineering and mechanics, 66(5), 665-676. DOI: http://dx.doi.org/10.12989/sem.2018.66.5.665
- Belarbi, M. O., Tati, A., & Khechai, A. (2015). Efficient layerwise finite element model for multilayer sandwich plates analysis.Design and modeling of mechanical systems-II (pp. 305-314). Cham: Springer. https://doi.org/10.1007/978-3-319-17527-0_30
- Van Long, N., Quoc, T. H., & Tu, T. M. (2016). Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite-element method. International journal of advanced structural engineering, 8(4), 391-399. https://doi.org/10.1007/s40091-016-0140-y
- Reddy, J. N. (2000). Analysis of functionally graded plates. International journal for numerical methods in engineering, 47(1‐3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
- Zenkour, A. M. (2006). Generalized shear deformation theory for bending analysis of functionally graded plates. Applied mathematical modelling, 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009
- Bui, T. Q., Van Do, T., Ton, L. H. T., Doan, D. H., Tanaka, S., Pham, D. T., ... & Hirose, S. (2016). On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory. Composites part b: engineering, 92, 218-241. https://doi.org/10.1016/j.compositesb.2016.02.048
- Van Do, T., Nguyen, D. K., Duc, N. D., Doan, D. H., & Bui, T. Q. (2017). Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory. Thin-walled structures, 119, 687-699. https://doi.org/10.1016/j.tws.2017.07.022
- Pandey, S., & Pradyumna, S. (2018). Analysis of functionally graded sandwich plates using a higher-order layerwise theory. Composites part b: engineering, 153, 325-336. https://doi.org/10.1016/j.compositesb.2018.08.121
- Brischetto, S. (2009). Classical and mixed advanced models for sandwich plates embedding functionally graded cores. Journal of mechanics of materials and structures, 4(1), 13-33.
- Carrera, E., Brischetto, S., Cinefra, M., & Soave, M. (2011). Effects of thickness stretching in functionally graded plates and shells. Composites part b: engineering, 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005
- Neves, A. M. A., Ferreira, A. J., Carrera, E., Cinefra, M., Jorge, R. M. N., & Soares, C. M. M. (2012). Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects. Advances in engineering software, 52, 30-43. https://doi.org/10.1016/j.advengsoft.2012.05.005
)