Method of lines for functionally gradient materials^①

来源期刊：中南大学学报(英文版)2005年第2期

论文作者：戴耀 燕秀发 王海军 何家文 韩志海

文章页码：145 - 149

Key words：method of lines; functionally gradient material; crack; stress intensity factor

Abstract: The method of lines(MOL) for solving the problems of functionally gradient materials(FGMs) was studied. Navier s equations for FGMs were derived, and were semi-discretized into a system of ordinary differential equations(ODEs) defined on discrete lines with the finite difference. By solving the system of ODEs, the solutions to the problem can be obtained. An example of three-point bending was given to demonstrate the application of MOL for a crack problem in the FGM. The computational results show that the more accurate results can be obtained with less computational time and resources. The obvious difficulties of numerical method for crack problems in FGMs, such as the effect of material nonhomogeneity and the existence of high gradient stress and strain near a crack tip, can be overcome without additional consideration if this method is adopted.