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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.8 P.1324~1328

10.1631/jzus.2006.A1324


Pure bending of simply supported circular plate of transversely isotropic functionally graded material


Author(s):  LI Xiang-yu, DING Hao-jiang, CHEN Wei-qiu

Affiliation(s):  Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   Leexy@zju.edu.cn, dinghj@zju.edu.cn, chenwq@zju.edu.cn

Key Words:  Transversely isotropic, Functionally graded materials (FGMs), Pure bending problem, Simply supported circular plate, Axisymmetric deformation


LI Xiang-yu, DING Hao-jiang, CHEN Wei-qiu. Pure bending of simply supported circular plate of transversely isotropic functionally graded material[J]. Journal of Zhejiang University Science A, 2006, 7(8): 1324~1328.

@article{title="Pure bending of simply supported circular plate of transversely isotropic functionally graded material",
author="LI Xiang-yu, DING Hao-jiang, CHEN Wei-qiu",
journal="Journal of Zhejiang University Science A",
volume="7",
number="8",
pages="1324~1328",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A1324"
}

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%T Pure bending of simply supported circular plate of transversely isotropic functionally graded material
%A LI Xiang-yu
%A DING Hao-jiang
%A CHEN Wei-qiu
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 8
%P 1324~1328
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A1324

TY - JOUR
T1 - Pure bending of simply supported circular plate of transversely isotropic functionally graded material
A1 - LI Xiang-yu
A1 - DING Hao-jiang
A1 - CHEN Wei-qiu
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 8
SP - 1324
EP - 1328
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A1324


Abstract: 
This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Bian, Z.G., 2005. Coupled Problems of Functionally Graded Materials Plates and Shells. Ph.D Thesis, Zhejiang University, Hangzhou (in Chinese).

[2] Chen, W.Q., Ye, G.R., Cai, J.B., 2002. Thermoelastic stresses in a uniformly heated functionally graded isotropic hollow cylinder. Journal of Zhejiang University SCIENCE, 3(1):1-5.

[3] Chen, W.Q., Bian, Z.G., Ding, H.J., 2003. Three-dimensional analysis of a thick FGM rectangular plate in thermal environment. Journal of Zhejiang University SCIENCE, 4(1):1-7.

[4] Chi, S.H., Chung, Y.L., 2006. Mechanical behavior of functionally graded material plates under transverse load. International Journal of Solids and Structures, 43(13):3657-3674.

[5] Ding, H.J., Xu, B.H., 1988. General solutions of axisymmetric problems in transversely isotropic body. Applied Mathematics and Mechanics, 9(2):143-151.

[6] Kashtalyan, M., 2004. Three-dimensional elastic solutions for bending of functionally graded rectangular plates. European Journal of Mechanics A/Solids, 23(5):853-864.

[7] Lekhnitskii, S.G., 1981. Theory of Elasticity of an Anisotropic Elastic Body. Mir Publishers, Moscow.

[8] Mian, A.M., Spencer, A.J.M., 1998. Exact solutions for functionally graded and laminated elastic materials. Journal of the Mechanics and Physics of Solids, 42(12):2283-2295.

[9] 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(2):185-199.

[10] Timoshenko, S.P., Goodier, J.N., 1970. Theory of Elasticity, 3rd Ed. McGraw-Hill, New York.

[11] Wu, C.P., Tsai, Y.H., 2004. Asymptotic DQ solutions of functionally graded annular spherical shells. European Journal of Mechanics A/Solids, 23(2):283-299.

[12] Wu, Z., Chen, W.J., 2006. A higher order theory and refined triangular element for functionally graded plate. European Journal of Mechanics A/Solids, 25(3):447-463.

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