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 homogeneous 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).
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References
Bian, Z.G., 2005. Coupled Problems of Functionally Graded Materials Plates and Shells. Ph.D Thesis, Zhejiang University, Hangzhou (in Chinese).
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.
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.
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. [doi:10.1016/j.ijsolstr.2005.04.011]
Ding, H.J., Xu, B.H., 1988. General solutions of axisymmetric problems in transversely isotropic body. Applied Mathematics and Mechanics, 9(2):143–151.
Kashtalyan, M., 2004. Three-dimensional elastic solutions for bending of functionally graded rectangular plates. European Journal of Mechanics A/Solids, 23(5):853–864. [doi:10.1016/j.euromechsol.2004.04.002]
Lekhnitskii, S.G., 1981. Theory of Elasticity of an Anisotropic Elastic Body. Mir Publishers, Moscow.
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. [doi:10.1016/S0022-5096(98)00048-9]
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. [doi:10.1016/S0997-7538(99)80011-4]
Timoshenko, S.P., Goodier, J.N., 1970. Theory of Elasticity, 3rd Ed. McGraw-Hill, New York.
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. [doi:10.1016/j.euromechsol.2003.11.002]
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. [doi:10.1016/j.euromechsol.2005.09.009]
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Project (Nos. 10472102 and 10432030) supported by the National Natural Science Foundation of China
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Li, Xy., Ding, Hj. & Chen, Wq. Pure bending of simply supported circular plate of transversely isotropic functionally graded material. J. Zhejiang Univ. - Sci. A 7, 1324–1328 (2006). https://doi.org/10.1631/jzus.2006.A1324
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DOI: https://doi.org/10.1631/jzus.2006.A1324
Key words
- Transversely isotropic
- Functionally graded materials (FGMs)
- Pure bending problem
- Simply supported circular plate
- Axisymmetric deformation