3D ELASTICITY SOLUTION FOR THE STATIC ANALYSIS OF VARIABLE THICKNESS BI-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR PLATES SUBJECTED TO NON-UNIFORM ASYMMETRIC BOUNDARY CONDITIONS

Year 2014, , 52 - 74, 01.09.2014

A.behravan Rad K. Mohammadi Majd

https://doi.org/10.24107/ijeas.251222

Abstract

This paper investigates the static behavior of non-uniform bi-directional functionally graded (FG) circular plates embedded on gradient elastic foundations (Winkler- Pasternak type) and subjected to non-uniform asymmetric transverse and in-plane shear loads. The governing state equations are derived in terms of displacements based on 3D theory of elasticity, and assuming the material properties of the plate except the Poisson’s ratio varies continuously throughout the thickness and radial directions according to an exponential function. These equations are solved by means semianalytical method using state-space based differential quadrature method. Numerical results are displayed to clarify the effects of foundation stiffnesses, material heterogeneity indices, various foundation patterns, foundation grading indices, loads ratio and geometric parameters on the displacement and stress fields. The results are reported for the first time and the new results can be used as a benchmark solution for future researches

Keywords

Functionally graded, circular Plate, Gradient elastic foundation, Elasticity, Semi-analytical method, Boundary condition

References

• [1]Nemat-Alla M. Reduction of thermal stresses by developing two-dimensional functionally graded materials, Int. J. Solids Struct., 40, 7339-7356 (2003).
• [2]Saidi AR, Rasouli A, Sahraee S. Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory. Compos Struct., 89(1):110–9 (2009).
• [3]Nosier A., Fallah F., Non-linear analysis of functionally graded circular plates under asymmetric transverse loading, Int. J. Non-linear Mech., 44, 928-942 (2009).
• [4]Sahraee S, Saidi AR. Axisymmetric bending analysis of thick functionally graded circular plates using fourth-order shear deformation theory. Eur. J Mech. A/Solids 28(5):974–84 (2009).
• [5]Malekzadeh P., Golbahar Haghighi M.R., Atashi M.M., Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment, meccanica, 47(2), 321-333 (2011).
• [6]Safaeian Hamzehkolaei N., Malekzadeh P., Vaseghi J, Thermal effect on axisymmetric bending of functionally graded circular and annular plates using DQM, Steel Compos. Struct., 11(4), 341-358(2011).
• [7]Kumar Y., Lal R., prediction of frequencies of free axisymmetric vibration of two directional functionally graded annular plates on Winkler foundation, Eur. J. Mech. A-Solid., 42, 219- 228 (2013).
• [8]Shariyat M., Alipour M.M., Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations, Arch. Appl. Mech., 81(9), 1289-1306 (2011).
• [9]Abbasi S., Farhatnia F., Jazi SR., A semi-analytical solution on static analysis of circular plate exposed to non-uniform axisymmetric transverse loading resting on Winkler elastic foundation, Archives of Civil and Mechanical Engineering, DOI: 10.1016/ j. acme. 2013.09.007.
• [10] Li XY., Ding HJ. , Chen W.Q., Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load q k r , Int. J. Solids Struct., 45(1), 191–210 (2008).
• [11] Wang, Y, Xu, RQ, and Ding, HJ. Three-dimensional solution of axisymmetric bending of functionally graded circular plates, Compos. Struct., 92: 1683–1693 (2010).
• [12]Yun W., Rongqiao X., Haojiang D., Three-dimensional solution of axisymmetric bending of functionally graded circular plates, Compos. Struct., 92, 1683-1693 (2010).
• [13]Sburlati R., Bardella L., Three-dimensional elastic solutions for functionally graded circular plates, Eur. J. Mech. A-Solid., 30, 219-235 (2011).
• [14]Nie GJ. , Zhong Z., Axisymmetric bending of two-directional funcionally graded circular and annular plates. Acta Mech. Solid Sin., 20(4), 289-295 (2007)
• [15]Lu C.F., Lim C.W., Chen W.Q., Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions,Int. J. Num. Meth. Eng., 79, 25 – 44 (2009).
• [16]Davoodi K. I., Ghayour M., Mirdamadi H. R., Free vibration analysis of multi-directional functionally graded circular and annular plates, Mech. Sci. Tech., 26(11), 3399-3410, 2012.
• [17]Behravan Rad A., Semi-analytical solution for functionally graded solid circular and annular plates resting on elastic foundations subjected to axisymmetric transverse loading, Adv. Appl. Math. Mech., 4(2), 205 – 222, 2012.
• [18]Behravan Rad A., Alibeigloo A., Semi-analytical solution for the static analysis of 2D functionally graded circular and annular circular plates resting on elastic foundation, Mech. Adv. Mat. Struc. 20(7), 515-528, 2013.
• [19]Shu, C., Differential Quadrature and Its Application in Engineering, Springer, New York, (2000).
• [20]Zong Z., Zhang Y., Advanced Differential Quadrature Methods. CRC Press, New York, (2009