Stress Analysis of Two-directional FGM Moderately Thick Constrained Circular Plates with Non-uniform Load and Substrate Stiffness Distributions

Journal of Solid Mechanics

مقاله 2، دوره 2، شماره 4، اسفند 2010، صفحه 316-331   

نوع مقاله: Research Paper

نویسندگان

M.M Alipour؛ M Shariyat^*

Faculty of Mechanical Engineering, K.N. Toosi University of Technology

چکیده

In the present paper, bending and stress analyses of two-directional functionally graded (FG) circular plates resting on non-uniform two-parameter foundations (Winkler-Pasternak foundations) are investigated using a first-order shear-deformation theory. To enhance the accuracy of the results, the transverse stress components are derived based on the three dimensional theory of elasticity. The solution is obtained by employing the differential transform method (DTM). The material properties are assumed to vary in both transverse and radial directions according to power and exponential laws, respectively. Intensity of the transverse load is considered to vary according to a second-order polynomial. The performed convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the approach. A sensitivity analysis consisting of evaluating effects of different parameters (e.g., exponents of the material properties, thickness to radius ratio, trend of variations of the foundation stiffness, and edge conditions) is carried out. Results reveal that in contrast to the available constitutive-law-based solutions, present solution guarantees continuity of the transverse stresses at the interfaces between layers and may also be used for stress analysis of the sandwich panels. The results are reported for the first time and are discussed in detail.

کلیدواژه‌ها

Bending stress analysis؛ three-dimensional theory of elasticity؛ two-directional functionally graded materials؛ Circular plates؛ Elastic foundation؛ Differential transform method

مراجع

[1] Reddy J.N., Wang C.M., Kitipornchai S., 1999, Axisymmetric bending of functionally graded circular and annular plates, European Journal of Mechanics A/Solids 18: 185-199.

[2] Ma L.S., Wang T.J., 2004, Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory, International Journal of Solids and Structures 41: 85-101.

[3] Saidi A.R., Rasouli A., Sahraee S., 2009, Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory, Composite Structures 89: 110-119.

[4] Sahraee S., Saidi A.R., 2009, Axisymmetric bending analysis of thick functionally graded circular plates using fourth-order shear deformation theory, European Journal of Mechanics A/Solids 28: 974-984.

[5] Jomehzadeh E., Saidi A.R., Atashipour S.R., 2009, An analytical approach for stress analysis of functionally graded annular sector plates, Materials and Design 30: 3679-3685.

[6] Golmakani M.E., Kadkhodayan M., 2011, Nonlinear bending analysis of annular FGM plates using higher-order shear deformation plate theories, Composite Structures 93: 973-982.

[7] Nie G., Zhong Z., 2007, Axisymmetric bending of two-directional functionally graded circular and annular plates, Acta Mechanica Solida Sinica 20: 289-295.

[8] Li X.Y., Ding H.J., Chen W.Q., 2008, Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk, International Journal of Solids and Structures 45: 191-210.

[9] Li X.Y., Ding H.J., Chen W.Q., 2008, Three-dimensional analytical solution for functionally graded magneto–electro-elastic circular plates subjected to uniform load, Composite Structures 83: 381-390.

[10] Yang B., Ding H.J., Chen W.Q., 2008, Elasticity solutions for a uniformly loaded annular plate of functionally graded materials, Structural Engineering and Mechanics 30(4): 501-512.

[11] Lei Z., Zheng Z., 2009, Exact solution for axisymmetric bending of functionally graded circular plate, Tsinghua Science and Technology 14: 64-68.

[12] Wang Y., Xu R.Q., Ding H.J., 2010, Three-dimensional solution of axisymmetric bending of functionally graded circular plates, Composite Structures 92: 1683-1693.

[13] Nie G.J., Zhong Z., 2010, Dynamic analysis of multi-directional functionally graded annular plates, Applied Mathematical Modelingl. 34(3): 608-616.

[14] Sepahi O., Forouzan M.R., Malekzadeh P., 2010, Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM, Composite Structures 92(10): 2369-2378.

[15] Sburlati R., Bardella L., 2010, Three-dimensional elastic solutions for functionally graded circular plates, European Journal of Mechanics A/Solids 2011, dx.doi.org/10.1016/j.euromechsol.2010.12.008.

[16] Shariyat M., Alipour M.M., 2011, Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials, resting on elastic foundations, Archive of Applied Mechanics 81: 1289-1306.

[17] Alipour M.M., Shariyat M., Shaban M., 2010, A semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations, International Journal of Mechanics and Materials in Design 6(4): 293-304.

[18] Reddy J.N., 2007, Theory and Analysis of Elastic Plates and shells, Second Edition, CRC/Taylor and Francis, Philadelphia.

[19] Shen, H.-S., 2009, Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press, Taylor and Francis Group, Boca Raton.

[20] Ugural A.C., Fenster S.K, 2003, Advanced Strength and Applied Elasticity, Forth Edition, Prentice Hall, New Jersey.

[21] Reddy J.N., Wang C.M., Kitipornchai S., 1999, Axisymmetric bending of functionally graded circular and annular plates, European Journal of Mechanics A/Solids 18: 185-199.

[22] Nosier A., Fallah F., 2008, Reformulation of Mindlin–Reissner governing equations of functionally graded circular plates, Acta Mechanica 198: 209-233.

[23] Shariyat M., 2011, Non-linear dynamic thermo-mechanical buckling analysis of the imperfect laminated and sandwich cylindrical shells based on a global-local theory inherently suitable for non-linear analyses, International Journal of Non-Linear Mechanics46(1):253-271.

[24] Shariyat M., 2011, A double-superposition global-local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: A complex modulus approach, Archive of Applied Mechanics81: 1253-1268.

[25] Lezgy-Nazargah M., Shariyat M., Beheshti-Aval S.B., 2011, A refined high-order global-local theory for finite element bending and vibration analyses of the laminated composite beams, Acta Mechanica217: 219-242.

[26] Lezgy-Nazargah M., Beheshti-Aval S.B., Shariyat M., 2011, A refined mixed global-local finite element model for bending analysis of multi-layered rectangular composite beams with small widths, Thin-Walled Structures49: 351-362.

[27] Hosseini S.M., Sladek J., Sladek V., 2011, Meshless local Petrov–Galerkin method for coupled thermoelasticity analysis of afunctionally graded thick hollow cylinder, Engineering Analysis with Boundary Elements. 35: 827-835.