Relationship between Bending Solutions of FGM and Homogenous Circular Cylindrical Shells

Abstract:

Based on the Loves shell theory, relationship between bending solutions of functionally graded materials (FGM) and homogenous circular cylindrical shells was studied. By comparing the displacement-type governing equations for axially symmetrically bending of FGM and homogenous circular cylindrical shells, an analogous transform relation between the deflections of FGM circular cylindrical shell and those of homogenous one was obtained. By giving the material properties of FGM circular cylindrical shell changing as continuous functions in the thickness direction, the corresponding transition factor between the solutions of the two kind circular cylindrical shells were derived, which reflect the non-uniform properties of the functionally graded material circular cylindrical shell. Numerical example shows that the numerical solutions of the maximum of non-dimensional deflections are almost in agreement with the transformational solutions when n equals approximately 5, where n is the volume fraction index. As a result, solutions for axially symmetrically bending of a non-homogenous circular cylindrical shell can be reduced to that of a homogenous one and the calculation of the transformation factors.

• Periodical: Applied Mechanics and Materials (Volumes 353-356)
• Pages: 3236-3242
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.353-356.3236
• Online since: August 2013
• Authors: Ze Qing Wan*, Shi Rong Li
• Keywords: Analogous Transformation, Bending Solution, Circular Cylindrical Shell, Functionally Graded Material (FGM)

References

[1] Li Shirong, Zhang Wenxun, Zhang Jinghua. Analytical solution of axi-symmetrical bending of cylindrical shells with functional gradient, Journal of Lanzhou University of Technology(In Chinese), Vol. 35(4) (2009), pp.158-162.

[2] C. T. Loy, K. Y. Lam, J. N. Reddy. Vibration of functionally graded cylindrical shells. International Journal of Mechanical Sciences. Vol. 41 (1999), pp.309-324.

DOI: 10.1016/s0020-7403(98)00054-x

[3] Huaiwei Huang, Qiang Han, Nengwen Feng, et al. Buckling of Functioanlly Graded shells under Combined Loads. Mechanics of Advanced Materials and Structure, Vol. 18(2011), pp.337-346.

DOI: 10.1080/15376494.2010.516882

[4] J. N. Reddy, C.M. Wang, G.T. Lim, K. H. Ng. Bending solutions of Levinson beams and plates in terms of the classic theories. International Journal of Solids and Structures, Vol. 38(2001), pp.4701-4720.

DOI: 10.1016/s0020-7683(00)00298-5

[5] Li Shirong, Liu Ping. Analogous transformation of static and dynamic solutions between functionally graded material beams and uniform beams, Mechanics in Engineering(In Chinese), Vol. 32(5) (2010), pp.45-49.

[6] Li Shirong, Zhang Jinghua and Xu Hua. Linear transformation between the bending solutions if functionally graded and homogenous circular plates, Chinese Journal of Theoretical and Applied Mechanics(In Chinese), Vol. 43(5) (2011): 871-877.

[7] Love AEH. A treatise on the mathematical theory of elasticity. 4th ed., Cambridge: Cambridge University Press, (1952).

[8] Wilhelm Flügge. Stresses in Shells (Second Edition), Springer-Verlag Berlin Heidelberg, New York (1973).