Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion

doi:10.1007/s10483-016-2086-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (6): 683-694.doi: https://doi.org/10.1007/s10483-016-2086-6

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Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion

Bo YANG¹, Weiqiu CHEN^2,3, Haojiang DING⁴

1. Department of Civil Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China;
2. State Key Laboratory of CAD & CG, Zhejiang University, Zijingang Campus, Hangzhou 310058, China;
3. Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Soft Matter Research Center, Department of Engineering Mechanics, Zhejiang University, Yuquan Campus, Hangzhou 310027, China;
4. Department of Civil Engineering, Zhejiang University, Zijingang Campus, Hangzhou 310058, China

Received:2015-10-07 Revised:2016-02-03 Online:2016-06-01 Published:2016-06-01
Contact: Bo YANG E-mail:bo.young@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11202188, 11321202, and 11172263) and the Program for Innovative Research Team of Zhejiang Sci-Tech University

Abstract

Abstract:

The problem of a transversely isotropic functionally graded material (FGM) plate welded with a circular inclusion is considered. The analysis starts with the general-ized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional (3D) general solution in terms of four analytic functions. Several an-alytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples.

Key words: plate, analytical solution, functionally graded material (FGM), welded circular inclusion

2010 MSC Number:

74B05

Bo YANG, Weiqiu CHEN, Haojiang DING. Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion. Applied Mathematics and Mechanics (English Edition), 2016, 37(6): 683-694.

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References

[1] Yao, Z. H., Kong, F. Z., Wang, H. T., and Wang, P. B. 2D simulation of composite materials using BEM. Engineering Analysis with Boundary Elements, 28, 927-935 (2004)
[2] Muskhelishvili, N. I. Some Basic Problems of the Mathematical Theory of Elasticity, Noordholf, The Netherlands (1953)
[3] Savin, G. N. Stress Distribution Around Hole, Pergamon Press, New York (1961)
[4] Lekhnitskii, S. G. Anisotropic Plate, Gordon and Breach, New York (1968)
[5] Wang, X., Pan, E., and Roy, A. K. A functionally graded plane with a circular inclusion under uniform antiplane eigenstrain. Journal of Applied Mechanics, 75, 1-4 (2008)
[6] Fang, X. Q., Liu, J. X., Wang, X. H., Zhang, T., and Zhang, S. Dynamic stress from a cylindrical inclusion buried in a functionally graded piezoelectric material layer under electro-elastic waves. Composites Science and Technology, 69, 1115-1123 (2009)
[7] Yang, Q. Q. and Gao, C. F. Non-axisymmetric thermal stress of a functionally graded coated circular inclusion in an infinite matrix. Mechanics Research Communications, 50, 27-32 (2013)
[8] Mian, M. A. and Spencer, A. J. M. Exact solutions for functionally graded and laminated elastic materials. Journal of the Mechanics and Physics of Solids, 46, 2283-2295 (1998)
[9] England, A. H. Bending solution for inhomogeneous and laminated elastic plates. Journal of Elasticity, 82, 129-173 (2006)
[10] England, A. H. Stiffness coefficients for inhomogeneous elastic plates. International Journal of Engineering Science, 47, 438-451 (2009)
[11] Yang, B., Ding, H. J., and Chen, W. Q. Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported. Applied Mathematical Modelling, 36, 488-503(2012)
[12] Yang, B., Chen, W. Q., and Ding, H. J. Elasticity solutions for functionally graded annular plates subject to biharmonic loads. Archive of Applied Mechanics, 84, 51-65 (2014)
[13] Yang, B., Chen, W. Q., and Ding, H. J. 3D elasticity solutions for equilibrium problems of transversely isotropic FGM plates with holes. Acta Mechanica, 226, 1571-1590 (2015)
[14] Yang, B., Chen, W. Q., and Ding, H. J. Three-dimensional elastostatic solutions for transversely isotropic functionally graded material plates containing elastic inclusion. Applied Mathematics and Mechanics (English Edition), 36(4), 417-426 (2015) DOI 10.1007/s10483-015-1950-9

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Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion

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