Materials 2012, 5(2), 210-226; doi:10.3390/ma5020210
Article

Stresses and Displacements in Functionally Graded Materials of Semi-Infinite Extent Induced by Rectangular Loadings

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Received: 24 November 2011; in revised form: 16 January 2012 / Accepted: 17 January 2012 / Published: 30 January 2012
(This article belongs to the Special Issue Advances in Functionally Graded Materials)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: This paper presents the stress and displacement fields in a functionally graded material (FGM) caused by a load. The FGM is a graded material of Si3N4-based ceramics and is assumed to be of semi-infinite extent. The load is a distributed loading over a rectangular area that is parallel to the external surface of the FGM and either on its external surface or within its interior space. The point-load analytical solutions or so-called Yue’s solutions are used for the numerical integration over the distributed loaded area. The loaded area is discretized into 200 small equal-sized rectangular elements. The numerical integration is carried out with the regular Gaussian quadrature. Weak and strong singular integrations encountered when the field points are located on the loaded plane, are resolved with the classical methods in boundary element analysis. The numerical integration results have high accuracy.
Keywords: functionally graded materials; FGM; elasticity; multilayered solids; Yue’s solution; Kelvin solution; stress analysis; numerical integration
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MDPI and ACS Style

Xiao, H.-T.; Yue, Z.-Q. Stresses and Displacements in Functionally Graded Materials of Semi-Infinite Extent Induced by Rectangular Loadings. Materials 2012, 5, 210-226.

AMA Style

Xiao H-T, Yue Z-Q. Stresses and Displacements in Functionally Graded Materials of Semi-Infinite Extent Induced by Rectangular Loadings. Materials. 2012; 5(2):210-226.

Chicago/Turabian Style

Xiao, Hong-Tian; Yue, Zhong-Qi. 2012. "Stresses and Displacements in Functionally Graded Materials of Semi-Infinite Extent Induced by Rectangular Loadings." Materials 5, no. 2: 210-226.

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