stresses and displacements in functionally graded materials of semi-infinite extent induced by rectangular loadings应力和位移在功能梯度材料的半无限矩形载荷引起的程度.pdfVIP

Materials 2012, 5, 210-226; doi:10.3390/ma5020210 OPEN ACCESS materials ISSN 1996-1944 /journal/materials Article Stresses and Displacements in Functionally Graded Materials of Semi-Infinite Extent Induced by Rectangular Loadings Hong-Tian Xiao 1 and Zhong-Qi Yue 2,* 1 Shandong Key Laboratory of Civil Engineering Disaster Prevention Mitigation, Shandong University of Science and Technology, Shandong, Qingdao 266590, China; E-Mail: xiaohongtian@ 2 Department of Civil Engineering, The University of Hong Kong, Hong Kong, China * Author to whom correspondence should be addressed; E-Mail: yueqzq@hku.hk; Tel.: +85-2 Fax: +85-2 Received: 24 November 2011; in revised form: 16 January 2012 / Accepted: 17 January 2012 / Published: 30 January 2012 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 Si N -based ceramics 3 4 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 integ