Static and Free Vibration Analyses of Orthotropic FGM Plates Resting on Two-Parameter Elastic Foundation by a Mesh-Free Method
الموضوعات :
H Momeni-Khabisi
1
(Department of Mechanical Engineering, University of Jiroft , Jiroft , Iran)
الکلمات المفتاحية: Free vibration, FGM plate, Orthotropic, Mesh-Free, Static,
ملخص المقالة :
In this paper, static and free vibrations behaviors of the orthotropic functionally graded material (FGM) plates resting on the two-parameter elastic foundation are analyzed by the a mesh-free method based on the first order shear deformation plate theory (FSDT). The mesh-free method is based on moving least squares (MLS) shape functions and essential boundary conditions are imposed by transfer function method. The orthotropic FGM plates are made of two orthotropic materials and their volume fractions are varied smoothly along the plate thickness. The convergence of the method is demonstrated and to validate the results, comparisons are made with finite element method (FEM) and the others available solutions for both homogeneous and FGM plates then numerical examples are provided to investigate the effects of material distributions, elastic foundation coefficients, geometrical dimensions, applied force and boundary conditions on the static and vibrational characteristics of the orthotropic FGM plates.
[1] Koizumi M., 1997, FGM activities in Japan, Composites Part B 28: 1-4.
[2] Thai H.T., Choi D.H., 2011, A refined plate theory for functionally graded plates resting on elastic foundation, Composites Science and Technology 71: 1850-1858.
[3] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC.
[4] Reissner E., 1945, The effect of transverse shear deformation on the bending of elastic plates, Journal of Applied Mechanics 12: 69-72.
[5] Mindlin R.D., 1951, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, Journal of Applied Mechanics 18: 31-38.
[6] Thai H.T., Choi D.H., 2012, An efficient and simple refined theory for buckling analysis of functionally graded plates, Applied Mathematical Modelling 36: 1008-1022.
[7] Reddy J. N., 1984, A simple higher order theory for laminated composite plates, Journal of Applied Mechanics 51: 745-752.
[8] Matsunaga H., 2008, Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory, Composite Structures 82: 499-512.
[9] Malekzadeh P., 2009, Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations, Composite Structures 89: 367-373.
[10] Yas M.H., Sobhani B., 2010, Free vibration analysis of continuous grading fibre reinforced plates on elastic foundation, International Journal of Engineering Science 48: 1881-1895.
[11] Ferreira A.J.M., Castro L.M.S., Bertoluzza S., 2009, A high order collocation method for the static and vibration analysis of composite plates using a first-order theory, Composite Structures 89: 424-432.
[12] Ferreira A.J.M., Roque C.M.C., Martins P.A.L.S., 2003, Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method, Composites Part B 34: 627-636.
[13] Nie G.J., Batra R.C., 2010, Static deformations of functionally graded polar-orthotropic cylinders with elliptical inner and circular outer surfaces, Composites Science and Technology 70: 450-457.
[14] Zhang W., Yang J., Hao Y., 2010, Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory, Nonlinear Dynamic 59: 619-660.
[15] Farid M., Zahedinejad P., Malekzadeh P., 2010, Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic, differential quadrature method, Materials and Design 31: 2-13.
[16] Zhu P., Lei Z.X., Liew K.M., 2012, Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory, Composite Structures 94: 1450-1460.
[17] Jam J.E., Kamarian S., Pourasghar A., Seidi J., 2012, Free vibrations of three-parameter functionally graded plates resting on pasternak foundations, Journal of Solid Mechanics 4: 59-74.
[18] Alibeigloo A., Liew K.M., 2013, Thermoelastic analysis of functionally graded carbon nanotube-reinforced composite plate using theory of elasticity, Composite Structures 106: 873-881.
[19] Asemi K., Shariyat M., 2013, Highly accurate nonlinear three-dimensional finite element elasticity approach for biaxial buckling of rectangular anisotropic FGM plates with general orthotropy directions, Composite Structures 106: 235-249.
[20] Mansouri M.H., Shariyat M., 2014, Thermal buckling predictions of three types of high-order theories for the heterogeneous orthotropic plates, using the new version of DQM, Composite Structures 113: 40-55.
[21] Mansouri M.H., Shariyat M., 2015, Biaxial thermo-mechanical buckling of orthotropic auxetic FGM plates with temperature and moisture dependent material properties on elastic foundations, Composites Part B 83: 88-104.
[22] Shariyat M., Asemi K., 2014, Three-dimensional non-linear elasticity-based 3D cubic B-spline finite element shear buckling analysis of rectangular orthotropic FGM plates surrounded by elastic foundations, Composites Part B 56: 934-947.
[23] Sofiyev A.H., Huseynov S.E., Ozyigit P., Isayev F.G., 2015, The effect of mixed boundary conditions on the stability behavior of heterogeneous orthotropic truncated conical shells, Meccanica 50: 2153-2166.
[24] Moradi-Dastjerdi R., Payganeh Gh., Malek-Mohammadi H., 2015, Free vibration analyses of functionally graded CNT reinforced nanocomposite sandwich plates resting on elastic foundation, Journal of Solid Mechanic 7: 158-172.
[25] Foroutan M., Moradi-Dastjerdi R., Sotoodeh-Bahreini R., 2012, Static analysis of FGM cylinders by a mesh-free method, Steel and Composite Structures 12: 1-11.
[26] Mollarazi H.R., Foroutan M., Moradi-Dastjerdi R., 2012, Analysis of free vibration of functionally graded material (FGM) cylinders by a meshless method, Journal of Composite Materials 46: 507-515.
[27] Foroutan M., Moradi-Dastjerdi R., 2011, Dynamic analysis of functionally graded material cylinders under an impact load by a mesh-free method, Acta Mechanica 219: 281-290.
[28] Moradi-Dastjerdi R., Foroutan M., 2014, Free Vibration Analysis of Orthotropic FGM Cylinders by a Mesh-Free Method, Journal of Solid Mechanics 6: 70-81.
[29] Dinis L.M.J.S., Natal Jorge R.M., Belinha J., 2010, A 3D shell-like approach using a natural neighbour meshless method: Isotropic and orthotropic thin structures, Composite Structures 92:1132-1142.
[30] Rezaei Mojdehi A., Darvizeh A., Basti A., Rajabi H., 2011, Three dimensional static and dynamic analysis of thick functionally graded plates by the meshless local Petrov–Galerkin (MLPG) method, Engineering Analysis with Boundary Elements 35: 1168-1180.
[31] Lei Z.X., Liew K.M., Yu J.L., 2013, Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method, Composite Structures 98:160-168.
[32] Lei Z.X., Liew K.M., Yu J.L., 2013, Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment, Composite Structures 106:128-138.
[33] Yaghoubshahi M., Alinia M.M., 2015, Developing an element free method for higher order shear deformation analysis of plates, Thin-Walled Structures 94: 225-233.
[34] Zhang L.W., Lei Z.X., Liew K.M., 2015, An element-free IMLS-Ritz framework for buckling analysis of FG–CNT reinforced composite thick plates resting on Winkler foundations, Engineering Analysis with Boundary Elements 58: 7-17.
[35] Zhang L.W., Song Z.G., Liew K.M., 2015, Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method, Composite Structures 128: 165-175.
[36] Efraim E., Eisenberger M., 2007, Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of Sound and Vibration 299: 720-738.
[37] Lancaster P., Salkauskas K., 1981, Surface generated by moving least squares methods, Mathematics of Computation 37: 141-158.
[38] Hyer M.W., 1998, Mechanics of Composite Materials, McGraw-Hill.
[39] Akhras G., Cheung M.S., Li W., 1994, Finite strip analysis for anisotropic laminated composite plates using higher-order deformation theory, Composite Structures 52: 471-477.
[40] Reddy J.N., 1993, Introduction to the Finite Element Method, New York, McGraw-Hill.
[41] Baferani A.H., Saidi A.R., Ehteshami H.,2011, Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation, Composite Structures 93: 1842-1853.
