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# A Generalized Kelvin Solution Based BEM for Contact Problems of Elastic Indenter on Functionally Graded Materials

H. T. Xiao1, Z. Q. Yue2
Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation, Shandong University of Science and Technology, Qingdao, 266510, China
Department of Civil Engineering, The University of Hong Kong, Hong Kong, China. Corresponding Author. Tel: 852-28591967; Fax: 852-25595337; Email: yueqzq@hkucc.hku.hk

Computer Modeling in Engineering & Sciences 2009, 52(2), 159-180. https://doi.org/10.3970/cmes.2009.052.159

### Abstract

This paper presents a three-dimensional boundary element method for contact problems of an elastic indenter on the surface of functionally graded materials (FGMs). The FGM elastic properties can have any irregular variations with depth. The indenter is subjected to the loading normal to the flat contact surface. The classical Kelvin solution is used for the mathematical formulation of the homogeneous elastic indenter. The generalized Kelvin solution is used for the mathematical formulation of the FGM base. The contact variables are defined with respect to each of the surfaces using local coordinate systems. The corresponding contact equations are used to couple the two sets of the linear equation systems for the indenter and the FGM. The numerical verifications illustrate that the proposed method can obtain accurate results for the contact displacement and stress. Numerical results for an elastic rectangular plate centrically or eccentrically indenting a FGM of actual depth variation property are presented and analyzed.

### Keywords

functionally graded materials, FGM, contact problem, BEM, elastic indenter, rigid indenter, frictional contact surface

Xiao, H. T., Yue, Z. Q. (2009). A Generalized Kelvin Solution Based BEM for Contact Problems of Elastic Indenter on Functionally Graded Materials. CMES-Computer Modeling in Engineering & Sciences, 52(2), 159–180.

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