Xiao Hong-Tian, Yue Zhong-Qi
Shandong Key Laboratory of Civil Engineering Disaster Prevention & Mitigation, Shandong University of Science and Technology, Shandong, Qingdao 266590, China.
Department of Civil Engineering, The University of Hong Kong, Hong Kong, China.
Materials (Basel). 2012 Jan 30;5(2):210-226. doi: 10.3390/ma5020210.
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.
本文给出了由载荷引起的功能梯度材料（FGM）中的应力和位移场。该功能梯度材料是一种基于Si₃N₄的陶瓷梯度材料，假定为半无限延伸。载荷是作用在与功能梯度材料外表面平行的矩形区域上的分布载荷，该区域要么在其外表面上，要么在其内部空间中。点载荷解析解或所谓的Yue解用于在分布载荷区域上进行数值积分。加载区域被离散为200个大小相等的小矩形单元。数值积分采用常规高斯求积法进行。当场点位于加载平面上时遇到的弱奇异和强奇异积分，采用边界元分析中的经典方法进行求解。数值积分结果具有很高的精度。
