پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 158 |
| تعداد شمارهها | 6,226 |
| تعداد مقالات | 67,708 |
| تعداد مشاهده مقاله | 115,012,122 |
| تعداد دریافت فایل اصل مقاله | 89,695,438 |
Innovative Efficient Element for Analysis of FGM Plates Using FEM | ||
| Civil Engineering Infrastructures Journal | ||
| دوره 56، شماره 1، شهریور 2023، صفحه 205-219 اصل مقاله (969.75 K) | ||
| نوع مقاله: Research Papers | ||
| شناسه دیجیتال (DOI): 10.22059/ceij.2022.318133.1739 | ||
| نویسندگان | ||
| Farid Shahnavaz1؛ Reza Attarnejad* 2؛ Kooshiar Shaloudegi3؛ R. Kazemi Firouzjaei4 | ||
| 1M.Sc., Researcher, School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran. | ||
| 2Professor, School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran. | ||
| 3M.Sc., Researcher, School of Civil Engineering, Clarkson, Potsdam, USA. | ||
| 4M.Sc., Researcher, School of Civil Engineering, Polytechnic University of Catalonia (UPC), Barcelona, Spain. | ||
| چکیده | ||
| In order to obtain accurate results from displacement-based Finite Element Method (FEM), it is crucial to introduce accurate shape functions that interpolate the displacement field within an element. This paper attempts to provide such a new component by using Finite Element method using Basic Displacement Function (BDFs) for the free vibration analysis of plates with in-plane Functionally Graded Material (FGM). The first step is to introduce displacement functions and compute them using the energy method. Later, new shape functions are developed based on stiffness and force methods used to model the mechanical behavior of the element, wherein the shape functions benefit from the generality and accuracy of the stiffness and force methods. Last, the plate is analyzed using Finite Element method to derive the structural matrices from new shape functions. Several numerical examples demonstrate the accuracy and efficiency of the method, and a special material graded index named Ns is introduced. | ||
| کلیدواژهها | ||
| Basic Displacement Functions (BDFs)؛ Finite Element Method (FEM)؛ Free Vibration؛ Functionally Graded Materials (FGMs)؛ Kirchhoff-Love Plate Theory | ||
| مراجع | ||
|
Attarnejad, R., Semnani, S.J. and Shahba, A. (2010). “Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams”, Finite Elements in Analysis and Design, 46(10), 916-929, https://doi.org/10.1016/j.finel.2010.06.005.
Bacciocchi, M., Eisenberger, M., Fantuzzi, N., Tornabene, F. and Viola, E. (2016). “Vibration analysis of variable thickness plates and shells by the generalized differential quadrature method”, Composite Structures, 156, 218-237, https://doi.org/10.1016/j.compstruct.2015.12.004.
Bramble, J. H. and Zlámal, M. (1970). “Triangular elements in the finite element method”, Mathematics of Computation, 24(112), 809-820, https://doi.org/10.1090/S0025-5718-1970-0282540-0.
Cheng, Z.Q. and Batra, R.C. (2000). “Three-dimensional thermoelastic deformations of a functionally graded elliptic plate”, Composites Part B: Engineering, 31(2), 97-106, https://doi.org/10.1016/S1359-8368(99)00069-4.
Chiba, R. (2019). “Natural convection analysis of water near its density extremum between finite vertical plates: A differential transform approach”, International Journal of Mathematical Modelling and Numerical Optimisation, 9(4), 429-448, https://doi.org/10.1504/IJMMNO.2019.102601.
Das, R.R. (2010). “Adhesion failure and delamination of bonded tubular joints made with laminated FRP composites and functionally graded materials”, Doctoral Dissertation, IIT Kharagpur, http://dx.doi.org/10.1016/j.compstruct.2020.113386.
Fallah, F. and Karimi, M. (2019). “Non-linear analysis of functionally graded sector [lates with simply supported radial edges under transverse loading”, Mechanics of Advanced Composite Structures, 6(1), 65-74, https://doi.org/10.22075/macs.2019.16171.116.
Fallah, N., Parayandeh-Shahrestany, A. and Golkoubi, H. (2017). “A Finite Volume formulation for the elasto-plastic analysis of rectangular Mindlin-Reissner plates, a non-layered approach”, Civil Engineering Infrastructures Journal, 50(2), 293-310, https://doi.org/ 10.7508/ceij.2017.02.006.
Goupee, A.J. and Vel, S.S. (2006). “Optimization of natural frequencies of bidirectional functionally graded beams”, Structural and Multidisciplinary Optimization, 32(6), 473-484, https://doi.org/10.1007/s00158-006-0022-1.
Gupta, A. (2020). “Functionally graded structures: Design and analysis of tailored advanced composites”, In Characterization, Testing, Measurement, and Metrology, (pp. 33-55), CRC Press.
Hadji, L., Zouatnia, N. and Bernard, F. (2019). “An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models”, Structural Engineering and Mechanics, 69(2), 231-241, https://doi.org/10.12989/sem.2019.69.2.231.
Hamrit, F. and Necib, B. (2018). “Analysis of mechanical structures using plate finite element method under different boundary conditions”, Diagnostyka, 19(2), 3-9, http://dx.doi.org/10.29354/diag/86257.
Kaplunov, J., Erbas, B. and Ege, N. (2021). “An asymptotic theory for a functionally graded plate”, BGSIAM’21, 32, Bulgaria.
Kumar, V., Singh, S.J., Saran, V.H. and Harsha, S.P. (2021). “Vibration characteristics of porous FGM plate with variable thickness resting on Pasternak's foundation”, European Journal of Mechanics-A/Solids, 85(1 January), 104124, https://doi.org/10.1016/j.euromechsol.2020.104124.
Kumar, Y. (2018). “The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review”, Journal of Vibration and Control, 24(7), 1205-1227, https://doi.org/10.1177/1077546317694724.
Lal, R. and Saini, R. (2020). “Vibration analysis of FGM circular plates under non-linear temperature variation using generalized differential quadrature rule”, Applied Acoustics, 158(15 January), 107027, https://doi.org/10.1016/j.apacoust.2019.107027.
Leissa, A.W. (1969). “Vibration of plates”, Washington: NASA SP-160, US Government Printing Office,
Liu, D.Y., Wang, C.Y. and Chen, W.Q. (2010). “Free vibration of FGM plates with in-plane material inhomogeneity”, Composite Structures, 92(5), 1047-1051, https://doi.org/10.1016/j.compstruct.2009.10.001.
Liu, Y.Y., Shu, C., Zhang, H.W., Yang, L.M. and Lee, C. (2021). “An efficient high-order least square-based finite difference-finite volume method for solution of compressible Navier-Stokes equations on unstructured grids”, Computers and Fluids, 222(30 May), 104926, https://doi.org/10.1016/j.compfluid.2021.104926.
Makvandi, H., Moradi, S., Poorveis, D. and Heidari Shirazi, K. (2019). “Crack identification in postbuckled plates using differential quadrature element method and sequential quadratic programming”, Amirkabir Journal of Mechanical Engineering, 51(3), 51-60, https://doi.org/10.22060/mej.2018.13543.5660.
Malekzadeh, P., Setoodeh, A.R. and Shojaee, M. (2018). “Vibration of FG-GPLs eccentric annular plates embedded in piezoelectric layers using a transformed differential quadrature method”, Computer Methods in Applied Mechanics and Engineering, 340(1 October), 451-479, https://doi.org/10.1016/j.cma.2018.06.006.
Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (Eds.). (2013). Functionally graded materials: design, processing and applications, Vol. 5, Springer Science & Business Media.
Mora, P., Ducasse, E. and Deschamps, M. (2016). “Interaction of guided waves with cracks in an embedded multilayered anisotropic plate by using a Boundary Element approach”, Physics Procedia, 70, 326-329, https://doi.org/10.1016/j.phpro.2015.08.217.
Naumenko, K. and Eremeyev, V.A. (2017). “A layer-wise theory of shallow shells with thin soft core for laminated glass and photovoltaic applications”, Composite Structures, 178, 434-446, https://doi.org/10.1016/j.compstruct.2017.07.007.
Njim, E.K., Al-Waily, M. and Bakhy, S.H. (2021). “A critical review of recent research of free vibration and stability of functionally graded materials of sandwich plate”, In IOP Conference Series: Materials Science and Engineering, Vol. 1094, No. 1, p. 012081, IOP Publishing, https://doi.org/10.1088/1757-899x/1094/1/012081.
Pachenari, Z. and Attarnejad, R. (2014a). “Free vibration of tapered Mindlin plates using basic displacement functions”, Arabian Journal for Science and Engineering, 39(6), 4433-4449, https://doi.org/10.1007/s13369-014-1071-1.
Pachenari, Z. and Attarnejad, R. (2014b). “Analysis of tapered thin plates using basic displacement functions”, Arabian Journal for Science and Engineering, 39(12), 8691-8708, https://doi.org/10.1007/s13369-014-1407-x.
Ramkumar, R.L., Chen, P.C. and Sanders, W.J. (1987). “Free vibration solution for clamped orthotropic plates using Lagrangian multiplier technique”, AIAA Journal, 25(1), 146-151, https://doi.org/10.2514/3.9594.
Reddy, J. (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%3C663::AID-NME787%3E3.0.CO;2-8.
Saidi, H. and Sahla, M. (2019). “Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium”, Frattura ed Integrità Strutturale, 13(50), 286-299, https://doi.org/10.3221/IGF-ESIS.50.24.
Shahir, H. and Delfan, S. (2021). “Numerical investigation of nailing pattern effect on nailed wall performance”, Civil Engineering Infrastructures Journal, 54(2), 331-350, https://doi.org/10.22059/ceij.2021.298632.1659.
Şimşek, M. (2016). “Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions”, Composite Structures, 149(1 August), 304-314, https://doi.org/10.1016/j.compstruct.2016.04.034.
Szilard, R. (2004). “Theories and applications of plate analysis: Classical, numerical and engineering methods”, Applied Mechanics Reviews, 57(6), B32-B33, https://doi.org/10.1115/1.1849175.
Teimouri, H., Davoodi, M.R., Mostafavian, S.A. and Khanmohammadi, L. (2021). “Damage detection in double layer grids with modal strain energy method and Dempster-Shafer theory”, Civil Engineering Infrastructures Journal, 54(2), 253-266, https://doi.org/10.22059/ceij.2020.294512.1644.
Tenenbaum, J., Deutsch, A. and Eisenberger, M. (2020). “Analytical buckling loads for rectangular orthotropic and symmetrically laminated plates”, AIAA Journal, 58(2), 907-917, https://doi.org/10.2514/1.J058536.
Van Vinh, P., Dung, N.T. and Tho, N.C. (2021, February). “Modified single variable shear deformation plate theory for free vibration analysis of rectangular FGM plates”, Structures, 29(1 February), 1435-1444, https://doi.org/10.1016/j.istruc.2020.12.027.
Vatani Oskouei, A. and Kiakojouri, F. (2015). “Non-linear dynamic analysis of steel hollow I-core sandwich panel under air blast loading”, Civil Engineering Infrastructures Journal, 48(2), 323-344, https://doi.org/10.7508/ceij.2015.02.008.
Vidal, P., Gallimard, L., Polit, O. and Valot, E. (2021). “Analysis of functionally graded plates based on a variable separation method”, Mechanics of Advanced Materials and Structures, 29(26), 4890-4901, https://doi.org/ 10.1080/15376494.2021.1942597.
Wang, X., Liang, X. and Jin, C. (2017). “Accurate dynamic analysis of functionally graded beams under a moving point load”, Mechanics Based Design of Structures and Machines, 45(1), 76-91, https://doi.org/10.1080/15397734.2016.1145060.
Zakeri, M., Modarakar Haghighi, A. and Attarnejad, R. (2016). “On the analysis of FGM beams: FEM with innovative element”, Journal of Solid Mechanics, 8(2), 348-364, https://dorl.net/dor/20.1001.1.20083505.2016.8.2.9.9. | ||
|
آمار تعداد مشاهده مقاله: 255 تعداد دریافت فایل اصل مقاله: 636 |
||